Concordia
COMM 308
Course Prep Booklet
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Table of Contents
Chapter 1. Introduction to Finance
1.1. Introduction to Finance
1.1.1. Finance and Financial Managers
1.1.2. Markets
1.2. Corporate Structures
1.2.1. Sole-proprietorships
1.2.2. Partnerships
1.2.3. Corporations
2.5. Effective Periodic Rate
2.5.1. Effective Periodic Rates
2.5.2. Example
2.5.3. Practice
2.5.4. Example
2.5.5. Practice
2.6. Effective Rates with Continuous
Compounding
2.6.1. Continuous Compounding
1.3. The Principle-Agent Problem
2.6.2. Example
1.3.1. The Agency Problem
2.6.3. Practice
Chapter 2. Time Value of Money
2.7. Lump Sum Calculations
2.1. Introduction to TVM
2.7.1. Lump Sum Calculations
2.1.1. What is Time Value of Money?
2.7.2. Example
2.1.2. The Financial Calculator
2.7.3. Practice
2.2. Simple Interest
2.7.4. Example
2.2.1. Simple Interest
2.7.5. Practice
2.2.2. Example
2.8. Annuities
2.2.3. Practice
2.8.1. Annuities
2.2.4. Practice
2.8.2. Example
2.3. Compound Interest
2.8.3. Practice
2.3.1. Compound Interest
2.3.2. Example
2.8.4. Annuity-Due
2.8.5. Example
2.3.3. Practice
2.8.6. Practice
2.4. Effective Annual Rate
2.9. Perpetuities
2.4.1. Annual Percentage Rate (APR) and
Effective Annual Rate (EAR)
2.9.1. Perpetuities
2.9.2. Example
2.4.2. Example
2.9.3. Practice
2.4.3. Practice
2.10. Growing Annuities
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2.10.1. Growing Annuities
3.2. Bond Valuation
2.10.2. Example
3.2.1. Bond Valuation
2.10.3. Practice
3.2.2. Example
2.10.4. Example
3.2.3. Example
2.10.5. Practice
3.2.4. Practice
2.10.6. Practice
3.2.5. Practice
2.11. Growing Perpetuities
3.3. The Current Yield
2.11.1. Growing Perpetuities
3.3.1. The Current Yield
2.11.2. Practice
3.3.2. Example
2.11.3. Practice
3.3.3. Practice
2.12. Forward and Backward Starting Cash
Flows
3.4. Cash Price vs Quoted Price
2.12.1. Forward and Backward Starting Cash
Flows
3.4.2. Example
2.12.2. Example
2.12.3. Practice
2.12.4. Example
2.12.5. Practice
2.13. Pure-Discount Loan
2.13.1. Pure-Discount Loan
2.13.2. Example
2.13.3. Practice
2.14. Amortized (Instalment) Loan
2.14.1. Amortized Loans (Instalment Loans)
2.14.2. Break-down of the Payment on an
Instalment Loan
2.14.3. Example
3.4.1. Cash Price vs Quoted Price
3.5. Consols
3.5.1. Perpetual Bonds (Consols)
3.5.2. Example
3.5.3. Practice
3.6. Interest Rate Risk
3.6.1. Pricing Sensitivity and Factors Affecting
Bond Yields
3.6.2. Example
3.6.3. Practice
3.7. Return on Investment
3.7.1. Return on Investment
3.7.2. Example
3.7.3. Practice
2.14.4. Practice
Chapter 4. Equity Valuation
2.14.5. Example
4.1. Equity Basics
2.14.6. Practice
4.1.1. Equity Basics
Chapter 3. Bond Valuation
4.1.2. Common Equity vs Preferred Equity
3.1. Introduction to Bonds
3.1.1. What is a Bond?
4.1.3. The Dividend Discount Model
4.2. Common Shares (No Growth)
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4.2.1. Dividend Discount Model (Zero Growth)
5.3.1. Standard Deviation
4.2.2. Example
5.3.2. Example
4.2.3. Practice
5.3.3. Practice
4.3. Common Shares (Constant Growth) Gordon Growth Model
5.4. Expected Return and Ex-Ante Standard
Deviation
4.3.1. Gordon Growth Model
5.4.1. Expected Return and Standard Deviation
4.3.2. Example
5.4.2. Example
4.3.3. Practice
5.4.3. Practice
4.3.4. Practice
5.5. Covariance and Correlation
4.3.5. Practice
5.5.1. Covariance
4.3.6. Example
5.5.2. Correlation Coefficient
4.3.7. Practice
5.5.3. Example
4.4. Common Shares (Non-Constant Growth)
5.5.4. Practice
4.4.1. Non-Constant Growth Model
5.6. Portfolio Risk and Return
4.4.2. Example
5.6.1. What is a Portfolio?
4.4.3. Practice
5.6.2. Expected Return and Risk of a Portfolio
4.5. Preferred Shares
5.6.3. Example
4.5.1. Preferred Share Valuation
5.6.4. Practice
4.5.2. Example
5.6.5. Example
4.5.3. Practice
5.6.6. Practice
Chapter 5. Risk, Return & Portfolio
5.7. Portfolio Standard Deviation (Special
Cases)
Theory
5.1. Ex-Post Risk and Return
5.7.1. Standard Deviation with Perfect
Correlations
5.1.1. Return on Investment
5.7.2. Example
5.1.2. Example
5.7.3. Practice
5.1.3. Practice
5.7.4. Portfolio Standard Deviation with No
Correlation
5.2. Average Returns and Standard
Deviation
5.7.5. Example
5.2.1. Average Returns
5.7.6. Practice
5.2.2. Example
5.2.3. Practice
5.7.7. Portfolio Standard Deviation with a RiskFree Asset
5.3. Ex-Post Standard Deviation
5.7.8. Example
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5.7.9. Practice
6.6.1. The Market Line (SML)
5.8. The Efficient Frontier
6.6.2. Pricing Stocks Using CAPM
5.8.1. The Efficient Frontier
6.6.3. Example
5.9. Types of Risk
6.6.4. Practice
5.9.1. Types of Risk
Chapter 6. CAPM
6.1. Risk-Free Investing
6.1.1. Risk-Free Investing
6.1.2. Example
6.1.3. Practice
6.2. Risk-Free Borrowing
6.2.1. Risk-Free Borrowing
6.6.5. Example
6.6.6. Practice
6.7. Alpha
6.7.1. Alpha
6.7.2. Example
6.7.3. Practice
Chapter 7. Market Efficiency
7.1. The Efficient Market Hypothesis
6.2.2. : Risk-Free Borrowing
7.1.1. The Efficient Market Hypothesis (EMH)
6.2.3. Practice: Risk-Free Borrowing
7.2. Levels of Market Efficiency
6.3. Introduction to Risk
7.2.1. Weak Form Efficiency
6.3.1. Shorting Stocks
6.3.2. Example
6.3.3. Practice
6.4. Capital Market Line (CML)
7.2.2. Semi-Strong Form Efficiency
7.2.3. Strong Form Efficiency
7.2.4. Example
7.2.5. Practice
6.4.1. The Market Portfolio and The Capital
Market Line
Chapter 8. Options
6.4.2. Example
8.1.1. What are Options?
6.4.3. Practice
6.4.4. Example
6.4.5. Practice
6.5. Beta
6.5.1. Market Risk and Beta
6.5.2. Example
6.5.3. Practice
6.5.4. Example
6.5.5. Practice
6.6. Security Market Line (SML)
8.1. Option Basics
8.2. Call Options
8.2.1. Call Options
8.2.2. Example
8.2.3. Practice
8.3. Put Options
8.3.1. Put Options
8.3.2. Example
8.3.3. Practice
8.4. Option Premium
8.4.1. Option Premiums
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8.4.2. Example
9.6. Profitability Index
8.4.3. Practice
9.6.1. Profitability Ratio (PI)
8.4.4. Example
9.6.2. Example
8.4.5. Practice
9.6.3. Practice
8.5. Option Strategies
9.7. Cross-over Rate
8.5.1. Covered Calls
9.7.1. The Cross-Over Rate
8.5.2. Protective Puts
9.7.2. Example
8.5.3. Long Straddle
9.7.3. Practice
8.5.4. Short Straddle
9.8. Equivalent Annual NPV
8.5.5. Long Strangle
9.8.1. Equivalent Annual Net Present Value
(EANPV)
8.5.6. Short Strangle
Chapter 9. Capital Budgeting
9.1. Introduction to Capital Budgeting
9.8.2. Example
9.8.3. Practice
9.1.1. What is Capital Budgeting?
Chapter 10. Cash Flow Estimation
9.2. Payback Period
10.1. Cash Flow Basics
9.2.1. Payback Period
10.1.1. Cash Flow Estimation Rules
9.2.2. Example
10.2. Net Working Capital
9.2.3. Practice
10.2.1. Net Working Capital
9.3. Discounted Payback Periods
10.2.2. Example
9.3.1. Theory
10.2.3. Practice
9.3.2. Example
10.3. The Initial Cash Outlay
9.3.3. Practice
10.3.1. Initial Cash Flow (CF0)
9.4. Net Present Value
10.3.2. Example
9.4.1. Net Present Value (NPV)
10.3.3. Practice
9.4.2. Example
10.4. Annual Cash Cash Flows
9.4.3. Practice
10.4.1. Annual Cash Flows
9.4.4. Example
10.4.2. CCA Using the Straight-Line Method
9.4.5. Practice
10.4.3. Example
9.5. Internal Rate of Return
10.4.4. Practice
9.5.1. Internal Rate of Return (IRR)
10.5. Ending Cash Flow
9.5.2. Example
10.5.1. Ending Cash Flow (ECFt)
9.5.3. Practice
10.5.2. Example
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10.5.3. Practice
11.2. Cost of Equity
10.6. Net Present Value
11.2.1. Cost of Equity
10.6.1. Calculating NPV
11.2.2. Example
10.6.2. Example
11.2.3. Example
10.6.3. Example
11.2.4. Practice
10.6.4. Practice
11.2.5. Practice
Chapter 11. Cost of Capital
11.3. Weighted-Average Cost of Capital
11.1. Cost of Debt
11.1.1. Cost of Debt
11.1.2. Example
11.1.3. Practice
11.3.1. Weighted-Average Cost of Capital
11.3.2. Example
11.3.3. Practice
11.3.4. Example
11.3.5. Practice
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1. Introduction to Finance
1.1
Introduction to Finance
1 .1 .1
Introduction to Finance
What is Finance?
Finance is defined as the management of money and includes activities such as investing, borrowing,
lending, budgeting, saving, and forecasting. It relates people or organizations with money to invest,
to those that need money invested in them.
Accounting vs Finance
● Accounting measures historical income whereas finance deals with future cash flows.
● Accounting deals with book value (historical cost) whereas financiers are interested in market
value.
● Accounting income includes many non-cash items (ex: depreciation and amortization).
Financial Management
Role of Financial Managers
Financial managers are in charge of raising capital through financial markets by issuing debt and
equity, deciding where to invest the firm's capital, managing the cash that is reinvested in the
company or distributed to owners in the form of dividends.
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The Goal of Financial Management
The goal of financial management, and the goal of managers in general, is to maximize the
shareholders' wealth. Accomplished by operating a business in such a way that maximizes the price
of its shares (the firm's value).
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1 .1 .2
Markets
The Role of Financial Markets
● Brings buyers and sellers together:
o Enables businesses to raise funding
o Enables investors to invest in financial assets and trade (buy/sell) financial assets
● Provides liquidity
● Continuously values financial assets
● Enables transfer of risk through financial assets
Primary Market
● “Original sale of securities”
o Issued by corporations (equity and bonds) or governments (bonds)
o To initial investors (placement) / banks (bought-deal)
o Not actually a “market” as much as it is a description of individual transaction
o Negotiated prices between the issuer and initial counterparty
Secondary Market
● “Where securities are bought and sold after the initial sale”
o Between investors/market makers/banks
o Usually on organized private/public exchanges such as the NYSE (New York Stock Exchange)
and TSX (Toronto Stock Exchange)
o Market-established prices through demand/supply
Major Assets
● Real asset are tangible assets like buildings, vehicles, equipment and commodities.
● Financial assets are intangible like receivables, stocks, bonds and cash.
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Watch the video tutorial for this lesson (01:22)
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1.2
Corporate Structures
1 .2 .1
Sole-proprietorship
The most simple form of business organization is the sole-proprietorship, however, roughly 72% of
businesses fall into this category.
Characteristics of a Sole-proprietorship
● Owned by a single individual
● The owner and the business are the same
legal entity.
● Income added to owner's personal income for
tax purposes.
Advantages
● Simple and inexpensive to set up.
● Owner receives all profits earned by the business.
● Easily dissolvable
Disadvantages
● Owner is personally responsible (liable) for the business's debts (unlimited liability).
● Difficult to raise capital.
Watch the video tutorial for this lesson (01:21)
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1 .2 .2
Partnerships
When two or more people wish to go into business together, the most basic form of corporate
organization available to them is a partnership.
Characteristics of a Partnership
● Owned by two or more people.
● No separate legal entity.
● Formalized in a written partnership
agreement that describes:
○ Each partner's contribution
○ How profits are shared
○ How to resolve disputes
Advantages
● Easy to form.
● More capital available.
Disadvantages
● Owners are personally responsible for obligations (unlimited liability)
○ Except for limited/silent partners (limited liability)
● Potential for conflicts
● Profit-sharing can be complicated.
● Difficult to dissolve or to transfer ownership.
Watch the video tutorial for this lesson (02:10)
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1 .2 .3
Corporations
Corporations account for less than 20% of all organizations' businesses, however, they are
responsible for over 80% of sales.
Characteristics of a Corporation
● A separate legal entity from its owners
(called shareholders)
● Can be public or private
Advantages
● Owners are not personally responsible for
business obligations (limited liability)
● Indefinitely (Unlimited) legal life
● Ownership is easily transferrable
● Easier to raise capital
Disadvantages
● More costly and more complex to set up than sole-proprietorships and partnerships.
● Double taxation
○ Corporation's income is taxed at the corporate level
○ Owners are taxed on dividends at the personal level
Watch the video tutorial for this lesson (02:21)
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1.3
The Principle-Agent Problem
1 .3 .1
The Agency Relationship
The Agent
An "agent" is a representative of a "principal" that acts on behalf of them. In business, the agents
are the managers that run the company on behalf of the owners or shareholders (the principals).
The Agency Problem
When the agent does not act in the best interest of the principal and instead acts in his or her own
best interest.
Agency Costs
Agency costs are costs that a company incurs because of agency problems. There are two types:
● Direct: Costs incurred when the manager acts in their own best interest. E.g. Using the
corporate jet to take a personal vacation or accepting a deal that would increase their bonus
despite it being a bad deal for the company.
● Indirect: Costs incurred in order to prevent direct agency costs. This includes costs that arise
from any restrictions placed on actions of management, costs associated with monitoring
management, and costs associated with compensation schemes that will provide managers
with incentives to act in the shareholders' best interests.
How to Resolve the Agency Problem
The best way to resolve the agency problem and to align managers' interests with those of the
shareholders is to remove financial incentives that encourage conflicts of interest and to instead
use a stock-based compensation scheme which would effectively turn the managers into
shareholders as well.
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Watch the video tutorial for this lesson (02:00)
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2. Time Value of Money
2.1
Introduction to TVM
2 .1 .1
What is Time Value of Money?
● The relationship between money, time and interest rates.
● Interest rates cause the value of money to change over time.
Real Life Applications of TVM
●
●
●
●
●
Loans and mortgages
Savings
Credit cards
Stocks and bonds
Car leases
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Watch the video tutorial for this lesson (00:52)
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2 .1 .2
The Financial Calculator
Most TVM operations can be performed on a financial calculator, replacing the need to use some
complicated formulae.
Please use the Texas Instrument BA-II Plus Calculator as it is the most
widely used calculator and contains the most easy to use features.
Setting Up Your Calculator
Step 1: Set the decimal places to 9
Step 2: Restore default setting for P/Y and C/Y
When doing this you should see P/Y = 1 and if you press the up or down arrow you should also see
C/Y = 1.
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Entering the TVM Variables
● First enter the value
● Then press the variable you wish to assign it to.
○ For example: To enter the present value as $1,000:
■ Step 1: Enter 1,000
■ Step 2: Press the [PV] button
WIZ E TIP
On the financial calculator, always enter rates in percentage format. For example, if you wish
to enter a rate of 5.1%, simply enter 5.1.
Computing a TVM Variable
● First enter the TVM variables you have
● Then press [CPT] followed by the TVM variable you wish to compute.
○ For example: To compute the future value:
■ Step 1: Enter the TVM variables you have
■ Step 2: Press the [CPT] button followed by the [FV] button.
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2.2
Simple Interest
2 .2 .1
Simple Interest
● Interest on the principal amount only
● Does not include interest-on-interest
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2 .2 .2
Example: Simple Interest
You deposit $1,000 into an account earning 10% simple interest per year. How much will you have in
the account in 3 years?
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2 .2 .3
Practice: Simple Interest
Steve just deposited $5,000 into an account earnings 7% simple interest. How much will Steve have
in his account in 8 years?
Answer
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2 .2 .4
Practice: Simple Interest
You deposit $4,000 today at the bank. At the beginning of year 3 you deposit another $25,000. Your
bank pays a simple interest rate of 8% a year.
How much do you have in your bank account at the end of 5 years?
Answer
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Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/2/core/2/4
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2.3
Compound Interest
2 .3 .1
Compound Interest
● Interest on the principal and previous interest payments (interest-on-interest)
● Most widely used form of interest
Future Value
Total Interest
Interest-on-Interest
● Interest that is earned on previous interest payments.
● Increases over time, unlike simple interest.
● It is the difference between compound interest and simple interest.
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Watch the video tutorial for this lesson (01:32)
https://www.wizeprep.com/online-courses/20009/chapter/2/core/3/1
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2 .3 .2
Example: Compound Interest
Today you have $1,000 and will earn 10% interest compounded annually.
1. How much will you have in your account in 4 years?
2. How much total interest will you earn in 4 years?
3. How much interest-on-interest will you earn in 4 years?
Watch the video tutorial for this lesson (01:39)
https://www.wizeprep.com/online-courses/20009/chapter/2/core/3/2
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2 .3 .3
Practice: Compound Interest
Mary invested $10,000 and will earn 12% interest compounded annually for 10 years.
