Intro to Financial Decision Making
-
Personal finance: how to evaluate mortgage, save, retirement fund etc.
Corporate Finance: launching products, adding value to business, borrowing
Capital Markets: investing in assets, risks of investing
The main objective of financial decision making is to maximize the value of the business.
A narrower objective is to maximize shareholder wealth ie. maximizing the price of shares
Decisions to maximize the business’ value:
1.
The Investment Decision, eg. whether or not to invest in a product
2.
The Financing Decision, eg. how to fund the development/production
3.
Working Capital Management Decision, eg. making sure the company has
cash to manage day-today production of a product
Investment Decision
Definitions:
Assets – what a firm owns
Liabilities – what a firm owes
Equity – capital received from investors
Example: Starting a book selling business
Assets: books, shelves, computer
Liabilities: loan from bank, personal money, equity
Total Assets = Equity + Liability
Financing Decision
There are TWO ways in which a business can raise money:
1. Debt (firm promises to make fixed payments in the future = principal + interest)
o
Contractual obligation
o
Usually fixed term
2. Equity
o
Keeps the earnings
o
Perpetual
The Balance Sheet:
Forms of Business
Sole Proprietorship – one person is responsible for providing capital and managing the
business.
Features:
Owned by a single person
No separation of ownership and management
Advantages:
Simple to form and wind up
Least expensive and regulated form of business
No sharing of profit and loss
Taxed once as personal income
Disadvantages:
Unlimited liability
Limited access to capital
Costly to transfer ownership
Partnership – two or more owners have joined together legally to manage a business and
share its profits.
Two types of partnerships:
1.
General partnership – all of the partners are owners and active in
management
2.
Limited partnership – has both general partners who are owners and
managers; and limited partners, who are owners but not managers
Advantages:
Two or more owners
More capital available
Easy to start
Taxed once as personal income
Disadvantages:
Unlimited liability (general partnership)
Partnership dissolves when one partner dies or wishes to sell]
Difficult to transfer ownership
Corporation – incorporation is the legal process used to form a corporate entity (company)
Advantages:
Separate from its owner’s legal entity
Easy to transfer ownership
Limited liability (founders’ personal assets are protected in bankruptcy)
Disadvantages:
Separation of ownership and management may create conflicts of interest
All profits are taxed at a corporate tax rate
Costly to establish and register
Competing Interest in a Corporation
Agency Problems
An agency problem is a potential cost incurred due to conflict between principal and agent,
which may diminish firm value:
Managers can make decisions which hurt firm value
Managers lie to shareholders by holding back good/bad news about the
company or fabricate financial information
Managers can waste firm resources to satisfy personal need
Tyco is an example of a firm with agency problems. These ethical issues include:
1.
Unethical CEO leadership
2.
Unethical practice of subordinates
3.
Unethical auditory practice
Disciplinary Mechanisms to prevent Agency Problems
Shareholders annual meeting – shareholders gather to evaluate the managers’ performance
For most shareholders, the cost of attending a meeting exceeds the benefit of going.
Board of Directors – body that oversees management of a firm
The board often fails at its assigned role, protecting the interest of shareholders.
Members on average work 227.5 hours per year, and only 24 hours were meetings.
Compensation plan – tying compensation to the performance review process (salary, bonus,
stock-based incentive)
Evidence suggests that pay for performance is ineffective, as it may induce managers
to take company-killing risks.
How Does a Business Raise Money?
1.
Firm sells securities (shares and bonds) to savers with a surplus of resource.
2.
Firm receives money from savers and invests in profitable projects.
3.
Firm distributes cash back to savers (from capital gain and increased share
prices).
The financial market facilitates transfer of funds from investors to companies. It is where
shares and bonds are traded.
In exchange for their money, what do investors get back?
Shareholders (provide equity):
Ownership claims
To have a share in earnings
Debt Holders (lend money)
Return of principal investment
Percentage of interest on the lend
Contractual obligation
Primary vs Secondary Market
Time Value of Money
Assets can be:
- Physical: Business entity, property, equipment
- Financial: Stocks, bonds etc.
- Intangible: Knowledge, reputation, opportunities
An asset is anything that can generate a cash flow.
Assets and Cash Flows:
Value of Asset = [CF1, CF2, CF3, CFt]
(t = time)
A dollar today is more valuable than a dollar later. This is the time value of money.
Future Value
Future value of a single cash flow is calculated by:
FV = PV ´ (1 + r )
t
FV – future value
PV – present value
r – interest rate per period
t – number of periods
Interest rate is a rate which is paid for the use of assets. It is determined by a combination
of:
Time preference (current consumption vs future consumption)
+ Uncertainty premium
+ Inflation premium
Simple interest is the interest rate on the principal investment paid at each time period.
Compound interest = simple interest + interest on interest
Interest Rate can mean:
- Rate of return (payoff as a % of initial investment)
- Discount rate (to find present value)
- Implied rate of interest
Compounding Frequency
à The higher the compounding frequency, the higher the return.
Time Value of Money II
Rates of Change
APR – Annual percentage rate. Interest rate using simple interest. Per annum
EAR – Effective annual rate. Interest rate takes compounding into account. Per annum
Ordinary Perpetuity
- Cash Flows are equally spaced in time
- Cash Flows are infinite
- The first cash flow occurs starting one period from t=0
- Cash Flows are equal: CF1=CF2=CF3…
- PV =
!
"
§
§
C is the value of the cash flows
r is annual rate of return
Growing Perpetuity
- Cash Flows are equally spaced in time
- Cash Flows are infinite
- The first cash flow occurs starting one period from t=0
- Cash Flows are not equal. They grow at constant rate of g per period.
- Growing perpetuity has constraint: r > g
Multiple Cash Flows
If there are multiple cash flows, the present values of future payments must be calculated.
Example:
PV = FV1/(1+r) t1 + FV2/(1+r) t2 + FV3/(1+r) t3
PV = 2000/1.08 + 5000/1.082 + 3000/1.083
PV = $8520.04
ð
The instalment plan of 3 payments is cheaper.
Ordinary Annuity
- Cash Flows are equally spaced in time
- Cash Flows are equal: CF1=CF2=CF3…
- Cash Flows occur at the end of the payment period
- Cash Flows are finite in number
-
§
t is the number of payments (no. of
periods)
§
Ord. Annuity must be less than Ord.
Perpetuity
Blended Cash Flow
If there is are multiple different types of cash flows, the present value must be worked
backwards from the future value, accounting for the different types. Example:
15 payments starting at t=5 means last payment will be at t=19. This means PVA at t=4 must
be calculated as Ordinary Annuity, then from t=0 to t=4 will be single cash flow. PVA at t=4 is
$41 941.45. Using the single cash flow formula, the PVA at t=0 is $30 828.21.
Multiple Cash Flows
You may also have to calculate multiple cash flows occurring at the same time. Example:
Single cash flow is occurring alongside ordinary annuity. The value of the single cash flow
after 18 years is 1000 x 1.118 = $5 559.92. The value of the ordinary annuity after 18 years
can be calculated with t=14, C=400 and r=0.1 to be $11 189.99. Therefore,
i) 5559.92 + 11189.99 = $16 749.91
ii) 16749.91 x 1.1(65-18) = $1 477 299.94
Annuity Due
- Cash Flows are equally spaced