Round your final answers to 2 decimal places
How much total interest will Mary earn?
How much interest-on-interest will Mary earn?
View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/2/core/3/3
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2.4
Effective Annual Rate
2 .4 .1
Annual Percentage Rate vs Effective Annual Rate
Annual Percentage Rate
● APR is a quoting convention where short-term interest rates (monthly, quarterly, semiannually, etc.) are multiplied by the number of periods in a year.
● Not particularly useful because APR does not take into account compounding!
● An interest rate is “APR” when:
○ A quotation is provided;
○ Compounding frequency is indicated; or
○ The periodicity of the interest rate is not annual and is not specified to be “effective” (e.g.
“monthly” interest rate).
● Also called the nominal rate, stated rate, or quoted rate
WIZ E TIP
APR is quoted as [APR, periodicity of compounding], ex: [0.10, 4] is read 10% APR compounded
quarterly.
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Effective Annual Rate
● The actual interest rate that is earned or paid, computed by adjusting the APR to reflect the
number of compounding periods per year.
● Effective rate increases as compounding frequency increases because interest is calculated
more often.
Where:
m = number of compounding periods per year
Watch the video tutorial for this lesson (01:17)
https://www.wizeprep.com/online-courses/20009/chapter/2/core/4/1
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2 .4 .2
Example: Effective Annual Rate
APR of 10% compounded monthly is equal to what effective annual rate?
Watch the video tutorial for this lesson (01:36)
https://www.wizeprep.com/online-courses/20009/chapter/2/core/4/2
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2 .4 .3
Practice: Effective Annual Rate
Steve is planning on investing his money into a new account offered by his bank. The ad for the new
account stated that the account earns 5.1% APR compounded monthly. His current account pays 5%
compounded daily. Which account should he choose?
A) New account because it has a higher APR
B) Current account because it compounds interest more often.
C) New account because it has a higher EAR
D) Cannot compare because the accounts do not have the same APR
View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/2/core/4/3
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2.5
Effective Periodic Rate
2 .5 .1
Effective Periodic Rates
● APR must be converted to the appropriate effective periodic rate before cash flow valuation is
performed.
● An effective periodic rate is a rate that corresponds with the frequency of the payments.
○ For example, if payments occur monthly, an effective monthly rate is required to perform
time value operations.
Where:
m = number of compounding periods per year
f = number of payments per year (periodicity desired)
WIZ E TIP
If m and f are the same, you can quickly find the periodic rate by simply dividing the APR.
For Example: 6% interest compounded monthly and paid monthly, the periodic rate is 6% / 12 =
0.5%
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Converting Effective Rates
Useful when you have an effective period rate and wish to find an equivalent rate with a different
periodicity.
For example: converting an effective quarterly rate to an effective monthly rate.
Watch the video tutorial for this lesson (02:49)
https://www.wizeprep.com/online-courses/20009/chapter/2/core/5/1
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2 .5 .2
Example: Effective Periodic Rate
What is the effective quarterly rate of an APR of 12%, compounded monthly?
Watch the video tutorial for this lesson (00:40)
https://www.wizeprep.com/online-courses/20009/chapter/2/core/5/2
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2 .5 .3
Practice: Effective Periodic Rate
You are planning on borrowing money to buy a new TV. The TV costs $1,200 and the store is offering
you a financing of 5% APR compounded semi-annually (twice per year). You will make monthly
payments on this loan, what is the effective monthly rate you would need to calculate your monthly
payment?
A) 5%
B) 0.4167%
C) 0.4124%
D) 2.5%
View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/2/core/5/3
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2 .5 .4
Example: Effective-to-Effective
Convert a 2% effective quarterly rate to an effective monthly rate.
Watch the video tutorial for this lesson (00:58)
https://www.wizeprep.com/online-courses/20009/chapter/2/core/5/4
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2 .5 .5
Practice: Effective-to-Effective
Convert a 3.5% effective semi-annual rate to an effective four-year rate. Round your final answer to
2 decimal places.
Effective four-year rate
%
View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/2/core/5/5
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2.6
Effective Rates with Continuous
Compounding
2 .6 .1
Continuous Compounding
Continuous compounding is the mathematical limit that compound interest can reach if it's
calculated and reinvested into an account's balance over a theoretically infinite number of periods.
While this is not possible in practice, the concept of continuously compounded interest is important
in finance.
Where:
n = Periodicity desired expressed in years (monthly = 1/12, weekly = 1/52, etc)
e = The base of the natural log (2.71828...)
Watch the video tutorial for this lesson (01:23)
https://www.wizeprep.com/online-courses/20009/chapter/2/core/6/1
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2 .6 .2
Example: Continuous Compounding
A savings account advertised on Facebook caught your eye because it claims to offer a savings rate
of APR 5.2% compounded continuously. Your current account is paying you an effective annual rate of
5.3%, should you switch your savings to the new account?
Watch the video tutorial for this lesson (01:12)
https://www.wizeprep.com/online-courses/20009/chapter/2/core/6/2
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2 .6 .3
MAR K YO UR SE LF Q UE STIO N
Try the problem yourself, and check the solutions to see how you did. Then mark yourself right or wrong.
Practice: Continuous Compounding
You borrowed money from your friend's uncle Rocco. The money was lent under the terms 6% APR
compounded continuously, and you intend on making monthly payments over the next few years to
pay it off.
What is the interest rate required to compute the payment on your loan?
View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/2/core/6/3
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2.7
Lump Sum Calculations
2 .7 .1
Lump-Sum Calculations
● A lump sum is a single amount at a specific point in time.
● Lump-sum calculations involve finding the present or future value of single amounts.
○ Example: You have $5,000 today, what will this be worth in 7 years?
● Finding the present value of some future value is called discounting.
● Finding the future value of some present value is called compounding.
Watch the video tutorial for this lesson (01:04)
https://www.wizeprep.com/online-courses/20009/chapter/2/core/7/1
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2 .7 .2
Example: Future Value of a Lump Sum
You deposit $1,000 into an account, earning 10% interest compounded annually.
a) How much will you have in your account in 3 years?
b) How long will it take for your money to grow to $2,000?
c) What interest rate would triple your money in 5 years?
Watch the video tutorial for this lesson (04:12)
https://www.wizeprep.com/online-courses/20009/chapter/2/core/7/2
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2 .7 .3
Practice: Future Value of a Lump Sum
You deposit $4,000 today at the bank into your earning which earns 6% interest compounded
monthly.
Round your answers to 2 decimal places.
How much do you have in your bank account at the end of 5 years?
How many years will it take to double your money?
What annual interest rate (in %) would you need to earn to grow your money to $6,500 in 2 years?
View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/2/core/7/3
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2 .7 .4
Example: Present Value of a Lump Sum
At the end of Year 2, Rabi will receive a $60,000 cheque from his father. At the end of Year 5, Rabi
will receive a $35,000 cheque from his mother. The effective annual interest rate is 3.25%.
What is the total present value of Rabi’s cheques from his parents as of Year 0?
Watch the video tutorial for this lesson (01:38)
https://www.wizeprep.com/online-courses/20009/chapter/2/core/7/4
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2 .7 .5
MAR K YO UR SE LF Q UE STIO N
Try the problem yourself, and check the solutions to see how you did. Then mark yourself right or wrong.
Practice: Present Value of a Lump Sum
One night, Sean dreamed that a magic wizard offered him two gift options. The first gift option
provides $1,000 in Year 2 and Year 4. The second gift option provides $950 in Year 1 and Year 3.
If Sean’s dream were to be true, which option should he select if the effective annual interest rate is
7.50%?
View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/2/core/7/5
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2.8
Annuities
2 .8 .1
Annuities
● A series of payments or cash flows with the following characteristics
○ Equal value
○ Equal time between cash flow
○ Equal interest rate
○ Finite number of cash flows
● Payments can take place at the end of the period (ordinary annuity) or at the beginning of the
period (annuity-due).
Present Value of an Ordinary Annuity
● Sum of the present value of the individual cash flows one period before the first payment.
● Can be solved using a formula or with a financial calculator.
● In both cases, you will need:
○ Value of the cash flow
○ Effective periodic rate
○ Number of cash flows
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Present Value Formula
Financial Calculator Method
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Future Value of an Ordinary Annuity
● Sum of the future value of the individual cash flows at the same period of time as the last cash
flow.
● Can be solved using a formula or with a financial calculator.
● In both cases, you will need:
○ Value of the cash flow
○ Effective periodic rate
○ Number of cash flows
Future Value Formula
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Financial Calculator Method
Watch the video tutorial for this lesson (02:38)
https://www.wizeprep.com/online-courses/20009/chapter/2/core/8/1
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2 .8 .2
Example: Ordinary Annuities
Joey is calculating the present value of his future federal GST rebates. He estimates that he will
receive $300 in each quarter of a calendar year. Joey's bank account earns an APR of 1.25% that
compounds monthly.
1. What is the present value of Joey's total future GST rebates over a seven-year period?
2. If Joey decides that he will leave everything he's received in the bank, what will be his account
balance in seven years?
Watch the video tutorial for this lesson (05:59)
https://www.wizeprep.com/online-courses/20009/chapter/2/core/8/2
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2 .8 .3
Practice: Ordinary Annuities
Richard is mulling over purchasing an investment for $200,000. The investment will pay him $5,000
every 6 months for 40 years.
Part 1
Richard can earn 10% per year on his other investments compounded monthly, should he make this
investment today?
A) Yes because he will receive more than $200,000
B) Yes because the present value of the return is greater than $200,000
C) No because the future value of the investment is less than $200,000
D) No because the present value of the return is less than $200,000
Practice: Ordinary Annuities
Richard is mulling over purchasing an investment for $200,000. The investment will pay him $5,000
every 6 months for 40 years.
Part 2
Assuming Richard decides to make this investment and reinvests everything he collects in his other
investment portfolio earnings 14% per year compounded monthly. How much will Richard have in his
account in 10 years?
Round your effective rate to at least 6 decimal places and your final answer to the nearest dollar.
Answer
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View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/2/core/8/3
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2 .8 .4
Annuity-Due
● Annuities with payments at the beginning of the period.
● For example, you will receive $100 per year for 6 years, starting today.
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base or retrieval system, without the prior written permission of Wizedemy Inc.
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Watch the video tutorial for this lesson (01:20)
https://www.wizeprep.com/online-courses/20009/chapter/2/core/8/4
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2 .8 .5
Example: Annuity-Due
Carmen and Carrie are sisters. Carmen donates $30 to World Vision Canada at the beginning of
each month. Carrie donates $30 to World Vision Canada at the end of each month. Their bank
accounts both offer an effective annual interest rate of 1.25%. Calculate, separately, the present
value of each sister’s donations over the next ten years.
Watch the video tutorial for this lesson (02:18)
https://www.wizeprep.com/online-courses/20009/chapter/2/core/8/5
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2 .8 .6
Practice: Annuity-Due
You plan on retiring in 40 years and have decided you will begin saving $500 per month, starting
today. Your investment account earns 8% interest compounded quarterly, and you will make 480
total deposits. How much will you have in your account when you retire?
Round the effective rate to at least 6 decimal places and your final answer to the nearest dollar.
Answer
View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/2/core/8/6
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2.9
Perpetuities
2 .9 .1
Perpetuities
Perpetuities are simply annuities that never end. All other characteristics of annuities are also
characteristics of perpetuities.
● Perpetuities have indefinite lives, there is no value for n or FV
● Payments can be at the end of the period (ordinary perpetuities) or at the beginning of the
period (perpetuity-due)
Present Value or Ordinary Perpetuity
Present Value or Perpetuity-Due
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Watch the video tutorial for this lesson (00:48)
https://www.wizeprep.com/online-courses/20009/chapter/2/core/9/1
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2 .9 .2
Example: Perpetuities
Assume you expect to receive $100 per year forever starting from today. If the appropriate discount
rate is 6%.
A) What is the present value of these cash flows?
B) What is the present value if the payments begin today?
Watch the video tutorial for this lesson (00:45)
https://www.wizeprep.com/online-courses/20009/chapter/2/core/9/2
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2 .9 .3
Practice: Perpetuities
Steve just won a lottery that will pay him $1,000 per month forever, starting in one month. He is
considering selling his winning ticket but needs your help in deciding how much he should sell it for.
Assuming the appropriate discount rate is 10% compounded semi-annually, what is the minimum he
should accept to sell his ticket?
Round the effective rate to at least 6 decimal places and your final answer to the nearest dollar.
Answer
View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/2/core/9/3
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2.10
Growing Annuities
2 .1 0 .1
Growing Annuities
A series of payments occurring over a finite period of time that increase by a constant percentage
called the growth rate.
● Present value is found using the first payment of the annuity, the effective rate, the growth rate,
and the number of payments.
● Present value is always one period before the first payment.
Present Value of a Growing Annuity
Present Value of a Growing Annuity (when r = g)
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Future Value of a Growing Annuity
Watch the video tutorial for this lesson (01:51)
https://www.wizeprep.com/online-courses/20009/chapter/2/core/10/1
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2 .1 0 .2
Example: Growing Annuities
You will receive the first of 10 payments next year. The first payment will be $200, and each of the
following payments will increase by 5%. Using a discount rate of 8%, what is the present value of this
cash flow?
Watch the video tutorial for this lesson (01:07)
https://www.wizeprep.com/online-courses/20009/chapter/2/core/10/2
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2 .1 0 .3
Practice: Growing Annuities
Your sister has asked you to lend her money and has promised to repay you over 20 years. The first
payment will be in one year, and each of the following payments will increase by 7%. How much is
the first payment if your sister borrowed $60,000 from you at a rate of 9% compounded monthly?
Round the effective rate to at least 6 decimal places and your final answer to 2 decimal places.
Answer
View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/2/core/10/3
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2 .1 0 .4
Example: Growing Annuities
You will deposit the first of 10 payments next year into your savings account. The first payment will
be $200, and each of the following payments will increase by 8%. Using a discount rate of 8%, what
is the future value of this cash flow?
Watch the video tutorial for this lesson (02:29)
https://www.wizeprep.com/online-courses/20009/chapter/2/core/10/4
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2 .1 0 .5
Practice: Growing Annuities
You just won a lottery that will pay you $1,000 in one year and 10% more each year thereafter for a
total of 20 payments. What is the present value of your winnings if your opportunity cost is 10%?
Round your final answer to 2 decimal places.
Answer
View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/2/core/10/5
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2 .1 0 .6
Practice: Growing Annuities
You have decided to start saving for retirement. You plan to deposit $6,000 in 3 months into your
retirement account which earns 12% interest compounded monthly, and 2% more each quarter. How
much will you have saved up when you retire in 40 years?
Round the effective rate to at least 6 decimal places, and your final answer to the nearest dollar.
Answer
View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/2/core/10/6
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2.11
Growing Perpetuities
2 .1 1 .1
Growing Perpetuities
Perpetuities where the recurring payments/cash flows grow at a constant rate (g) each period in
perpetuity. Again, because the payments grow each period, the dollar value of the payments is not
equal.
Growing perpetuities have the following characteristics:
● Constant growth rate (g) each period in perpetuity;
● Regular time interval of payout; and
● No end date. Continues forever
WATC H O UT!
In a growing perpetuity, the discount rate (r) must be greater than the growth rate (g).
Watch the video tutorial for this lesson (01:07)
https://www.wizeprep.com/online-courses/20009/chapter/2/core/11/1
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2 .1 1 .2
Example: Growing Perpetuity
Diane plans to make a donation each year to her favourite charity. One year from today, she wishes
to make the first donation of $1,000 and plans to increase her donations by 5% per year. How much
should she deposit today so that there will always be money available for her donations if her
account earns 8% compounded semi-annually (twice per year)?
Watch the video tutorial for this lesson (02:19)
https://www.wizeprep.com/online-courses/20009/chapter/2/core/11/2
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2 .1 1 .3
Practice: Growing Perpetuities
In two years you will receive $600 from an investment. Every two years after that, your return will
increase by 8%. What is the present value of your investment using a rate of 10% compounded
monthly?
Answer
View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/2/core/11/3
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2.12
Forward and Backward Starting Cash
Flows
2 .1 2 .1
Forward and Backward Starting Cash Flows
Cashflows typically start at t=0, but in some cases, they do not, solving these requires a bit more
work.
● Cash flow that does not start at t=0
● Can start before t=0 (backward starting) or after t=0 (forward starting)
Computing the Present Value of a Forward or Backward Starting Cash Flow
Step 1: Compute the present value at the start of the cash flow
Step 2: Discount or compound the present value to the desired time period
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Watch the video tutorial for this lesson (01:18)
https://www.wizeprep.com/online-courses/20009/chapter/2/core/12/1
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2 .1 2 .2
Example: Forward Starting Cash Flow
Find the present value of a 6-year annuity starting at the end of year 7. The annuity will pay $100
per year for 10 years and the APR is 10% compounded semi-annually.
Watch the video tutorial for this lesson (03:25)
https://www.wizeprep.com/online-courses/20009/chapter/2/core/12/2
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2 .1 2 .3
MAR K YO UR SE LF Q UE STIO N
Try the problem yourself, and check the solutions to see how you did. Then mark yourself right or wrong.
Practice: Forward Starting Cash Flow
You are considering investing $5,000 into a new project that your friend told you about. The
investment will pay you $800 per year for 10 years but the first payment will not be received until
the end of year 4. If the effective annual rate is 5%, should you make this investment?
View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/2/core/12/3
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2 .1 2 .4
Example: Backward Starting Cash Flow
An investment will pay you $500 every 2 years, starting one year from today. What is the present
value of the investment if your opportunity cost is 10% per year?
Watch the video tutorial for this lesson (02:09)
https://www.wizeprep.com/online-courses/20009/chapter/2/core/12/4
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2 .1 2 .5
Practice: Backward Starting Cash Flow
You will receive a payment of $X every three years starting one year from today. The present value
of your investment is $2,400 and the interest rate is 8% compounded monthly. What is the value of
X?
Round the effective rates to at least 6 decimal places and the final answer to 2 decimal places.
Answer
View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/2/core/12/5
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2.13
Pure-Discount Loan
2 .1 3 .1
Pure Discount Loan
A pure discount loan is a loan that requires only a single lump-sum payment at the end of the term
which includes the principal borrowed plus all accumulated interest.
The amount to be repaid is the future value of the loan.
Watch the video tutorial for this lesson (01:15)
https://www.wizeprep.com/online-courses/20009/chapter/2/core/13/1
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2 .1 3 .2
Example: Pure-Discount Loan
You agree to borrow $40,000 today using a pure-discount loan with an effective annual rate of 6%
for 6 years. How much will you repay at the end of the 6th year?
Watch the video tutorial for this lesson (00:50)
https://www.wizeprep.com/online-courses/20009/chapter/2/core/13/2
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2 .1 3 .3
Practice: Pure-Discount Loan
Eight years ago you borrowed money to pay for a 4-month long trip to Australia. Today is the due
date of the pure-discount loan, and you must repay $89,009.33. The loan carried an 8.9% annual
interest rate, how much did you borrow?
Round your final answer to the nearest dollar.
Answer
View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/2/core/13/3
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2.14
Amortized (Instalment ) Loan
2 .1 4 .1
Amortized Loans (Instalment Loans)
● A loan that is paid off in equal payments throughout the term of the loan.
● Each payment consists of an interest portion and a principal portion.
○ Interest portion: The interest on the remaining balance that has accumulated since the
previous payment.
○ Principal portion: The amount of the payment that is used to reduce the debt owing.
Mortgages
● A mortgage is an instalment loan specifically used to purchase real estate properties, like
houses, condos, cottages, revenue properties.
● In Canada, mortgages are compounded semi-annually.
● In the US, mortgages are compounded monthly.
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Interest and Principal
● The payment remains constant each period.
● The interest portion decreases with each payment because the remaining balance of the debt
decreases.
● The principal portion increases with each payment because the payment is constant and
interest decreases.
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Amortization Schedule
Watch the video tutorial for this lesson (02:04)
https://www.wizeprep.com/online-courses/20009/chapter/2/core/14/1
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2 .1 4 .2
Break-down of the Payment on an Instalment Loan
Amortized loans have fixed payments at some constant interval of time. For this reason, we can use
an ordinary annuity to solve for the instalment that must be paid each period.
Calculating the Loan Payment
● The payment on an instalment loan is found using the ordinary annuity formula or a financial
calculator.
● The effective rate used must match the frequency of the payment.
○ For example, if a loan is paid monthly the rate must be an effective monthly rate.
Calculating the Interest Portion
● The interest portion of a loan payment is based on the remaining balance of the debt and the
effective rate.
● It can be found by multiplying the balance by the effective rate, or by using your financial
calculator's amortization function.
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Calculating the Principal Portion
The principal portion is the difference between the loan payment and the interest portion.
Calculating the Remaining Balance
● The remaining balance is the amount that is still owed to the lender at a specific point in time.
● It is based on the effective rate, the number of remaining payments, and the payment.
● The balance is found using the present value of an annuity formula or a financial calculator,
solving for the PV.
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Using the Financial Calculator
● Financial calculators have an amortization function that can speed up finding these values
● Compute the payment on the loan, then in the amortization function enter the range of
payments you wish to gather the information for.
○ For example, if you'd like to know the interest portion of the 5th payment, simply enter into
the calculator P1 = 5 and P2 = 5. The calculator understands this as a range.
Watch the video tutorial for this lesson (02:18)
https://www.wizeprep.com/online-courses/20009/chapter/2/core/14/2
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2 .1 4 .3
Example: Amortized Loans
Gerald took out a 10-year loan of $10,000 for his small business. His payment terms are 10 equal
annual payments at an effective annual rate of 2.5%.
1. What is the outstanding principal balance at the end of Year 4?
2. What was the amount of principal repayment at the end of Year 4?
3. What was the amount of interest payment at the end of Year 4?
Watch the video tutorial for this lesson (06:11)
https://www.wizeprep.com/online-courses/20009/chapter/2/core/14/3
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2 .1 4 .4
Practice: Amortized Loan
You just borrowed $75,000 to renovate your apartment. The bank quoted a rate of 6.9%
compounded monthly. You play to make bi-weekly payments on the loan for 10 years to pay it off.
Round the effective rate to at least 6 decimal places and your final answers to 2 decimal places.
How much is the bi-weekly loan payment?
How much will you owe after making your 15th payment?
What is the interest portion of the 16th payment?
What is the principal portion of the 16th payment?
View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/2/core/14/4
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2 .1 4 .5
Example: Mortgages
Karla is purchasing a Condo in New York City for $1,200,000. She has saved enough for a 20% down
payment and will finance the rest. The bank has quoted her a mortgage rate of 2.6% for a term of 5
years. The payment is based on an amortization period of 25 years.
1. What is Karla's monthly mortgage payment?
2. What is the interest portion of her 50th payment?
3. How much principal will be repaid in the 4th year?
Watch the video tutorial for this lesson (07:49)
https://www.wizeprep.com/online-courses/20009/chapter/2/core/14/5
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2 .1 4 .6
Practice: Mortgages
Steve is purchasing a cottage in Mont Tremblant, Canada. The price of the cottage is $1,000,000,
and he has $250,000 in cash for a down payment. The term of the mortgage is 4 years, 2.99%
interest. The amortization period is 30 years.
Round the effective rate to at least 6 decimal places and your final answers to 2 decimal places.
Part 1
What is Steve's monthly mortgage payment?
Answer
Practice: Mortgages
Steve is purchasing a cottage in Mont Tremblant, Canada. The price of the cottage is $1,000,000,
and he has $250,000 in cash for a down payment. The term of the mortgage is 4 years, 2.99%
interest. The amortization period is 30 years.
Round the effective rate to at least 6 decimal places and your final answers to 2 decimal places.
Part 2
How much total interest will Steve pay on this mortgage?
Answer
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Practice: Mortgages
Steve is purchasing a cottage in Mont Tremblant, Canada. The price of the cottage is $1,000,000,
and he has $250,000 in cash for a down payment. The term of the mortgage is 4 years, 2.99%
interest. The amortization period is 30 years.
Round the effective rate to at least 6 decimal places and your final answers to 2 decimal places.
Part 3
What fraction of the 14th payment will be taken in interest? Answer as a percentage.
Answer
Practice: Mortgages
Steve is purchasing a cottage in Mont Tremblant, Canada. The price of the cottage is $1,000,000,
and he has $250,000 in cash for a down payment. The term of the mortgage is 4 years, 2.99%
interest. The amortization period is 30 years.
Round the effective rate to at least 6 decimal places and your final answers to 2 decimal places.
Part 4
What will be the balance of the mortgage at the end of the first term?
Answer
View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/2/core/14/6
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3. Bond Valuation
3.1
Introduction to Bonds
3 .1 .1
What is a Bond?
A bond is a long-term debt instrument that promises fixed payments and has a maturity of more
than 10 years. Bonds are issued by corporations that require funding for future projects.
Basic Structure of Bond
The issuer (seller) agrees to pay periodic payments to the holder (buyer) in the form of
coupons/interest and repays the principal amount at the maturity date (balloon/bullet payment).
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Bond Components
● Face Value: The principal amount of the bond that the investor (lender) will receive from the
issuer (borrower) when the bond matures. This is typically $1,000.
● Coupon Rate: The annual interest rate paid to the investor expressed in percentage.
● Coupon Payment: The annual interest paid to the investor expressed in dollars.
● Maturity: The length of time before the bond will be paid and the interest payments will stop.
● Yield to Maturity: The annual rate of return earned by a bondholder if the bond is held until
maturity. It is also the discount rate used to value bonds.
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Types of Bonds
● Debenture: Bond that is unsecured by collateral.
● Secured Bonds: Bond that is secured by assets belonging to the issuer
● Callable Bonds: Bond that the issuer may redeem, or call back, before it reaches the stated
maturity date. A callable bond allows the issuing company to pay off its debt early.
● Convertible Bonds: A bond that the holder can convert into a specified number of shares of
common stock in the issuing company or cash of equal value.
Watch the video tutorial for this lesson (01:45)
https://www.wizeprep.com/online-courses/20009/chapter/3/core/1/1
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3.2
Bond Valuation
3 .2 .1
Bond Valuation
The coupon payment is the periodic interest payment the bondholder (investor) will receive from the
issuer (borrower). This is calculated by multiplying the coupon rate by the face value of the bond and
then dividing it by the number of payments per year (typically annual or semi-annual).
Step 1: Compute the periodic coupon payment
Where:
I = coupon payment (in dollars)
F = Face value of the bond
CR = coupon rate (in %)
k = number of payments per year
WIZ E TIP
Step 2: Computing the Periodic Discount Rate
The discount rate used to compute the price of the bond is the yield to maturity (YTM) divided by the
number of coupon payments per year.
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Step 3: Compute the Present Value of the Coupon Payments and the Present Value of the Face
Value
Using the Formula
Structurally a bond is nothing more than a stream of equal coupon payments (annuity) and a face
value amount at the maturity date (future value)
Using the Financial Calculator
Watch the video tutorial for this lesson (01:53)
https://www.wizeprep.com/online-courses/20009/chapter/3/core/2/1
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3 .2 .2
Example: Bond Valuation
Two years ago, Golden Residential Real Estate Investment Trust (“Golden”) issued coupon bond
securities to raise capital. The face value of each bond is $1,000. The coupon rate is 10%; coupons
are paid on an annual basis. The term was 10 years. The current market effective annual rate is 5%.
What is the current price of a Golden coupon bond security?
View this lesson online
https://www.wizeprep.com/online-courses/20009/chapter/3/core/2/2
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3 .2 .3
Example: Bond Valuation
Seattle Dairy Cooperative has issued 25-year bond securities —each of which has a face value of
$1,000. The bond securities offer a coupon rate of 5% and pays coupons on a semi-annual basis.
Main Street Journal reports a YTM of 4%. What is the current price of each bond security?
Watch the video tutorial for this lesson (01:53)
https://www.wizeprep.com/online-courses/20009/chapter/3/core/2/3
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3 .2 .4
Practice: Bond Valuation
The WIZE Real Estate Investment Trust just issued a pure discount bond of $1,000. The bond term is
10 years. If the bond is yielding 3.5%, what is the amount that WIZE will receive upon the issuance of
the pure discount bond?
Round your final answer to 2 decimal places.
Answer
View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/3/core/2/4
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3 .2 .5
Practice: Bond Valuation
Three years ago, Angus invested in a 25-year coupon bond. The face value of the bond is $1,000.
The bond offers a coupon rate of 3.5% and pays interest on a monthly basis. As at present, the YTM
is 3%. What is the current price of the bond?
Round your work to at least 4 decimal places and your final answer to 2 decimal places.
Answer
View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/3/core/2/5
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3.3
The Current Yield
3 .3 .1
The Current Yield
● One year return based on current price of the bond.
● Ratio of the annual coupon and bond price.
WIZ E TIP
The current yield should be between the coupon rate and YTM.
Watch the video tutorial for this lesson (01:00)
https://www.wizeprep.com/online-courses/20009/chapter/3/core/3/1
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3 .3 .2
Example: Current Yield
A bond is currently trading for $1041.43. It has a coupon rate of 8% and a face value of $1,000.
What is the current yield?
Watch the video tutorial for this lesson (00:27)
https://www.wizeprep.com/online-courses/20009/chapter/3/core/3/2
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3 .3 .3
Practice: Current Yield
An 8-year bond with a coupon rate of 9% paid semi-annually is yielding 10%. What is the bond's
current yield?
Round your work to at least 6 decimal places and final answer to 2 decimal places.
%
View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/3/core/3/3
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3.4
Cash Price vs Quoted Price
3 .4 .1
Cash Price vs. Quoted Price
● Cash price is the actual amount a buyer will pay a seller for a bond.
○ Cash price includes accrued interest (accumulated interest since previous payment was
made).
○ Cash price is also called the invoice price or the dirty price.
● Quoted price is the present value of the bond excluding any accrued interest.
○ Quoted price is also called the clean price.
WIZ E TIP
When counting the number of days of accrued interest, you have to count the number of days
since the previous coupon was paid excluding the date of the previous coupon payment but
including the current date in the question.
WATC H O UT!
There are 181 days between January 1st and June 30th, and there are 184 days between July
1st and December 31st.
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Watch the video tutorial for this lesson (01:57)
https://www.wizeprep.com/online-courses/20009/chapter/3/core/4/1
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3 .4 .2
Example: Cash Price
Today is October 11 and a bond is quoted at 98.44. The bond has a face value of $1,000, coupon
rate of 6% and is paid semi-annually on December 31st and June 30th.
a. What is the quoted price?
b. How much interest has accrued?
c. What is the cash price?
Watch the video tutorial for this lesson (03:25)
https://www.wizeprep.com/online-courses/20009/chapter/3/core/4/2
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3.5
Consols
3 .5 .1
Consols
● A bond that pays coupons forever.
● These bonds never mature so the investor never receives the face value.
● These bonds are treated as perpetuities when solving for their value.
Watch the video tutorial for this lesson (00:29)
https://www.wizeprep.com/online-courses/20009/chapter/3/core/5/1
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3 .5 .2
Example: Perpetual Bonds (Consols)
Assuming the YTM on a consol is 6% and that a bond has a face value of $1,000 with a coupon rate
of 5%. What is the bond's price?
Watch the video tutorial for this lesson (00:56)
https://www.wizeprep.com/online-courses/20009/chapter/3/core/5/2
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3 .5 .3
Practice: Perpetual Bonds (Consols)
An investor has the option between two bonds:
Bond A: 7% bond, F = 1,000, 10 year maturity, coupons paid semi-annually.
Bond B: 7% consol, F = 1,000, coupons paid semi-annually.
If the YTM on bonds is currently 8%, what is the difference between the price of the two bonds?
Round your work to at least 4 decimal places and your final answer to 2 decimal places.
Answer
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Solutions to these questions, as well as step-by-step breakdowns of the answers at:
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3.6
Interest Rate Risk
3 .6 .1
Bond Price Sensitivity
Market interest rates have an inverse relationship with bond prices, that is because if market interest
rates (YTM) rise, the present value of existing bonds will decrease. However not all bonds move
equally, some bonds are very sensitive to changes in interest rates, while others are less sensitive.
Sensitive bonds will decrease or increase in price by more than less sensitive bonds.
What does the Price-Yield Curve tell us?
● Bonds are more sensitive to change in interest rates when yields are lower.
● Bonds are more sensitive when rates/yields decrease then when they increase.
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Characteristics that increase bond sensitivity
●
●
●
●
Long maturities
Low coupons
Low YTM
Higher frequency of payments
For Example:
Consider the following two bonds, both have a face value of $1,000
Bond A: 10-year maturity, 5% coupons paid annually
Bond B: 30-year maturity, 5% coupons paid annually
Bond A: When YTM = 6%, Bond A is priced at $926.40; if YTM increases to 7% the price decreases
by 7.21% to $859.53
Bond B: When YTM = 6%, Bond B is priced at $862.35; if YTM increases to 7% the price decreases
by 12.82% to $751.82
Watch the video tutorial for this lesson (02:11)
https://www.wizeprep.com/online-courses/20009/chapter/3/core/6/1
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3 .6 .2
Example: Bond Price Sensitivity
ABC Inc. has bonds outstanding with a $1,000 face value. The coupon rate on these bonds is 7% and
coupons are paid annually. The bonds mature in 10 years. What is the percentage change in the
price of the bond if the yield to maturity increases from 7% to 8%?
View this lesson online
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3 .6 .3
Practice: Bond Price Sensitivity
ABC Inc. has bonds outstanding with a $1,000 face value. The coupon rate on these bonds is 6% and
coupons are paid semi-annually. The bonds mature in 8 years. The bond's are currently priced at
par. What will be the percentage change in the price of the bond if the yield to maturity decreases
by 50 basis points?
The percentage change in price is
%
Round your final answer to 2 decimal places.
View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/3/core/6/3
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3.7
Return on Investment
3 .7 .1
Return on Investment
The return on investment is how much an investor has received from the investment, typically
expressed as a percentage of the initial investment.
●
●
●
●
Measures the return vs the initial investment
Includes income generated from the investment and the change in the asset's value.
Can be positive or negative
Nominal return because it does not consider inflation.
Watch the video tutorial for this lesson (01:10)
https://www.wizeprep.com/online-courses/20009/chapter/3/core/7/1
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3 .7 .2
Example: Return on Investment
Stephen paid $895 for a 5-year bond that offers a 5% coupon and pays coupons on a semi-annual
basis. The bond has a face value of $1,000. YTM is 7%. Stephen held the bond for 4 years and sold it
today for $956. What was his holding period return on investment?
Watch the video tutorial for this lesson (01:24)
https://www.wizeprep.com/online-courses/20009/chapter/3/core/7/2
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3 .7 .3
Practice: Return on Investment
What is the realized rate of return if an investor purchased a $1,000 face value 10-year bond at par
3 years ago and sells it today. The bond has a coupon rate of 6% and the coupons are paid semiannually and the current YTM on bonds is 7%. What is the holding period return on investment?
%
Round your final answer to 2 decimal places.
View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/3/core/7/3
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4. Equity Valuation
4.1
Equity Basics
4 .1 .1
Equity Basics
Stocks
● Are ownership positions in a corporation
● Payouts to common stock are dividends:
o Cash or Stock Dividends
● Unlike bonds, payouts are uncertain in both magnitude and timing
● Like bonds, equity can be sold at any point in time.
Legal Structure
● Residual claimant to corporate assets (paid after bondholders)
● Limited liability: worst-case scenario is not that extreme
● Voting rights on major corporate decisions
Dividends
● Profits that the company does not reinvest and instead distributes to the shareholders.
● The board of directors and management of the company determine how much they will pay to
shareholders.
Watch the video tutorial for this lesson (01:56)
https://www.wizeprep.com/online-courses/20009/chapter/4/core/1/1
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4 .1 .2
Common Vs Preferred Equity
Watch the video tutorial for this lesson (01:52)
https://www.wizeprep.com/online-courses/20009/chapter/4/core/1/2
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4 .1 .3
The Dividend Discount Model (DDM)
In finance and investing, the dividend discount model is a method of valuing the price of a company's
stock based on the fact that its stock is worth the sum of all of its future dividend payments,
discounted back to their present value.
How it Works
● All future dividends are discounted back to the present time
● The present value of future dividends is considered the fair value of the stock
● Discounting is done using a required rate of return that is based on how risky the stock is.
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Required Rate of Return
● The minimum return on investment investors expect to earn on a stock.
● Is found by adding a risk premium to the risk-free rate
○ Risk-free rate is the return an investor can earn by investing in risk-free government
investments.
○ Risk premium increases if a stock is more risky and decreases if a stock is less risky
Watch the video tutorial for this lesson (01:09)
https://www.wizeprep.com/online-courses/20009/chapter/4/core/1/3
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4.2
Common Shares (No Growth)
4 .2 .1
Zero-Growth Dividend Model
• Generalized model of discounting future dividends.
• Suitable for stable/mature companies and for preferred shares valuation
• Assumes no growth in dividend payments
• Assumes company lives on forever
Formula breakdown:
D = Constant dividend
r = Risk-adjusted effective periodic discount rate (expected return)
Watch the video tutorial for this lesson (00:58)
https://www.wizeprep.com/online-courses/20009/chapter/4/core/2/1
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4 .2 .2
Example: Dividend Discount Model (Zero Growth)
DT Bank pays a $4 dividend to its preferred shareholders. If the required rate of return on this stock
is 8%, what is the price today?
Watch the video tutorial for this lesson (00:37)
https://www.wizeprep.com/online-courses/20009/chapter/4/core/2/2
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4 .2 .3
MAR K YO UR SE LF Q UE STIO N
Try the problem yourself, and check the solutions to see how you did. Then mark yourself right or wrong.
Practice: Dividend Discount Model (Zero Growth)
Royal Bank of Saudi Arabia’s perpetual preferred stock pays annual dividends of $1.3750 and was
originally issued to be priced to yield at 5.5%.
What was the price of the preferred stock at issuance?
If your required rate of return is 8%, what is the reasonable price of the perpetual preferred stock
from your perspective?
View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/4/core/2/3
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4.3
Common Shares (Constant Growth) Gordon Growth Model
4 .3 .1
Growing Dividends
Gordon Growth Model (GGM) assumes that a company exists forever and that there is a constant
growth in dividends when valuing a company's stock.
• Richer model of stock valuation.
• Suitable for stable growth companies
• Assumes a constant dividend growth rate in perpetuity
• Assumes company lives on forever
Formula breakdown:
D1 = Dividend in period 1
P0 = Price of Stock at time zero (today)
r = Risk-adjusted effective periodic rate (expected return)
g = Constant growth rate of dividends
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Watch the video tutorial for this lesson (01:38)
https://www.wizeprep.com/online-courses/20009/chapter/4/core/3/1
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4 .3 .2
Example: Gordon Growth Model
ABC Inc. will pay a $2.00 dividend next year and the company is expected to grow by 4% per year.
Determine the price of a share in ABC Inc. today if investors have a required rate of return of 8%.
Watch the video tutorial for this lesson (01:25)
https://www.wizeprep.com/online-courses/20009/chapter/4/core/3/2
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4 .3 .3
MAR K YO UR SE LF Q UE STIO N
Try the problem yourself, and check the solutions to see how you did. Then mark yourself right or wrong.
Practice: Gordon Growth Model
White Rock Water sells water bottles to Asia. White Rock Water pays an annual dividend of $2.30
(just paid) that is expected to grow at 2% per annum—in line with the global economic growth rate.
Your required rate of return is 6%.
Is the stock over-valued from your perspective if a share of White Rock Water is trading at $25.60?
View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/4/core/3/3
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4 .3 .4
Example: Gordon Growth Model
ABC Inc. is growing at 8% per year. Its expected dividend payment next year is $4. The company’s
current share price is $85.
What is the company’s expected return?
Watch the video tutorial for this lesson (01:21)
https://www.wizeprep.com/online-courses/20009/chapter/4/core/3/4
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4 .3 .5
Practice: Gordon Growth Model
Investors have been receiving a dividend from ABC Corp for years and in recent years the company
has been increasing their dividend by 4% per year. This is expected to continue for the foreseeable
future, and today the company paid its annual dividend of $3 per share and the shares are currently
trading at $78 per share.
What is the required rate of return?
Answer
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Solutions to these questions, as well as step-by-step breakdowns of the answers at:
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4 .3 .6
Example: Gordon Growth Model
ABC Inc. just paid a $2 per share dividend and has announced it will decrease the amount it pays by
3% per year indefinitely as it has been having several financial issues in recent times. Investors
require a return of 15% on the stock given its high risk.
What is the current price of the stock?
Watch the video tutorial for this lesson (02:05)
https://www.wizeprep.com/online-courses/20009/chapter/4/core/3/6
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4 .3 .7
Practice: Gordon Growth Model
You just received your dividend from Happle Corporation, the dividend was $4 per share, a 5%
decrease from the previous year. The company is expected to continue decreasing its annual
dividends at this rate and the market's required rate of return on this stock is 10%.
How much can you sell the stock for today?
Answer
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Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/4/core/3/7
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4.4
Common Shares (Non-Constant
Growth)
4 .4 .1
Non-Constant Growth Model
Companies will often change the growth rate of their dividends for a variety of reasons, like offering
very high growth during periods during which they expect higher earnings or attracting additional
investments. When dividends are growing at a higher rate than normal, this is called super-normal
growth.
Solving for the stock price using non-constant growth models is done by segmenting the timeline into
multiple annuities and perpetuities and summing their respective present values.
Growing Annuities
A growing annuity is a recurring cash stream where payments are increasing at a constant rate for a
finite period of time. For example, receiving a $4 dividend this year and 5% more each year for 5
years.
Watch the video tutorial for this lesson (02:26)
https://www.wizeprep.com/online-courses/20009/chapter/4/core/4/1
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4 .4 .2
Example: Non-Constant Growth Model
ABC Inc. just paid a dividend of $2. It plans to increase its dividend by 15% for the next 5 years and
then decrease the growth rate to 4% indefinitely.
What is the current price of the company's stock if the required rate of return is 10%?
Watch the video tutorial for this lesson (06:11)
https://www.wizeprep.com/online-courses/20009/chapter/4/core/4/2
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4 .4 .3
Practice: Non-Constant Growth Model
Ocram Group will pay a $4 per share dividend next year. It just announced that it will grow its
dividends by 8% until year 5, then it will increase dividends by 10% per year until year 10 before
decreasing the growth rate to 3% indefinitely thereafter.
What is the price of one share if investors require a return of 14% per year?
Answer
View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/4/core/4/3
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4.5
Preferred Shares
4 .5 .1
Preferred Share Valuation
Price of a preferred share is based on dividend and required rate of return. Treat preferred shares as
ordinary perpetuities.
Preferred Share Pricing
● If dividend rate > required rate of return: Preferred shares are priced at a premium (Price >
Book Value)
● If dividend rate < required rate of return: Preferred shares are priced at a discount (Price <
Book Value)
● If dividend rate = required rate of return: Preferred shares are priced at par (Price = Book Value)
Computing the Dividend Payment
Based on the book value of the preferred shares and the dividend rate.
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Computing the Price of a Preferred Share
● The present value of future dividends
● The required rate of return is used as the discount rate
Where:
P = Price of the preferred share
D = Dividend
r = Required rate of return
Watch the video tutorial for this lesson (01:17)
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4 .5 .2
Example: Preferred Shares
Wize Corporation has preferred shares outstanding with a book value of $80. The company pays a
5% dividend on these shares each year and investors require a return of 10%. What it the price of
these shares?
Watch the video tutorial for this lesson (00:50)
https://www.wizeprep.com/online-courses/20009/chapter/4/core/5/2
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4 .5 .3
Practice: Preferred Shares
ABC Inc. wishes to issue new preferred shares at par. It currently has existing preferred shares
outstanding that are trading at $157.60 and pay an 8% annual dividend. If both the old and new
preferred shares have a book value of $100, what should the dividend rate be on the new shares?
%
Round your final answer to 2 decimal places.
View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/4/core/5/3
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5. Risk, Return & Portfolio
Theory
5.1
Ex-Post Risk and Return
5 .1 .1
Return on Investment
The total return on investment is made up of 2 components: the income yield and the capital gain
yield.
Income Yield
Income yield represents the return earned on income generated through owning an asset. Here are
some examples of incomes that an investor earns with different types of assets:
● Buildings: Rent
● Stocks: Dividends
● Bonds: Coupons
Use the following formula to measure the Income Yield of an investment
Where:
CF = Cash flows received (coupons, dividends, rent, etc)
P0= Purchase price
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Capital Gain Yield
Capital gains and losses represent the changes to the market value of the asset. Use the following
formula to compute the capital gain yield:
Where:
CF = Cash flows received (coupons, dividends, rent, etc)
P0 = Purchase price
P1 = Current price or Selling price
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Holding Period Return (Total Return)
The total return is the sum of the income yield and the capital gain yield:
Periodic Average Return (Geometric Average)
● The average return earned period period.
● Considers thats returns compound periodically
Where:
TR = Total return
t = Length of holding period
Watch the video tutorial for this lesson (02:34)
https://www.wizeprep.com/online-courses/20009/chapter/5/core/1/1
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5 .1 .2
Example: Return on Investment
a) A share of ABC Inc. was selling for $32.16 one year ago. The stock paid an annual dividend of
$3.45 during the year. Compute the total return on the stock if the current stock price is $37.74.
b) Steve purchased a bond of MPT Company for $985 three years ago. The bond paid a coupon of
$2.52 per year. What is the annualized holding period return on the bond if its current market value
is $989?
Watch the video tutorial for this lesson (03:06)
https://www.wizeprep.com/online-courses/20009/chapter/5/core/1/2
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5 .1 .3
Practice: Return on Investment
You purchased stock in ABC Inc. for $31.44 two years ago and sell today for $43.56. The company
issued annual dividends of $2 per share.
Compute the income yield, capital gain yield, holding period return and annualized holding period
return.
Round your final answers to 2 decimal places and enter in % form.
Income yield
Capital gain yield
Holding period return
Annualized holding period return
View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/5/core/1/3
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5.2
Average Returns and Standard
Deviation
5 .2 .1
Average Returns
Average returns can be measured in two ways:
1. Arithmetic mean (AM)
The numerical average of the returns.
2. Geometric mean (GM)
The geometric mean is the average compounding growth rate over n periods.
1
n
GM = [(1 + r1 ) (1 + r2 ) (1 + r3 ) ... (1 + rn )] − 1
​
​
​
​
​
WIZ E C O NC E P T
In finance, we use the geometric mean when evaluating an investment. The arithmetic mean
tends to overstate average returns because it does not considering the compounding effect.
Watch the video tutorial for this lesson (01:13)
https://www.wizeprep.com/online-courses/20009/chapter/5/core/2/1
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5 .2 .2
Example: Average Returns
Estimate the arithmetic mean (AM) and geometric mean (GM) for the following returns:
5.4%, 6.2%, 4.5%, -7.8% and 10.1%.
Watch the video tutorial for this lesson (02:50)
https://www.wizeprep.com/online-courses/20009/chapter/5/core/2/2
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5 .2 .3
Practice: Average Returns
Your portfolio earned the following returns over the last 5 months: 10%, -2%, 12%, -4%, 15%
What is the arithmetic average monthly return and the geometric average monthly return. Round
your final answers to 2 decimal places.
Arithmetic average monthly return
%
Geometric average monthly return
%
View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/5/core/2/3
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5.3
Ex-Post Standard Deviation
5 .3 .1
Measuring Risk
Risk implies that an outcome is not certain, the way we quantify risk in this context is by measuring
the standard deviation. To compute the standard deviation of returns that have already occurred
(historical) use the following formula:
Formula breakdown:
Alternatively, you can use your Texas Instrument financial calculator to solve it.
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How to Compute Standard Deviation on Financial Calculator
Formula breakdown:
R1, R2, R3 = Individual returns (as many as necessary)
Watch the video tutorial for this lesson (02:00)
https://www.wizeprep.com/online-courses/20009/chapter/5/core/3/1
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5 .3 .2
Example: Standard Deviation
You have observed the following annual returns for Motherboard Inc.: 25%, 15%, -20%, 30%, and
-15%.
What is the standard deviation of returns?
Watch the video tutorial for this lesson (02:46)
https://www.wizeprep.com/online-courses/20009/chapter/5/core/3/2
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5 .3 .3
MAR K YO UR SE LF Q UE STIO N
Try the problem yourself, and check the solutions to see how you did. Then mark yourself right or wrong.
Practice: Standard Deviation
A stock has year-end prices and dividends as below.
a) What is the Arithmetic Average return?
b) What is the Geometric Average return?
c) What is the standard deviation of returns?
View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/5/core/3/3
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5.4
Expected Return and Ex-Ante Standard
Deviation
5 .4 .1
Expected Return
An expected return is the estimated future return on investment based on probabilities. It is found
using the following formula:
Variance and Standard Deviation
The variance and standard deviations are used to quantify risk. The more a stock can deviate from
its expected return, the less predictable (and riskier) it is.
Variance
Standard Deviation
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Watch the video tutorial for this lesson (02:58)
https://www.wizeprep.com/online-courses/20009/chapter/5/core/4/1
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5 .4 .2
Example: Expected Return and Standard Deviation
Suppose you are given the following information for two stocks, A and B, where the return on each
varies with the state of the economy.
Estimate the expected return and standard deviation for each stock.
Watch the video tutorial for this lesson (02:44)
https://www.wizeprep.com/online-courses/20009/chapter/5/core/4/2
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5 .4 .3
MAR K YO UR SE LF Q UE STIO N
Try the problem yourself, and check the solutions to see how you did. Then mark yourself right or wrong.
Practice: Expected Return and Standard Deviation
Compute the expected return and standard deviation for each of the following 2 stocks.
View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/5/core/4/3
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5.5
Covariance and Correlation
5 .5 .1
Covariance and Correlation
The covariance and correlation coefficient measure the joint variability of two stocks. They measures
whether the stocks move in the same direction, or if they tend to move opposite to one another.
● If both stocks move in the same direction (up and down at the same time) the covariance and
correlation are positive and it is said that the stocks have a positive (or direct) relationship.
● If the stocks in opposite directions (one stock goes up when the other goes down), the
covariance and correlation are negative and it is said that the stocks have a negative (or
inverse) relationship.
WIZ E C O NC E P T
The magnitude of the covariance is not easily interpreted, we therefore only interpret the sign to
know if the stocks are positively or negatively correlated.
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Watch the video tutorial for this lesson (01:07)
https://www.wizeprep.com/online-courses/20009/chapter/5/core/5/1
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5 .5 .2
Correlation Coefficient
Measures the direction and strength of the relationship between two stocks.
● Relationship is stronger as correlation coefficient approaches -1 or 1
● Relationship is weaker as correlation coefficient approaches 0
WIZ E C O NC E P T
A perfect positive correlation means that the stocks move perfectly together, for example if
stock A increases by 10%, stock B will also increase by 10%.
A perfect negative correlation means that the stocks move exactly opposite to each other, for
example if stock A increases by 10%, stock B will decrease by 10%.
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Correlation and Diversification
● Investing in multiple stocks with a positive correlation increases risk, and investing in stocks
with a negative correlation decreases risk.
● Investing in stocks with a perfect positive correlation does not reduce risk because there is no
benefit of diversification since the stocks move in exactly the same way.
● To decrease risk and benefit from diversification, correlation should be less than 1.
Watch the video tutorial for this lesson (02:17)
https://www.wizeprep.com/online-courses/20009/chapter/5/core/5/2
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5 .5 .3
Example: Covariance
Compute the covariance and correlation coefficient between stocks A and B
Given
σA = 3.46%
σB = 1.30%
​
Watch the video tutorial for this lesson (02:55)
https://www.wizeprep.com/online-courses/20009/chapter/5/core/5/3
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5 .5 .4
Practice: Covariance
The following information is available for stocks A and B
Standard Deviations:
Stock A: 6.5567%
Stock B: 14.4377%
Compute the covariance and correlation coefficient between the stocks and interpret your result.
Part 1
What is the covariance?
Round your final answer to 4 decimal places and enter your answer in decimal form.
Answer
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Practice: Covariance
The following information is available for stocks A and B
Standard Deviations:
Stock A: 6.5567%
Stock B: 14.4377%
Compute the covariance and correlation coefficient between the stocks and interpret your result.
Part 2
What is the correlation coefficient?
Round your final answer to 4 decimal places and enter your answer in decimal form.
Answer
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Practice: Covariance
The following information is available for stocks A and B
Standard Deviations:
Stock A: 6.5567%
Stock B: 14.4377%
Compute the covariance and correlation coefficient between the stocks and interpret your result.
Part 3
Choose the best interpretation for the covariance
A) Since the covariance is positive, the two stocks are said to have a positive relationship meaning
that stock A will decrease when stock B increases.
B) When stock A goes up by 1%, stock B will go up by 1.2537%.
C) Since the covariance is positive, the two stocks are said to have a positive relationship meaning
that stock A will increase when stock B increases.
D) The direction of the relationship cannot easily be interpreted, we therefore cannot say if stocks
move in the same or opposite direction.
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Practice: Covariance
The following information is available for stocks A and B
Standard Deviations:
Stock A: 6.5567%
Stock B: 14.4377%
Compute the covariance and correlation coefficient between the stocks and interpret your result.
Part 4
Choose the best interpretation for the correlation coefficient
A) Stocks A and B have a strong positive relationship
B) Stocks A and B have a very strong positive relationship
C) Stocks A and B have a perfect positive relationship
D) Stocks A and B have a weak positive relationship
View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/5/core/5/4
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5.6
Portfolio Risk and Return
5 .6 .1
What is a Portfolio?
A portfolio is a collection of investments that are combined and considered a single asset. Could be
made up of different kinds of investments such as bonds and stocks.
The Weights of the Portfolio
● The weight of an asset is the proportion of the portfolio that is invested in that asset.
● Can be any value, including negative values and values over 100%.
○ Weights are negative and over 100% when the investor is shorting or borrowing
● Found by dividing the dollars invested in an asset by the total value of the portfolio.
Example:
An investor constructs the following portfolio: $5,000 into Stock A, $2,000 into Stock B, and $9,000
into Stock C.
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Watch the video tutorial for this lesson (01:18)
https://www.wizeprep.com/online-courses/20009/chapter/5/core/6/1
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5 .6 .2
Expected Return
The expected return for an investment portfolio is the weighted average of the expected return of
each of its components. Components are weighted by the percentage of the portfolio's total value
that each accounts for.
Standard Deviation (Risk)
● The standard deviation of the rate of return on an investment portfolio.
● Used to measure the inherent volatility of an investment.
● It measures the investment's risk and helps in analyzing the stability of returns of a portfolio.
Standard Deviation of a 2 Asset Portfolio
Standard Deviation of a 3 Asset Portfolio
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Watch the video tutorial for this lesson (02:01)
https://www.wizeprep.com/online-courses/20009/chapter/5/core/6/2
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5 .6 .3
Example: Expected Return and Risk of a Portfolio
Suppose you are given the following information for two stocks, A and B, where the return on each
varies with the state of the economy. An investor invests $2,000 into Stock A and $3,000 into Stock
B.
a) Compute the expected return for each stock
b) Compute the standard deviation for each stock
c) Compute the covariance between the two stocks
d) Compute the expected return of the portfolio
e) Compute the standard deviation of the portfolio
Watch the video tutorial for this lesson (10:41)
https://www.wizeprep.com/online-courses/20009/chapter/5/core/6/3
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5 .6 .4
Practice: Expected Return and Risk of a Portfolio
You have $5,000 to invest and are considering investing $3,000 into Stock A and the rest into Stock
B.
Part 1
What is the expected return of the portfolio?
16.4%
11.48%
14.6%
6.8%
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Practice: Expected Return and Risk of a Portfolio
You have $5,000 to invest and are considering investing $3,000 into Stock A and the rest into Stock
B.
Part 2
What is the covariance between the two stocks?
0.005292
0.5292
5.292
-0.005292
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Practice: Expected Return and Risk of a Portfolio
You have $5,000 to invest and are considering investing $3,000 into Stock A and the rest into Stock
B.
Part 3
What is the standard deviation of the portfolio?
8.249%
6.416%
7.515%
11.48%
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Practice: Expected Return and Risk of a Portfolio
You have $5,000 to invest and are considering investing $3,000 into Stock A and the rest into Stock
B.
Part 4
Which of the following best describes the relationship between Stocks A and B?
They are perfectly positively correlated
They are perfectly negatively correlated
They are positively correlated but not perfectly
They are negative correlated but not perfectly
View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/5/core/6/4
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5 .6 .5
Example: Shorting
You construct the following portfolio:
● Long 500 shares of Stock A at $22.50 per share
● Short 100 shares of Stock B at $10.00 per share
What is the expected return of the portfolio if the expected returns of Stocks A and B are 23% and
12% respectively?
Watch the video tutorial for this lesson (01:57)
https://www.wizeprep.com/online-courses/20009/chapter/5/core/6/5
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5 .6 .6
Practice: Shorting
Using this information, answer the following questions:
ERX = 10%
ERY = 12%
σX = 20%
● σY = 15%
● ρX Y = 0.6
●
●
●
​
​
​
​
You construct a portfolio by investing $10,000 into stock Y, and shorting $5,000 of stock X.
Round your final answers to 2 decimal places and enter a percentage.
What is the expected return of the portfolio?
What is the standard deviation of the portfolio?
View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/5/core/6/6
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5.7
Portfolio Standard Deviation (Special
Cases)
5 .7 .1
Standard Deviation with Perfect Correlations
Investments are said to be perfectly correlated or negatively correlated if their correlation coefficient
is equal to 1 or -1. In these cases, the following rules apply:
Watch the video tutorial for this lesson (00:58)
https://www.wizeprep.com/online-courses/20009/chapter/5/core/7/1
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5 .7 .2
Example: Portfolio Standard Deviation with Perfect Correlations
Compute the standard deviation of a portfolio with 70% invested in Stock X and the rest in Stock Y.
The standard deviations of stocks X and Y are 14.4% and 8.65% respectively and the correlation
coefficient between the stocks is 1 (perfect positive correlation).
Watch the video tutorial for this lesson (00:51)
https://www.wizeprep.com/online-courses/20009/chapter/5/core/7/2
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5 .7 .3
Practice: Portfolio Standard Deviation with Perfect Correlations
The standard deviation of a portfolio containing stocks G and F is 8.95%. Stock G has a standard
deviation of 7.5% and stock F has a standard deviation of 12%. Stocks G and F have a perfect
positive correlation. If the portfolio has $10,000 in it, how much of that is invested in stock G?
Round your final answer to 2 decimal places.
Amount invested in Stock G
$
View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/5/core/7/3
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5 .7 .4
Standard Deviation with No Correlation
When two stocks are said to be completed unrelated, this means that the covariance and correlation
between them is 0.
Watch the video tutorial for this lesson (00:24)
https://www.wizeprep.com/online-courses/20009/chapter/5/core/7/4
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5 .7 .5
Example: Portfolio Standard Deviation with No Correlation
Stock G has a standard deviation of 15% and Stock H has a standard deviation of 22%. The stocks
are unrelated and you combine them in a portfolio by investing $7,500 into Stock G and $2,500 into
Stock H.
What is the standard deviation of the portfolio?
Watch the video tutorial for this lesson (00:55)
https://www.wizeprep.com/online-courses/20009/chapter/5/core/7/5
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5 .7 .6
Practice: Portfolio Standard Deviation with No Correlation
You've constructed a portfolio with a standard deviation of 18.4% using two completely unrelated
stocks, Stocks A and B. The portfolio contains twice as much Stock A as it does Stock B. If the
standard deviation of Stock A is 15%, what is the standard deviation of stock B?
Round your final answer to 2 decimal places
Standard deviation of Stock B
%
View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/5/core/7/6
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5 .7 .7
Standard Deviation of Portfolio with a Risk-Free Asset
In a 2 asset portfolio that contains a risk-free asset and a risky asset, the standard deviation of the
portfolio is the found using only the risky asset.
WIZ E C O NC E P T
This is because a risk free asset has a standard deviation (risk) of zero.
Watch the video tutorial for this lesson (00:38)
https://www.wizeprep.com/online-courses/20009/chapter/5/core/7/7
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5 .7 .8
Example: Portfolio Standard Deviation with a Risk-Free Asset
You wish to construct a portfolio using shares of Amazon and US treasury bills. Amazon's stock is
known to have a standard deviation of 15.6%. If you plan to invest equally into both assets, what will
be the standard deviation of your portfolio?
Watch the video tutorial for this lesson (01:01)
https://www.wizeprep.com/online-courses/20009/chapter/5/core/7/8
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5 .7 .9
Practice: Portfolio Standard Deviation with a Risk-Free Asset
You've constructed a portfolio with a standard deviation of 25% using Apple Inc.'s stock and US
treasury bills. The standard deviation of Apple's stock is 22%. What percentage of your portfolio is
invested in Apple's stock and what percentage is invested in the treasury bills?
Round your final answer to 2 decimal places
Weight of Apple stock
%
Weight of Treasury Bills
%
View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/5/core/7/9
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5.8
The Efficient Frontier
5 .8 .1
The Efficient Frontier
A portfolio is efficient if there is no better combination of the same assets. Meaning that you cannot
get a better return for the same amount of risk, or the same amount of return with less risk.
● Efficient Frontier is a term used in portfolio theory to describe the portfolios made up of specific
assets that offer the highest return at any given level of risk.
● It is often depicted on a risk-return plot with risk on the x-axis and return on the y-axis. It is the
top half of the parabola starting at the Minimum Variance Portfolio.
The efficient frontier tells us every possible portfolio that maximizes the expected return for every
level of risk.
● Any point below the frontier is not efficient because for the same risk you can get a higher
return, or you can get the same return for less risk.
● Any point above the frontier is not possible meaning that it is impossible to form a portfolio
using the assets in question that would have that particular combination of risk and return.
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Watch the video tutorial for this lesson (02:57)
https://www.wizeprep.com/online-courses/20009/chapter/5/core/8/1
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5.9
Types of Risk
5 .9 .1
Types of Risk
Risk Premium
Equity risk premium refers to the excess return that investing in the stock market provides over a
risk-free rate. This excess return compensates investors for taking on the relatively higher risk of
equity investing. The size of the premium varies depending on the level of risk in a particular portfolio
and also changes over time as market risk fluctuates.
Systematic and Unsystematic Risk
Systematic Risk
Systematic Risk does not have a specific definition but is an inherent risk existing in the stock market.
These risks are applicable to all sectors and affect the entire stock market at the same time. If there
is an announcement or event which impacts the entire stock market, a consistent reaction will flow in
which is a systematic risk. Systematic risk is often referred to as "market risk", and the symbol β is
used when measuring it.
For Example:
If Government Bonds is offering a yield of 5% in comparison to the stock market which offers a
minimum return of 10%. Suddenly, the government announces an additional tax burden of 1% on
stock market transactions, this will be a systematic risk impacting all the stocks and may make the
Government bonds more attractive.
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Unsystematic Risk
Unsystematic Risk is an industry or firm-specific threat in each kind of investment. It is also known as
"Asset-specific Risk" or "Diversifiable risk". These are risks which are existing but are unplanned
and can occur at any point in causing widespread disruption.
For Example:
If the staff of the airline industry goes on an indefinite strike, then this will cause risk to the shares of
the airline industry and a fall in the prices of the stock impacting this industry.
Total Risk = Unsystematic Risk + Systematic Risk
Watch the video tutorial for this lesson (02:49)
https://www.wizeprep.com/online-courses/20009/chapter/5/core/9/1
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6. CAPM
6.1
Risk-Free Investing
6 .1 .1
Risk-Free Investing
When an investor places his or her money into a portfolio containing a risky investment and a riskfree investment like a T-bill, the following formula is used to determine the expected return of the
portfolio.
Formula Breakdown:
a : a risky asset
RF: the risk-free rate
Watch the video tutorial for this lesson (00:54)
https://www.wizeprep.com/online-courses/20009/chapter/6/core/1/1
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6 .1 .2
Example: Risk-Free Investing
You invest $5,000 into AAPL with an expected return of 15% and standard deviation of 8%, you also
invest $4,000 into Canadian T-bills which will pay a risk-free return of 2%.
1. What is the expected return of your portfolio?
2. What is the standard deviation of your portfolio?
Watch the video tutorial for this lesson (02:16)
https://www.wizeprep.com/online-courses/20009/chapter/6/core/1/2
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6 .1 .3
Practice: Risk-Free Investing
You plan to invest part of your portfolio in stock of Netflix (NFLX) but want to limit your risk by also
investing in T-bills. Knowing the expected return and standard deviation of NFLX are 25% and 19%
respectively, what fraction of your money should you invest in T-bills so that your portfolio standard
deviation is 7%?
Enter your answer in decimal format and rounded to 4 decimal places.
Answer
View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/6/core/1/3
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6.2
Risk-Free Borrowing
6 .2 .1
Risk-Free Borrowing
Risk-free borrowing (investing on margin) means that an investor borrows money at a risk-free rate
in order to invest in some other risky asset.
Investors take advantage of margins offered by their banks or brokers in order to increase how much
they can invest in stock to maximize their gains, however, since the amount invested is borrowed
then there is also the risk of greater losses.
Computing Portfolio Expected Return and Standard Deviation with 2nd Asset is Risk-Free
Watch the video tutorial for this lesson (01:59)
https://www.wizeprep.com/online-courses/20009/chapter/6/core/2/1
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6 .2 .2
Example: Risk-Free Borrowing
You have $8,000 to invest and are considering investing in Stock X which has an expected return of
12% and a standard deviation of 9%. The stock is currently trading at $50 per share but you are so
sure in the stock that you use your margin account in order to buy 200 shares, meaning that you will
borrow what you are missing at the risk free rate to make this trade. The risk free rate is 3%.
1. What is the expected return?
2. What is the standard deviation?
Watch the video tutorial for this lesson (02:57)
https://www.wizeprep.com/online-courses/20009/chapter/6/core/2/2
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6 .2 .3
Practice: Risk-Free Borrowing
You have $10,000 to invest and decide to put it all in Apple's stock which is trading at $177.57. You
buy 80 shares by borrowing the amount you're missing from your broker at a risk-free rate of 4%.
Apple has an expected return of 20% and a standard deviation of 15%.
Part 1
What is the expected return of this portfolio?
The expected return is
%
Practice: Risk-Free Borrowing
You have $10,000 to invest and decide to put it all in Apple's stock which is trading at $177.57. You
buy 80 shares by borrowing the amount you're missing from your broker at a risk-free rate of 4%.
Apple has an expected return of 20% and a standard deviation of 15%.
Part 2
What is the standard deviation of this portfolio?
The standard deviation is
%
View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/6/core/2/3
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6.3
Introduction to Risk
6 .3 .1
Shorting Stocks
Investors can bet that a stock price will decrease and can earn profits if they are right by shorting
the stock. This is done by borrowing the stock from their bank or broker, selling it immediately at its
current price, and then repurchasing the stock in the future at a lower price in order to return it to the
bank.
For Example:
A share of Tesla is currently trading for $920 on the market and you believe it is over-valued. You
short 10 shares today and in two weeks the stock price decreases to $650. The profit earned from
this trade is 10 x (920 - 650) = $2,700.
Maintenance Margin
The maintenance margin is the required percentage of the total investment that is less than the
initial margin, and which the investor must maintain in their trading account in order to avoid a
margin call – a demand from their broker that they either deposit additional funds into their account
or liquidate a sufficient amount of their holdings to meet the margin call.
Margin Percentage =
Equity−Debt
Debt
​
When Using Margin to SELL stocks (shorting)
Equity = Amount of equity in the account initially (constant) + Proceeds from sale
Debt = # of Shares x Price
For Example:
You wish to short 100 shares of ABC Inc which are currently trading for $10 each, you first need to
borrow 100 shares from your broker and immediately sell them on the market. You have $800 cash
in your account to start and now have an additional $1,000 from the sale of the borrowed stocks.
Assuming your broker has a minimum maintenance margin of 40%.
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1,800−100(10)
100(10)
​
= 80%
If the stock price increases to $12 per share, your equity remains $1,800 but your debt is now
$1,200 (100 shares x $12 per share).
1,800−100(12)
100(12)
​
= 50%
If the stock price increases to $14 per share, your equity remains $1,800 but your debt is now
$1,400 (100 shares x $14 per share).
1,800−100(14)
100(14)
​
= 28.57%
Since the margin percentage has fallen below the broker's minimum of 40%, the investor will receive
a margin call to either add money to the account to increase this back above the minimum or to
repay some of what they owe.
Watch the video tutorial for this lesson (05:07)
https://www.wizeprep.com/online-courses/20009/chapter/6/core/3/1
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6 .3 .2
Example: Shorting Stocks
You plan on shorting 100 shares of ABC Inc which are currently trading at $100 per share. Your
broker has a minimum maintenance margin of 40% and you currently have $8,000 in your account.
At what market price will you receive a margin call?
Watch the video tutorial for this lesson (02:36)
https://www.wizeprep.com/online-courses/20009/chapter/6/core/3/2
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6 .3 .3
Practice: Shorting Stocks
Maria believes stock X is too overvalued and wishes to short the stock. Currently, Stock X is trading
for $100 per share and Maria calls her broker to short 50 shares of the stock. The broker's minimum
maintenance margin is 40% and Maria currently has $20,000 in her account.
At what price will she receive a margin call?
Answer
View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/6/core/3/3
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6.4
Capital Market Line (CML)
6 .4 .1
Market Portfolio & Capital Market Line
The Market Portfolio
The market portfolio (M) is a theoretical bundle of investments that includes every type of asset
available in the world financial market, with each asset weighted in proportion to its total presence
in the market.
Capital Market Line (CML)
The Capital Market Line (CML) is a straight line that begins at the risk-free rate and ends at the
highest possible expected return for any given risk level. The line shows the required expected return
for every possible level of risk and the risk-return ratio (the slope) is determined by the market
portfolio. The CML line tells us what portfolios investors will choose to hold efficient portfolios.
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Required Rate of Return
kp = RF +
​
(ERm −RF )
σm
​
​
​
⋅ σp
​
Sharpe Ratio
The Sharpe ratio is the ratio of an investment risk-premium to its level of risk (standard deviation).
The Sharpe ratio of the market is the slope of the CML line.
Pricing Investments
Every investment and every asset has a fair price or correct price, and this is determined by its riskreward ratio. An asset is said to be fairly priced when its risk-reward ratio is equal to that of the
market.
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● If SRi > SRM the investment is said to be under-valued or under-priced because it has a
greater risk-return ratio than the market (above the line).
● If SRi < SRM the investment is said to be over-valued or over-priced because it has a lower
risk-return ratio than the market (below the line).
● If SRi = SRM the investment is said to be at its correct price or efficient price because it has
the same risk-return ratio as the market.
​
​
​
​
​
​
Watch the video tutorial for this lesson (03:11)
https://www.wizeprep.com/online-courses/20009/chapter/6/core/4/1
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6 .4 .2
Example: The Market Portfolio and The Capital Market Line
Assume the risk-free rate is 3%. The expected return on the market is 8%, and it has a standard
deviation of 20%. Determine the required rate of return necessary for investors to hold an efficient
portfolio with a standard deviation of 25%.
Watch the video tutorial for this lesson (03:02)
https://www.wizeprep.com/online-courses/20009/chapter/6/core/4/2
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6 .4 .3
Practice: The Market Portfolio and The Capital Market Line
Portfolio A has an expected return of 9% and a standard deviation of 11%. The market's expected
return is 12% with a standard deviation of 15%. Canadian T-Bills are yielding 3% per year.
Part 1
What is the required rate of return for Portfolio A?
8.4%
9.0%
9.6%
10.2%
Practice: The Market Portfolio and The Capital Market Line
Portfolio A has an expected return of 9% and a standard deviation of 11%. The market's expected
return is 12% with a standard deviation of 15%. Canadian T-Bills are yielding 3% per year.
Part 2
The portfolio is currently
Overvalued
Undervalued
Efficient
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Solutions to these questions, as well as step-by-step breakdowns of the answers at:
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6 .4 .4
Example: The Market Portfolio and The Capital Market Line
The required rate of return of Stock B is 9.5% and its standard deviation is 12%. If the risk-free rate is
3% and the expected return and standard deviation of Stock A are 11% and 17%, what can be said
about the price of Stock A?
Watch the video tutorial for this lesson (03:49)
https://www.wizeprep.com/online-courses/20009/chapter/6/core/4/4
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6 .4 .5
Practice: The Market Portfolio and The Capital Market Line
A portfolio with an expected return of 23% and standard deviation of 12.8% is being considered. The
expected return of the market is 19.5%, and the standard deviation of the market is 7.4%. T-bills are
yielding 3%.
Part 1
What is the required rate of return of this portfolio? Round your answer to 2 decimal places
Required rate of return
%
Practice: The Market Portfolio and The Capital Market Line
A portfolio with an expected return of 23% and standard deviation of 12.8% is being considered. The
expected return of the market is 19.5%, and the standard deviation of the market is 7.4%. T-bills are
yielding 3%.
Part 2
What can be said about the portfolio?
A) It is correctly priced
B) It is overpriced
C) It is underpriced
D) Cannot be determined with this information
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View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/6/core/4/5
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6.5
Beta
6 .5 .1
Beta
Market risk (systematic risk) is the risk associated with the overall market and is measured using
beta (β ). The beta of a stock simply measures the change of the stock relative to the change in the
overall market. For example, if a stock has a beta of 2, it will move by 2% whenever the market
moves by 1%.
Important Betas to Remember
● The market always has a beta of 1
● Risk-free assets always have a beta of 0
WIZ E C O NC E P T
A risk-free asset always has a beta of zero, but not all assets with a beta of zero are risk-free.
An asset may have no systematic risk (beta = 0), but still have some risk (unsystematic).
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Portfolio Beta
A portfolio beta is simply the weighted average of the stock beta's that make up the portfolio. For
example, if a portfolio was 40% invested in Stock A with a beta of 1.2 and 60% invested in Stock B
with a beta of 0.7 the portfolio beta would be 0.4(1.2) + 0.6(0.7) = 0.9
Watch the video tutorial for this lesson (01:17)
https://www.wizeprep.com/online-courses/20009/chapter/6/core/5/1
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6 .5 .2
Example: Market Risk and Beta
ABC Inc.'s stock is known to have a correlation of 0.8 with the market portfolio and a standard
deviation of 10%. It is known that the market's standard deviation is 8%. What is the beta of ABC's
stock?
Watch the video tutorial for this lesson (01:13)
https://www.wizeprep.com/online-courses/20009/chapter/6/core/5/2
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6 .5 .3
Practice: Market Risk and Beta
The covariance between the market portfolio and Apple Inc. stock is 0.02151. The market portfolio's
standard deviation is 7%, what is the beta of Apple Inc's stock?
Answer
View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/6/core/5/3
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6 .5 .4
Example: Market Risk and Beta
You have 20% of your funds invested in the market portfolio, 50% invested in the TSLA stock with a
beta of 5.5, and the rest in Canadian T-bills. What is the beta of your portfolio?
Watch the video tutorial for this lesson (00:59)
https://www.wizeprep.com/online-courses/20009/chapter/6/core/5/4
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6 .5 .5
Practice: Market Risk and Beta
Your portfolio beta is 1.2 and it contains 10 different shares each with an equal amount of money
invested in them. You decide to sell your shares in one of the stocks having a beta of 1.5 and invest
that money into T-bills. What is your new portfolio beta? Round your answer to 4 decimal places.
Answer
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Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/6/core/5/5
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6.6
Security Market Line (SML)
6 .6 .1
The Security Market Line
The security market line (SML) is plotted by setting the expected return as the y-axis and beta as the
x-axis. The line starts at the risk-free rate and its slope is determined by the market. The line
indicates the required rate of return for every level of risk and is used in determining whether a stock
is over-priced, under-priced, or correctly priced.
Market Risk Premium:
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How to Interpret:
● Any point above the line represents a stock that is under-priced where the expected return is
greater than the required return.
● Any point below the line represents a stock that is over-priced where the expected return is
less than the required return.
● Any point on the line represents a stock that is correctly priced where the expected return is
equal to the required return.
Watch the video tutorial for this lesson (05:28)
https://www.wizeprep.com/online-courses/20009/chapter/6/core/6/1
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6 .6 .2
Pricing Stocks
The correct (efficient) price of a stock is the present value of future dividends discounted at the
required rate of return. When the market price of a stock is below its correct price, the expected
return is greater than the required rate of return.
For Example:
If a stock is expected to pay a dividend of $2 per year and the required rate of return is 10%, the
correct price for that stock is $20:
P0 =
​
2
0.10
​
= 20
If the stock price is currently $19 on the market, the dividend remains $2 so the expected return is
greater than the required rate of return:
19 =
ER =
2
19
​
2
k
​
= 10.52%
Watch the video tutorial for this lesson (01:01)
https://www.wizeprep.com/online-courses/20009/chapter/6/core/6/2
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6 .6 .3
Example: The Security Market Line
Stock X has a beta of 1.5, an expected return of 19%, and a standard deviation of 12%. The market
risk premium is 7% and the risk-free rate is 3%. Stock X is expected to pay a dividend of $3 next year
and increase their dividend by 5% per year thereafter.
1. What is the required rate of return on the stock?
2. Is the stock overpriced or underpriced?
3. What is the correct price of the stock and what is the current market price?
Watch the video tutorial for this lesson (04:22)
https://www.wizeprep.com/online-courses/20009/chapter/6/core/6/3
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6 .6 .4
Practice: The Market Line (SML)
The market expected return is 15% with a standard deviation of 11%. The risk-free rate is 4%. Stock
X has just paid a dividend of $2.50, which is expected to grow at a rate of 8 percent per year
indefinitely.
Part 1
What is the value of one share of Stock X if it has a beta of 1.7?
$18.37
$17.01
$20.27
$22.30
Practice: The Market Line (SML)
The market expected return is 15% with a standard deviation of 11%. The risk-free rate is 4%. Stock
X has just paid a dividend of $2.50, which is expected to grow at a rate of 8 percent per year
indefinitely.
Part 2
If the stock is currently trading at $21 per share, what is its expected return?
22.3%
22.7%
18.37%
20.86%
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View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/6/core/6/4
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6 .6 .5
Example: Pricing Stocks Using CAPM
ABC Inc. just paid a dividend of $2 to its shareholders and investors expect the company to increase
its dividend by 5% per year. The beta on ABC Inc's stock is 1.99 and the expected return of the
market is 12%. If treasury bills are yielding 3.5%, what is the current fair value of the stock using the
dividend discount model?
Watch the video tutorial for this lesson (01:28)
https://www.wizeprep.com/online-courses/20009/chapter/6/core/6/5
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6 .6 .6
Practice: Pricing Stocks Using CAPM
Stock X is expected to pay a dividend of $3 next year, and 8% more per year indefinitely. The stock
has a beta of 2.8 and the market risk premium is 11%. Risk free assets are yielding 2%, what is the
fair value of the stock?
Round your final answer to 2 decimal places
Fair value of Stock X
$
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Solutions to these questions, as well as step-by-step breakdowns of the answers at:
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6.7
Alpha
6 .7 .1
Alpha
Alpha is used in finance to measure the performance of a stock, portfolio, or other investment by
comparing its returns to the market.
● If alpha is positive, the investment outperformed the market.
● If alpha is negative, the investment underperformed the market.
Watch the video tutorial for this lesson (01:22)
https://www.wizeprep.com/online-courses/20009/chapter/6/core/7/1
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6 .7 .2
Example: Alpha
An investor invested in a stock with a beta of 1.2 last year and earned a return of 8.5%. The market
return this year was 6% and the risk-free rate is 4%. How did the stock perform?
Watch the video tutorial for this lesson (02:19)
https://www.wizeprep.com/online-courses/20009/chapter/6/core/7/2
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6 .7 .3
MAR K YO UR SE LF Q UE STIO N
Try the problem yourself, and check the solutions to see how you did. Then mark yourself right or wrong.
Practice: Alpha
Your portfolio manager claims to always beat the market and in the last year the money you've
invested with her has earned 20%. The beta of the portfolio the manager has put together is 1.7.
Last year the market return equally 14% and the risk-free rate was 3%. Did your portfolio manager
actually beat the market?
View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/6/core/7/3
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7. Market Efficiency
7.1
The Efficient Market Hypothesis
7 .1 .1
The Efficient Market Hypothesis
The EMH is a set of rules and beliefs about the market and the way information affects security
prices.
● States that markets are efficient
○ Security prices at a particular point in time reflect all available information.
● Investor's cannot consistently earn abnormal returns, they cannot "beat the market."
● The EMH is broken into three levels because not all investors have the same beliefs about the
market's level of efficiency and the type of information reflect in market prices.
○ Weak form
○ Semi-strong form
○ Strong form
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Watch the video tutorial for this lesson (01:36)
https://www.wizeprep.com/online-courses/20009/chapter/7/core/1/1
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7.2
Levels of Market Efficiency
7 .2 .1
Weak Form Efficiency
The first level of the efficient market hypothesis is the weak form EMH, which is a set of beliefs
regarding what can and cannot be used to predict future security prices.
Technical Analysis
● The study of historical trading and price information.
● Users try to identify patterns in past price changes in order to predict future price changes.
What is the Weak Form Efficient Hypothesis?
● Security prices reflect all market data
○ Market data refers to all past price and volume information.
○ Historical price information cannot be used to predict future price changes.
● Technical analysis is of no value.
● Only public and private information can be used to predict future price changes and earn
abnormal returns.
● Random walk hypothesis: theory that states that price changes follow a random walk,
meaning that security price changes over time are independent.
● Empirical evidence supports the weak form efficient market hypothesis more than the other
forms.
Watch the video tutorial for this lesson (01:05)
https://www.wizeprep.com/online-courses/20009/chapter/7/core/2/1
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7 .2 .2
Semi-Strong Form Efficiency
The second level of the efficient market hypothesis is the semi-strong form EMH, which is a set of
beliefs regarding what can and cannot be used to predict future security prices.
Fundamental Analysis
● Attempts to measure a security's value be analyzing economic and financial factors like
financial statements, earnings announcements, corporate press releases, economic indicators,
consumer behavior, corporate strategy, etc.
● Uses information that is publicly available to try and predict the value of a company, this
information can then be used to make investment decisions.
What is the Semi-Strong Form Efficient Hypothesis?
● The semi-strong form EMH includes the weak form EMH.
● Security prices reflect all market data and public information.
○ Public information refers to all new information that is legally available to the public.
● Technical analysis and fundamental analysis is of no value.
○ Technical analysis is the study of previous price, volume and patterns to predict future price
changes.
● Only private information can be used to predict future price changes and earn abnormal
returns.
● The semi-strong EMH is well supported by empirical evidence, however there is more
contradicting evidence for this form than there is for the weak form.
Watch the video tutorial for this lesson (01:10)
https://www.wizeprep.com/online-courses/20009/chapter/7/core/2/2
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7 .2 .3
Strong Form Efficiency
The third level of the efficient market hypothesis is the strong form EMH, which is a set of beliefs
regarding what can and cannot be used to predict future security prices.
What is the Strong Form Efficient Hypothesis?
● The strong form EMH includes the weak and semi-strong form EMH.
● Security prices reflect all information (market data, public and private)
○ Private information is information that has not been announced and is only known by
company insiders.
● Technical analysis, fundamental analysis and insider information are of no value.
● No information can be used to predict future price changes and earn abnormal returns.
● The strong form EMH is not very well supported by empirical evidence.
Watch the video tutorial for this lesson (00:29)
https://www.wizeprep.com/online-courses/20009/chapter/7/core/2/3
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7 .2 .4
Example: Levels of Market Efficiency
For each of the following scenarios, state if there is a violation of weak form, semi-strong form, strong
form, or if there is no violation.
1. Expo Manufacturing production facility in Toronto was burnt down due to a fire accident on Friday.
The company announced the bad news and on that day the stock price went up by 5%.
2. Pump and Dump Corporation publish their weekly stock picks in their newsletter. You came across
it one day and decided to invest in an ‘up and coming’ biotech company that they recommended.
3. Tina’s friend showed her a ‘cool’ software that allows her to analyze technical indicators on any
stock chart. As she tries some of the indicators she discovers that there are extremely negative signs
about a stock that she already owns, so she decides to sell.
4. “Insiders information is worthless, don’t even bother investing based on that”
5. Stocks have a tendency to increase in price in January because investors who sold their stocks in
December for tax purposes tend to repurchase them in January, increasing the demand and the price
of the stock.
Watch the video tutorial for this lesson (07:49)
https://www.wizeprep.com/online-courses/20009/chapter/7/core/2/4
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7 .2 .5
Practice: Levels of Market Efficiency
Answer the following multiple choice questions
Part 1
Which of the following statements is most correct
Semi-strong form market efficiency means that stock prices reflect all public information.
An individual who has information about past stock prices should not be able to profit from this
information in a weak-form efficient market
An individual who has inside information about a publicly traded company should be able to profit
from this information in a semi-strong form efficient market
Statements 1 and 3 are correct
All the statements above are correct.
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Practice: Levels of Market Efficiency
Answer the following multiple choice questions
Part 2
Assume that markets are semi-strong form efficient, but not strong-form efficient. Which of the
following statements is most correct?
Each common stock has an expected return equal to that of the overall market.
Bonds and stocks have the same expected return
Investors can expect to earn returns above those predicted by the SML if they have access to public
information.
Investors may be able to earn returns above those predicted by the SML if they have access to
information, which has not been publicly revealed.
Answers 2 and 3 are correct
Practice: Levels of Market Efficiency
Answer the following multiple choice questions
Part 3
What does the concept of an efficient market imply?
All shares of stock have the same market beta.
Selecting stocks by throwing darts at a page of stocks will yield the same return as a carefully
selected portfolio.
Prices reflect all available information.
Stock prices do not fluctuate.
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Practice: Levels of Market Efficiency
Answer the following multiple choice questions
Part 4
Which one of the following is NOT a market anomaly?
Monday effect
January effect
Turn-of-the-month effect
Unexpected earning spike
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Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/7/core/2/5
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8. Options
8.1
Option Basics
8 .1 .1
What are Options
An option is a contract that gives the buyer (the holder of the option) the right, but not the obligation,
to buy or sell a stock at a specific strike price on a specified date, depending on the form of the
option.
Derivative Securities
● Financial securities that derive their value from another underlying asset.
● Options derive their value from the underlying stock.
Types of Options
● Call options: give the holder the right to buy a stock at a predetermined price.
● Put options: give the holder the right to sell a stock at a predetermined price.
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Options Terminology
● Strike Price/Exercise Price (X): The predetermined price that the holder of the option can buy or
sell the stock for.
● Market Price (S): The current market value of a stock.
● Premium (P): The current market value of the option
● Payoff: The proceeds that would be generated if the stock option is exercised today.
● “In the Money”: The option would generate a payoff if exercised.
● "Out of the money": The option would not generate a payoff if exercised.
● Long Position: Holder (buyer) of the option, can exercise the option on a specified date if
profitable.
● Short Position: Issuer (seller, writer) of the option, must sell or purchase the stock on a specified
date if the holder exercises it.
● European Options: Can only be exercised at maturity.
● American Options: This can be exercised any time up to and including the expiration date
Watch the video tutorial for this lesson (03:18)
https://www.wizeprep.com/online-courses/20009/chapter/8/core/1/1
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8.2
Call Options
8 .2 .1
Call Options
A call option is the right to buy a stock at the strike price on a specified date. A call option is only
exercised if the strike price X is lower than the market price S and the pay off is the difference
between the strike price and stock price.
Intrinsic Value
The intrinsic value of a call option is the greater of: zero (0) or S - X (Stock Price - Strike Price).
For example:
A call option with a strike price of $30 has an intrinsic value of $20 when the underlying stock is
priced at $50, and the option has an intrinsic value of $0 when the underlying stock is priced at $10.
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Watch the video tutorial for this lesson (01:54)
https://www.wizeprep.com/online-courses/20009/chapter/8/core/2/1
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8 .2 .2
Example: Call Options
Complete the following table, giving the payoffs for various stock prices for a call option buyer who
buys a call option with a strike price of $40.
Graph the payoffs
Watch the video tutorial for this lesson (02:32)
https://www.wizeprep.com/online-courses/20009/chapter/8/core/2/2
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8 .2 .3
Practice: Call Options
Show the option pay-offs for both the long and short positions for a call option with a strike price of
$25. Show the pay-offs for the following stock prices: $0, $10, $20, $30, $40 and $50. Graph your
results.
$0
$10
$20
$30
$40
Long
payoff
Short
payoff
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Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/8/core/2/3
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8.3
Put Options
8 .3 .1
Put Options
A put option is the right to sell a stock at the strike price on a specified date. A put option is only
exercised if the strike price X is above the market price S and the pay off is the difference between
the strike price and stock price.
Intrinsic Value
The intrinsic value of a put option is the greater of: zero (0) or X - S (Strike Price - Stock Price).
For example:
A put option with a strike price of $30 has an intrinsic value of $10 when the underlying stock is
priced at $20, and the option has an intrinsic value of $0 when the underlying stock is priced at $60.
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Watch the video tutorial for this lesson (01:22)
https://www.wizeprep.com/online-courses/20009/chapter/8/core/3/1
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8 .3 .2
Example: Put Options
Complete the following table, giving the payoffs for various stock prices for a put option buyer and
seller for a put option with a strike price of $40.
Watch the video tutorial for this lesson (00:52)
https://www.wizeprep.com/online-courses/20009/chapter/8/core/3/2
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8 .3 .3
MAR K YO UR SE LF Q UE STIO N
Try the problem yourself, and check the solutions to see how you did. Then mark yourself right or wrong.
Practice: Put Options
Show the option pay-offs for both the long and short positions for a put option with a strike price of
$25. Show the pay-offs for the following stock prices: $0, $10, $20, $30, $40 and $50. Graph your
results.
View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/8/core/3/3
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8.4
Option Premium
8 .4 .1
Option Premiums
An option premium is the price the option holder pays to the issuer to purchase the option. This is the
income earned by option sellers.
For Long (Buyer): Premiums are negative because they pay the premiums to buy the options.
For Short (Seller): Premiums are positive because they collect the premiums when they sell the
options.
Time Value (TV)
● Value placed on the remaining til before the option expires.
● Time value is highest when there is more time remaining to use it (longer expiration).
● Time value, and therefore the option premium, decreases as time until expiration decreases,
this is called time decay.
WATC H O UT!
Time value can never be negative.
Contracts
Options are purchased in lots called contracts, which are bundles of 100 options.
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Watch the video tutorial for this lesson (01:56)
https://www.wizeprep.com/online-courses/20009/chapter/8/core/4/1
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8 .4 .2
Example: Option Premiums and Contracts
Bob purchases 8 $40-call contracts. The premium on these contracts is $3. On the maturity date of
the option, the underlying stock is trading for $45.
1. Determine the total price paid for the options
2. What is the net income earned on these options?
Watch the video tutorial for this lesson (01:45)
https://www.wizeprep.com/online-courses/20009/chapter/8/core/4/2
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8 .4 .3
Practice: Option Premiums and Contracts
You construct the following portfolio:
long 4 $50-put contracts with a premium of $2
short 5 $40-call contracts with a premium of $3
On the expiry date of these options the underlying stock is trading for $55. What is the net income on
these options?
Answer
View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
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8 .4 .4
Example: Time Value
What is the time value on the following option: $40 call option expiring June 30, 2028, with a
premium of $35.66. The underlying stock is trading at $44.
Watch the video tutorial for this lesson (00:52)
https://www.wizeprep.com/online-courses/20009/chapter/8/core/4/4
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8 .4 .5
Practice: Time Value
What is the time value on the following option under the different scenarios below.
$50 put option with a premium of $14.50.
Stock price = $60
$
Stock price = $40
$
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Solutions to these questions, as well as step-by-step breakdowns of the answers at:
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8.5
8 .5 .1
Option Strategies
Covered Calls
Covered Calls
● Short call options covered by a long position in the underlying stock.
● This protects the call writer (issuer) but upside risk.
● Covered means the call option is protected by the actual stock.
○ If the price of the stock increases the gain from the stock cancels out the loss from the option.
Watch the video tutorial for this lesson (01:11)
https://www.wizeprep.com/online-courses/20009/chapter/8/core/5/1
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8 .5 .2
Protective Puts
● Long position in the underlying stock protected by a long put option.
● This protects the investor's stock investment from downside risk.
Watch the video tutorial for this lesson (00:31)
https://www.wizeprep.com/online-courses/20009/chapter/8/core/5/2
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8 .5 .3
Straddle
Long Straddle
● Long position in both a call and a put with the same strike price and same expiration.
● This produces a profit if the stock price makes a big move either up or down, and loses money if
the stock price does not change much.
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Short Straddle
● Short position in both a call and a put with the same strike price and same expiration.
● Used when investor believes the stock price will not more significantly, but will lose money if
the stock makes a big move either up or down.
Watch the video tutorial for this lesson (00:50)
https://www.wizeprep.com/online-courses/20009/chapter/8/core/5/3
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8 .5 .4
Short Straddle
Short Straddle
● Short position in both a call and a put with the same strike price and same expiration.
● Used when investor believes the stock price will not more significantly, but will lose money if
the stock makes a big move either up or down.
View this lesson online
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8 .5 .5
Long Strangle
Strangles
Long Strangle
● Long position in both a call and a put. The strike price of the call option is higher than the strike
price on the put option.
● This produces a profit if the stock price makes a big move either up or down, and loses money if
the stock price remains between the strike prices.
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Short Strangle
● Short position in both a call and a put. The strike price of the call option is higher than the
strike price on the put option.
● This produces a profit if the stock price remains between the strike prices, and loses money if
the stock price makes a big move either up or down.
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Watch the video tutorial for this lesson (01:05)
https://www.wizeprep.com/online-courses/20009/chapter/8/core/5/5
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8 .5 .6
Short Strangle
Short Strangle
● Short position in both a call and a put. The strike price of the call option is higher than the
strike price on the put option.
● This produces a profit if the stock price remains between the strike prices, and loses money if
the stock price makes a big move either up or down.
View this lesson online
https://www.wizeprep.com/online-courses/20009/chapter/8/core/5/6
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9. Capital Budgeting
9.1
Introduction to Capital Budgeting
9 .1 .1
What is Capital Budgeting
Capital budgeting is the process of evaluating potential investments or projects to determine
whether or not they should be approved.
Examples of Capital Budgeting Decisions
● Constructing a new factory
● Acquiring or renovating a building
● Expanding business into a new geographic market
Watch the video tutorial for this lesson (00:34)
https://www.wizeprep.com/online-courses/20009/chapter/9/core/1/1
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9.2
Payback Period
9 .2 .1
The Payback Period
The payback period is the length of time required for an investment to recover its initial outlay in
terms of profits or savings.
● Measures the amount of time it will take to recoup initial investment.
● Payback period should be less than the cut-off of the investment.
● Disadvantage: uses only nominal cash flows and does not factor in time value of money and
the cost of capital.
Watch the video tutorial for this lesson (00:54)
https://www.wizeprep.com/online-courses/20009/chapter/9/core/2/1
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9 .2 .2
Example: Payback Period
You are considering 5-year investment that will require in initial cash outlay of $40,000. The
expected inflows in years 1 through 3 are $10,000; then $12,000 in year 4 and $20,000 in year 5.
What is the payback period?
Watch the video tutorial for this lesson (02:10)
https://www.wizeprep.com/online-courses/20009/chapter/9/core/2/2
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9 .2 .3
Practice: Payback Period
A project with an initial after-tax cash outlay of $40,000 is expected to return $6,000 per year
forever. What is the payback period?
Round your answer to 2 decimal places
The payback period is
years
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Solutions to these questions, as well as step-by-step breakdowns of the answers at:
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9.3
Discounted Payback Periods
9 .3 .1
Discounted Payback Period (DPB)
The discounted payback period is similar to the payback period but takes into account the time value
of money and the investors cost of capital. This can be used to evaluate investments.
● The amount of time needed to recoup the initial investment using discounted cash flows
(present values)
● Can be used to evaluate profitability of an investment because it considers the cost of capital.
○ Discounted payback period must be below the cut-off of the investment for it to be
profitable.
Watch the video tutorial for this lesson (00:55)
https://www.wizeprep.com/online-courses/20009/chapter/9/core/3/1
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9 .3 .2
Example: Discounted Payback Period
You are considering 5-year investment that will require in initial cash outlay of $40,000. The
expected inflows in years 1 through 3 are $10,000; then $12,000 in year 4 and $20,000 in year 5.
Your cost of capital is 12% per year.
What is the discounted payback period?
Watch the video tutorial for this lesson (03:29)
https://www.wizeprep.com/online-courses/20009/chapter/9/core/3/2
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9 .3 .3
Practice: Discounted Payback Period
An investment requires an initial after-tax cash outlay of $6,000 and will return $3,000 in the first
year, $3,000 in the second year and $4,000 in the third. If the investor's cost of capital if 9%, what is
the discounted payback period?
Round final answer to 2 decimal places
The discounted payback period is
years
View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/9/core/3/3
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9.4
Net Present Value
9 .4 .1
Net Present Value
● Net Present Value (NPV) is the difference between the present value of cash inflows and the
present value of cash outflows.
● NPV is used in capital budgeting to analyze the profitability of a projected investment or
project.
● A project with an NPV greater than zero is profitable, if the NPV is negative it is not profitable
and should be rejected.
Financial Calculator
● The financial calculator has a net present value feature that can replace the formula in most
cases.
● You must enter all the cash flows into the calculator along with the cost of capital, the
calculator will do the rest.
Watch the video tutorial for this lesson (01:02)
https://www.wizeprep.com/online-courses/20009/chapter/9/core/4/1
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9 .4 .2
Example: Net Present Value (NPV)
You are considering 5-year investment that will require in initial cash outlay of $40,000. The
expected inflows in years 1 through 3 are $10,000; then $12,000 in year 4 and $20,000 in year 5.
Your cost of capital is 12% per year.
What is the net present value of the investment?
Watch the video tutorial for this lesson (04:23)
https://www.wizeprep.com/online-courses/20009/chapter/9/core/4/2
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9 .4 .3
Practice: Net Present Value (NPV)
An investment requires an initial after-tax cash outlay of $6,000 and will return $3,000 in the first
year, $3,000 in the second year and $4,000 in the third. If the investor's cost of capital if 9%, what is
the net present value of this investment?
Round final answer to 2 decimal places
The net present value is
$
View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/9/core/4/3
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9 .4 .4
Example: Net Present Value
Calculate the net present value of an investment that requires an upfront outflow of $100,000 and
will return $24,000 per year forever. The investor's cost of capital is 15%.
Watch the video tutorial for this lesson (00:53)
https://www.wizeprep.com/online-courses/20009/chapter/9/core/4/4
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9 .4 .5
Practice: Net Present Value
An investment requires an initial after-tax cash outlay of $50,000. The investor will receive $8,000
per year indefinitely. At the end of the 5th year, the investor will be required to pay a one-time
$10,000 maintenance fee.
What is the net present value of this investment if the investor's cost of capital is 12%.
Round your final answer to 2 decimal places
The net present value is
$
View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/9/core/4/5
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9.5
Internal Rate of Return
9 .5 .1
Internal Rate of Return
Internal rate of return (IRR) is a metric used in capital budgeting, measuring the profitability of
potential investments.
● Internal rate of return is a discount rate that makes the net present value (NPV) of all cash
flows from a particular project equal to zero.
● When comparing two potential investments, the investment with a higher IRR is more
attractive.
○ If IRR > r, then NPV > 0 (investment is profitable)
○ If IRR < r, then NPV < 0 (investment is not profitable)
○ If IRR = r, then NPV = 0 (investment breaks-even)
● Exact value for IRR can be calculated quickly using financial calculator.
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Watch the video tutorial for this lesson (01:25)
https://www.wizeprep.com/online-courses/20009/chapter/9/core/5/1
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9 .5 .2
Example: Internal Rate of Return (IRR)
You are considering 5-year investment that will require an initial cash outlay of $40,000. The
expected inflows in years 1 through 3 are $10,000; then $12,000 in year 4 and $20,000 in year 5.
Your cost of capital is 12% per year.
What is the IRR of the investment and is the investment profitable
Watch the video tutorial for this lesson (02:21)
https://www.wizeprep.com/online-courses/20009/chapter/9/core/5/2
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9 .5 .3
Practice: Internal Rate of Return (IRR)
An investment requires an initial after-tax cash outlay of $6,000 and will return $3,000 in the first
year, $3,000 in the second year and $4,000 in the third. If the investor's cost of capital if 9%, what is
the internal rate of return of this investment?
Round final answer to 2 decimal places
The internal rate of return is
%
View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/9/core/5/3
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9.6
Profitability Index
9 .6 .1
Profitability Index
Profitability index (PI), also known as profit investment ratio (PIR) and value investment ratio (VIR), is
the ratio of payoff to the investment of a proposed project. It is a useful tool for ranking projects
because it allows you to quantify the amount of value created per unit of investment.
If PI > 1, then NPV > 0 (investment is profitable)
If PI < 1, then NPV < 0 (investment is not profitable)
If PI = 1, then NPV = 0 (investment breaks-even)
WIZ E TIP
To quickly calculate PV(Inflows) you can use your financial calculator's CF and NPV functions.
Just exclude any outflows when calculating NPV and your answer will the the PV(Inflows)
Watch the video tutorial for this lesson (00:46)
https://www.wizeprep.com/online-courses/20009/chapter/9/core/6/1
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9 .6 .2
Example: Profitability Ratio
You are considering 5-year investment that will require in initial cash outlay of $40,000. The
expected inflows in years 1 through 3 are $10,000; then $12,000 in year 4 and $20,000 in year 5.
Your cost of capital is 12% per year.
What is the profitability index of this investment and is this investment profitable?
Watch the video tutorial for this lesson (01:42)
https://www.wizeprep.com/online-courses/20009/chapter/9/core/6/2
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9 .6 .3
Practice: Profitability Ratio
An investment requires an initial after-tax cash outflow of $100,000. The investment is expected to
return $20,000 in each of the first 4 years and $60,000 in the fifth year. Assume your cost of capital
is 8%. Answer the following:
Part 1
What is the payback period?
(Round your answer to 4 decimal places)
Answer
Practice: Profitability Ratio
An investment requires an initial after-tax cash outflow of $100,000. The investment is expected to
return $20,000 in each of the first 4 years and $60,000 in the fifth year. Assume your cost of capital
is 8%. Answer the following:
Part 2
What is the discounted payback period?
(Round your answer to 4 decimal places)
Answer
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Practice: Profitability Ratio
An investment requires an initial after-tax cash outflow of $100,000. The investment is expected to
return $20,000 in each of the first 4 years and $60,000 in the fifth year. Assume your cost of capital
is 8%. Answer the following:
Part 3
What is the investments NPV?
(Round your answer to 2 decimal places)
Answer
Practice: Profitability Ratio
An investment requires an initial after-tax cash outflow of $100,000. The investment is expected to
return $20,000 in each of the first 4 years and $60,000 in the fifth year. Assume your cost of capital
is 8%. Answer the following:
Part 4
What is the investment's IRR?
(Enter your answer in decimal format rounded to 4 decimal places, 2.11325% = 0.0211
Answer
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Practice: Profitability Ratio
An investment requires an initial after-tax cash outflow of $100,000. The investment is expected to
return $20,000 in each of the first 4 years and $60,000 in the fifth year. Assume your cost of capital
is 8%. Answer the following:
Part 5
What is the investment's profitability index?
(Round your answer to 4 decimal places)
Answer
Practice: Profitability Ratio
An investment requires an initial after-tax cash outflow of $100,000. The investment is expected to
return $20,000 in each of the first 4 years and $60,000 in the fifth year. Assume your cost of capital
is 8%. Answer the following:
Part 6
This investment is:
Profitable
Not Profitable
View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/9/core/6/3
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9.7
Cross-over Rate
9 .7 .1
The Cross-over Rate
When multiple investment opportunities are present but only one can be selected, these investments
are said to be mutually exclusive. The crossover rate tells us when the NPV of two investments are
equal (cross over).
Steps to Compute Crossover Rate:
1. Compute the difference in cash outflows and inflows in the two investments
2. Use the differences to compute IRR
Using the Cross-Over Rate
● If r < cross-over rate, choose the the project with the lower IRR.
● if r > cross-over rate, choose the project with the higher IRR.
○ Unless r > IRR of both projects, then choose neither project.
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Watch the video tutorial for this lesson (02:21)
https://www.wizeprep.com/online-courses/20009/chapter/9/core/7/1
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9 .7 .2
Example: The Cross-Over Rate
A company is considering two mutually exclusive projects A and B. Project A requires an initial
investment of $100,000 and is expected to generate after-tax cash flows of $45,000 per year for
three years. Project B requires an initial investment of $150,000 and is expected to generate aftertax cash flows of $50,000 per year for four years. The appropriate discount rate is 10 percent. What
is the crossover rate for projects A and B?
Watch the video tutorial for this lesson (03:12)
https://www.wizeprep.com/online-courses/20009/chapter/9/core/7/2
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9 .7 .3
Practice: Cross-over Rate
You are considering two mutually exclusive investments. Investment A requires an initial after-tax
outlay of $120,000 and will return $25,000 per year for 6 years. Investment B requires an initial
after-tax outlay of $80,000 and will return $20,000 per year for 3 years and $15,000 per year for
the next 3 years. Your cost of capital is 5%.
Part 1
What is the cross-over rate?
The cross-over rate is
%
Practice: Cross-over Rate
You are considering two mutually exclusive investments. Investment A requires an initial after-tax
outlay of $120,000 and will return $25,000 per year for 6 years. Investment B requires an initial
after-tax outlay of $80,000 and will return $20,000 per year for 3 years and $15,000 per year for
the next 3 years. Your cost of capital is 5%.
Part 2
Which investment should you choose?
Investment A
Investment B
Neither
Both
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View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/9/core/7/3
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9.8
Equivalent Annual NPV
9 .8 .1
Equivalent Annual NPV (EANPV)
A way to compare projects is by finding the net present value of the individual projects and then
determining the amount of an annual annuity that is economically equivalent to the NPV generated
by each project over its respective time period.
Steps to find EANPV
1. Find NPV
2. Set NPV = PV and solve for PMT
Example:
A project with an NPV of $10,000 that takes 10 years is equivalent to $1,295.05 per year if the cost
of capital is 5%. A 1-year investment with an NPV of $2,000 is significantly better although it has a
much lower total NPV.
Watch the video tutorial for this lesson (01:14)
https://www.wizeprep.com/online-courses/20009/chapter/9/core/8/1
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9 .8 .2
Example: Equivalent Annual Net Present Value (EANPV)
A company is considering three separate, mutually exclusive projects, A, B, and C. Project A requires
a $10,000 cash outlay today and is expected to generate after‐tax cash flows of $7,000 in year 1
and $6,000 in year 2. Project B requires an $8,500 cash outlay today and is expected to generate
after‐tax cash flows of $4,000 in year 1 and $7,000 in year 2. Project C requires a $10,600 cash
outlay today and is expected to generate after-tax cash flows of $5,000 for each of the next three
years. Assume that 15 percent is the appropriate discount rate, compute the EANPV of each project.
Watch the video tutorial for this lesson (07:33)
https://www.wizeprep.com/online-courses/20009/chapter/9/core/8/2
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9 .8 .3
Practice: Equivalent Annual Net Present Value (EANPV)
You are considering two investments: Investment A will require an initial investment of $120,000 and
will return $40,000 per year for 5 years. Investment B will require an initial investment of $250,000
and will return $43,000 per year for 10 years. Your cost of capital is 10%.
Part 1
What is the EANPV of Investment A?
(Round final answer to 2 decimal places)
Answer
Practice: Equivalent Annual Net Present Value (EANPV)
You are considering two investments: Investment A will require an initial investment of $120,000 and
will return $40,000 per year for 5 years. Investment B will require an initial investment of $250,000
and will return $43,000 per year for 10 years. Your cost of capital is 10%.
Part 2
What is the EANPV of Investment B?
(Round final answer to 2 decimal places)
Answer
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Practice: Equivalent Annual Net Present Value (EANPV)
You are considering two investments: Investment A will require an initial investment of $120,000 and
will return $40,000 per year for 5 years. Investment B will require an initial investment of $250,000
and will return $43,000 per year for 10 years. Your cost of capital is 10%.
Part 3
You can only invest in one of the two choices, which should you choose?
Investment A
Investment B
Neither
View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/9/core/8/3
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10. Cash Flow Estimation
10.1
Cash Flow Basics
1 0 .1 .1
Cash Flow Estimation Rules
What are Cash Flow Estimation Problems
● Decisions on whether or not to invest in a new investment opportunity like purchasing a fixed
asset.
● Determines if the new project will yield a positive or negative net present value for the firm.
Inclusions and Exclusions
● EXCLUDE Sunk Costs: A cost that has already been incurred, and is independent of the
investment decision.
○ Example: A company may have hired a consulting firm to advise it on whether or not to
invest in a particular project. Since they must pay the consultants whether or not they go
ahead with the project, the consulting fees are considered a sunk cost, and are immaterial
to the investment decision.
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● INCLUDE Opportunity Costs: The most valuable alternative that we are giving up by
undertaking a particular investment.
○ Example: A company is considering building a factory on a piece of land they had
purchased 10 years ago at a cost of $5m, it is now worth $1m. The $5m is a sunk cost
because it is incurred whether or not the company builds the factory. The $1m is relevant
however, because if the company does not go ahead with the project, it can be sold for its
market value. The relevant cost is the opportunity cost of selling the land.
● INCLUDE Net Working Capital: Difference between current assets and current liabilities. A
project usually adds to NWC with additional inventories or more receivables from having
higher sales. NWC is decreased by using current liabilities to finance the project.
○ Example: A company wants to produce t-shirts, before production can begin; it must invest
in cotton for work in progress until the t-shirts can be sold.
Watch the video tutorial for this lesson (01:35)
https://www.wizeprep.com/online-courses/20009/chapter/10/core/1/1
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10.2
Net Working Capital
1 0 .2 .1
Net Working Capital
● Net Working Capital is simply the difference between a company's Current Assets and Current
Liabilities.
● When networking capital changes, a cash flow is created.
○ A decrease to NWC is a cash inflow
○ An increase to NWC is a cash outflow
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Watch the video tutorial for this lesson (01:06)
https://www.wizeprep.com/online-courses/20009/chapter/10/core/2/1
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1 0 .2 .2
Example: Net Working Capital
ABC Inc is considering purchasing a new piece of equipment to use in its operations. The purchase
price of the equipment is $250,000 and would require an additional $20,000 for delivery and
installation. In order to use the machine, the company will need to begin carrying $10,000 of
additional spare parts inventory. The machine has an estimated useful life of 4 years, and
management believes that at the end of year 1 it will need to increase the spare parts inventory to
$15,000. At the end of the 3rd year, spare parts can be decreased by $8,000 and will be completely
eliminated upon completion of the project.
What is the change in net working capital in each year?
Watch the video tutorial for this lesson (02:13)
https://www.wizeprep.com/online-courses/20009/chapter/10/core/2/2
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1 0 .2 .3
Practice: Net Working Capital
Wize Corporation is planning the acquisition of a new building in Austin, Texas. The cost of the
building is $1,000,000. The closing fees are expected to be $10,000 and the building will require
some repairs before it can be used, the cost of these repairs is estimated at $150,000. Once the
building begins being used, additional inventory of $20,000 will be acquired. Inventory will be
increase by $4,000 in the second year before the company begins decreasing it equally over the final
three years of the buildings useful life. The building will be used for 5 years, after which the company
plans on selling it for $2,200,000.
What is change in net working capital in each year?
Year
Change in NWC
Year 0
Year 1
Year 2
Year 3
Year 4
Year 5
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View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/10/core/2/3
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10.3
The Initial Cash Outlay
1 0 .3 .1
The Initial Cash Flow
The initial cash outflow/outlay required to start a project or investment, includes Net Working Capital
Cost invested and Opportunity Costs.
Capital Cost
● This refers to all the costs that were incurred in order to make an investment operational.
● Includes machinery, installation expenses, and so on. These costs can be depreciated for tax
purposes (CCA).
Net Working Capital
● Includes any change to current assets and/or current liabilities at the start of the project.
○ Increases in NWC are outflows of cash and increase the initial cost of the project.
○ Decreases in NWC are inflows of cash and decrease the initial cost of the project.
Opportunity Cost (OC)
● Possible income given up by undertaking the project.
● Typically the result of not being able to sell an existing asset if the project is started.
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Watch the video tutorial for this lesson (01:03)
https://www.wizeprep.com/online-courses/20009/chapter/10/core/3/1
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1 0 .3 .2
Example: Initial Cash Flow (CF0)
Wize Corporation is planning the construction of a new building in Austin, Texas. The cost of the
building is $1,000,000. Licensing and municipal taxes on the new building are expected to be
$10,000. The building will be built on a plot of land the company purchased five years ago for
$120,000, the land's current market value is $250,000. Once the building begins being used,
additional inventory of $20,000 will be acquired. The building will be used for 5 years, after which
the company plans on selling it for $2,200,000.
What is the initial cash flow?
Watch the video tutorial for this lesson (01:54)
https://www.wizeprep.com/online-courses/20009/chapter/10/core/3/2
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1 0 .3 .3
Practice: Initial Cash Flow (CF0)
ABC Inc. is considering a new 5-year project.
● The project requires the purchase of a new machine costing $600,000, delivery of the machine
is expected to cost $50,000, and the opportunity cost of the project is $30,000.
● The research cost associated with the project is $15,000.
● The machine has a useful life of 5 years and a $75,000 salvage value. Assets are depreciated
using the straight-line method.
● Management believes that sales will increase by $300,000 and related expenses are
expected to be $80,000 per year.
● Inventory will increase immediately by $15,000 and no additional working capital is required,
inventory will no longer be needed at the end of the project.
● The cost of capital is 12% and the marginal tax rate is 30%.
Compute the initial cash flow.
Round your final answer to the nearest whole dollar.
The initial cash flow is
$
View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
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10.4
Annual Cash Cash Flows
1 0 .4 .1
The Annual Cash Flows
The expected (estimated) future outflows are caused by the investment decision. This includes any
tax benefits incurred by the company for the project. The annual cash flow is made up of two
components: the after-tax operating cash flows and the CCA tax shield.
What are Operating Cash Flows
● Represent any changes (incremental) in operating cash caused by the investment or project.
○ Increases with any incremental revenue.
○ Decreases with any incremental cost.
● Additional income tax is deducted to net after-tax operating cash flows
CCA Tax Shield
● The tax shield is the amount of income tax that the company saves as a result of the
depreciation expense on the asset it is considering purchasing.
● Is treated as a cash inflow for capital budgeting pursposes
Watch the video tutorial for this lesson (01:04)
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1 0 .4 .2
Capital Cost Allowance (Straight-Line)
● CCA is the tax deductible depreciation expense.
● Measured on the basis of cost, residual value and useful life.
○ Cost: The total cost to of the asset including all capitalized expenditures.
○ Residual value: The amount of cash we believe we can recover when the asset is sold.
○ Useful life: The number of years we plan on using the asset for.
● Equal amount of depreciation in each year
Watch the video tutorial for this lesson (00:22)
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1 0 .4 .3
Example: Annual Cash Flows
ABC Inc. is considering a new 5-year project.
● The project requires the purchase of a new machine costing $600,000, delivery of the machine
is expected to cost $50,000, and the opportunity cost of the project is $30,000.
● The research cost associated with the project is $15,000.
● The machine has a useful life of 5 years and a $75,000 salvage value. Assets are depreciated
using the straight-line method.
● Management believes that sales will increase by $300,000 and related expenses are
expected to be $80,000 per year.
● Inventory will increase immediately by $15,000 and no additional working capital is required,
inventory will no longer be needed at the end of the project.
● The cost of capital is 12% and the marginal tax rate is 30%.
a. Compute the annual operating cash flow
b. Compute the present value of operating cash flows
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Watch the video tutorial for this lesson (05:00)
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1 0 .4 .4
Practice: Annual Cash Flows
Trans Canada Pipelines is considering a new 4-year project.
● The project requires the purchase of a new machine costing $550,000, installation costs are
$100,000.
● The new facility is to be built on a piece of land that the company bought for $200,000 five
years ago.
● The current market value of the land is $120,000.
● The research cost associated with the project is $10,000.
● The machine has a useful life of 4 years and a $120,000 salvage value.
● Assets are depreciated using the straight-line method.
● Management believes that sales will increase by $400,000 per year while related costs will
increase by $40,000 per year.
● The cost of capital is calculated in 10% and the marginal tax rate is 40%.
What is the annual cash flow per year and the present value of annual cash flows?
Round your final answer to the nearest dollar.
The annual cash flow per year is
$
The present value of annual cash flows is
$
View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/10/core/4/4
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10.5
Ending Cash Flow
1 0 .5 .1
The Ending Cash Flow
The total cash flow that is expected to be made in the final year of the project. This does not include
the projected expected cash flow for that year. It does include the salvage value and the recovered
net working capital at the end of the project's life.
Watch the video tutorial for this lesson (00:31)
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1 0 .5 .2
Example: Ending Cash Flow (ECFt)
Wize Corporation is planning the acquisition of a new building in Austin, Texas. The cost of the
building is $1,000,000. The closing fees are expected to be $10,000 and the building will require
some repairs before it can be used, the cost of these repairs is estimated at $150,000. Once the
building begins being used, additional inventory of $20,000 will be acquired. The building will be
used for 5 years, after which the company plans on selling it for $2,200,000.
What is the ending cash flow and present value of ending cash flow if the cost of capital is 10%?
Watch the video tutorial for this lesson (01:44)
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1 0 .5 .3
Practice: Ending Cash Flow (ECFt)
ABC Inc. is considering a new 5-year project.
● The project requires the purchase of a new machine costing $600,000, delivery of the machine
is expected to cost $50,000, and the opportunity cost of the project is $30,000.
● The research cost associated with the project is $15,000.
● The machine has a useful life of 5 years and a $75,000 salvage value. Assets are depreciated
using the straight-line method.
● Management believes that sales will increase by $300,000 and related expenses are
expected to be $80,000 per year.
● Inventory will increase immediately by $15,000 and no additional working capital is required,
inventory will no longer be needed at the end of the project.
● The cost of capital is 12% and the marginal tax rate is 30%.
Compute the ending cash flow and present value of ending cash flow, round your final answer to the
nearest whole dollar.
The ending cash flow is
$
The present value of the ending cash flow is
$
View Solutions on Wizeprep.com
Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/10/core/5/3
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10.6
Net Present Value
1 0 .6 .1
Net Present Value
Recall the Net Present Value from the previous chapter represents the profit of a project and must be
positive for a project or investment to be profitable.
Watch the video tutorial for this lesson (00:39)
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1 0 .6 .2
Example: Calculating NPV
Trans Canada Pipelines is considering a new 4-year project.
● The project requires the purchase of a new machine costing $550,000, installation costs are
$100,000.
● The new facility is to be built on a piece of land that the company bought for $200,000 five
years ago.
● The current market value of the land is $120,000.
● The research cost associated with the project is $10,000.
● The machine has a useful life of 4 years and a $120,000 salvage value.
● Assets are depreciated using the straight-line method.
● Management believes that sales will increase by $400,000 per year while related costs will
increase by $40,000 per year.
● The company will need to increase its Net Working Capital immediately by $10,000 and then
increase again to $15,000 in the first year of the project before decreasing it by $2,000 in Year
3 and then to zero in the final year. The cost of capital is calculated in 10% and the marginal
tax rate is 40%.
What is the NPV of the project?
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Watch the video tutorial for this lesson (12:38)
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1 0 .6 .3
Example: Calculating NPV
Trans Canada Pipelines is considering a new 4-year project.
● The project requires the purchase of a new machine costing $550,000; installation costs are
$100,000.
● The new facility is to be built on a piece of land that the company bought for $200,000 five
years ago.
● The current market value of the land is $120,000. The research cost associated with the
project is $10,000.
● The machine has a useful life of 4 years and a $60,000 salvage value.
● Assets are depreciated using a CCA rate of 25%, the half-year rule applies.
● Management believes that sales will increase by $300,000 in the first year and will grow by
7% per year, related expenses are expected to total 25% of revenue.
● Inventory will increase immediately by $15,000 and no additional working capital is required,
inventory will no longer be needed at the end of the project.
● The cost of capital is 10% and the marginal tax rate is 40%.
What is the NPV of the project?
View this lesson online
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1 0 .6 .4
Practice
ABC Inc. is considering a new 5-year project.
● The project requires the purchase of a new machine costing $600,000, delivery of the machine
is expected to cost $50,000, and the opportunity cost of the project is $30,000.
● The research cost associated with the project is $15,000.
● The machine has a useful life of 5 years and a $75,000 salvage value. Assets are depreciated
using the straight-line method.
● Management believes that sales will increase by $300,000 and related expenses are
expected to be $80,000 per year.
● Inventory will increase immediately by $15,000 and no additional working capital is required,
inventory will no longer be needed at the end of the project.
● The cost of capital is 12% and the marginal tax rate is 30%.
Compute the net present value, round your final answer to the nearest whole dollar.
The net present value is
$
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Solutions to these questions, as well as step-by-step breakdowns of the answers at:
https://www.wizeprep.com/online-courses/20009/chapter/10/core/6/4
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11. Cost of Capital
11.1
Cost of Debt
1 1 .1 .1
Cost of Debt
The cost of debt represents the annual cost of servicing debt obligations like bonds and long-term
notes.
● Cost of debt is a tax-reducing expense because it lowers the company's profits and therefore
the company's taxes.
● Before tax cost of debt is the Yield to Maturity on existing debt.
● After tax cost of debt is used to calculate the weighted-average cost of capital (WACC).
After Tax Cost of Debt
Watch the video tutorial for this lesson (00:52)
https://www.wizeprep.com/online-courses/20009/chapter/11/core/1/1
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1 1 .1 .2
Example: Cost of Debt
ABC Inc. has 5,000 outstanding bonds with a face value of $1,000. The bonds are currently priced to
yield 7.5% and coupons are paid semi-annually. The corporate tax rate is 25%. What is the after-tax
cost of debt?
Watch the video tutorial for this lesson (00:37)
https://www.wizeprep.com/online-courses/20009/chapter/11/core/1/2
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1 1 .1 .3
Practice: Cost of Debt
Orange Corporation has bonds outstanding with a yield to maturity of 5.3%. The coupons on these
bonds are paid quarterly and the company's tax rate is 33%.
Round your final answer to 3 decimal places.
Before-tax cost of debt
%
After-tax cost of debt
%
View Solutions on Wizeprep.com
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11.2
Cost of Equity
1 1 .2 .1
Cost of Equity
● The rate of return that a company pays out to equity investors.
● The required rate of return on the corporation's shares.
○ For common equity, this is found using CAPM and beta.
○ For preferred equity, this is based on the market price of the shares and the dividends paid
out.
Cost of Common Equity
Cost of Preferred Equity
Watch the video tutorial for this lesson (01:23)
https://www.wizeprep.com/online-courses/20009/chapter/11/core/2/1
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1 1 .2 .2
Example: Cost of Common Equity
What is the cost of common equity for ABC Inc's stock assuming the following information:
● The stock's beta is 1.5
● Treasury bills are yielding 2%
● The expected return of the market is 10%
Watch the video tutorial for this lesson (00:34)
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1 1 .2 .3
Example: Cost of Preferred Equity
ABC Inc. has preferred shares with a book value of $100. The shares are currently trading at 98.5%
and have a dividend rate of 8%. What is the cost of preferred equity?
Watch the video tutorial for this lesson (00:48)
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1 1 .2 .4
Practice: Cost of Common Equity
XYZ Corporation has ten million outstanding common shares with a book value of $18 per share. The
beta on these shares is 1.89. The risk-free rate and market expected return are 3% and 12%
respectively. What is the cost of common equity?
Round your final answer to 2 decimal places and enter a percentage.
Answer
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1 1 .2 .5
Practice: Cost of Preferred Equity
Orange Corporation has 600,000 preferred shares outstanding. The total book value of the preferred
shares is $42 million and the company pays a 9% dividend. What is the cost of preferred equity if the
preferred shares are currently trading at 105% of book value?
Round your final answer to 2 decimal places and enter in percentage.
Answer
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11.3
Weighted-Average Cost of Capital
1 1 .3 .1
The Weighted-Average Cost of Capital
Cost of Capital
● The weighted average cost of debt and equity.
○ This includes bonds, other long-term debt, common equity, and preferred equity.
○ The more capital that is raised through a specific channel, the most significant the cost of
that channel will be to the average.
○ Weights are based on the market values of debt and equity.
● Represents the average cost of every dollar of capital a firm controls.
Capital Structure
● The proportion of a company's capital (assets) that is financed through debt and equity.
● Typically measured using the debt-to-equity ratio
● Changes to capital structure affect a firm's cost of capital when the cost of debt and equity are
different.
Weighted-Average Cost of Capital Formula
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Formula Break-Down
● RI: After-tax cost of debt
● RP: Cost of preferred equity
● RE: Cost of common equity
● D: Market value of debt
● P: Market value of preferred shares
● E: Market value of common shares
Watch the video tutorial for this lesson (01:41)
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1 1 .3 .2
Example: Cost of Capital
ABC Inc. has a debt-to-equity ratio is 60%. The company's cost of debt is 7% and its the cost of
equity is 12%. What is the weighted average cost of capital if the company is subject to a 35% tax
rate?
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1 1 .3 .3
Practice: Weighted-Average Cost of Capital
The debt-to-equity ratio for XYZ Corporation is 120%. The cost of debt is 8% and the beta of the
company's stock is 1.2. What is the weighted-average cost of capital if the risk free rate is 3%, the
market's expected return is 10% and the tax rate is 40%?
Round your final answer to 2 decimal places and enter a percentage.
Answer
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1 1 .3 .4
Example: Cost of Capital
You have obtained the following information on the ABC Inc.
● Book values: assets = $250,000; common equity = $25,000; preferred stock = $150,000 and
debt = $75,000. Coupons on debt are paid once a year.
● Number of shares outstanding: 10,000 common and 25,000 preferred
● Market prices per share: common stock $25, preferred $10
● Preferred dividend $1.00 per share; coupon rate on debt is 8%; ABC does not pay dividends on
its common stock
● Beta of the stock is 1.25
● Yield to maturity of debt is equal to the coupon rate
● Tax rate is 35%, risk free rate is 2%, and expected return on the market is 15%.
Calculate the weighted average cost of capital (WACC) or the ABC Inc.
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1 1 .3 .5
Practice: Cost of Capital
● XYZ Corp. as 100,000 15-year 10% annual coupon bonds that were issued 6 years ago. The
current YTM on the bonds is 7%.
● XYZ Corp. also has 10,000,000 outstanding common shares with a beta of 1.2, the common
shareholders expect to receive a dividend of $2 next year and 5% more per year indefinitely.
● The company also has 500,000 outstanding preferred shares with a dividend rate of 4%, the
preferred shares are currently trading at 92% of par value.
● The standard deviation of the TSX returns is 19%, the expected Return on the market portfolio
is 9%, T-bills are yielding 5% and the company's tax rate is 40%.
What is the WACC?
Round your final answer to 2 decimal places and enter a percentage.
The WACC is
%
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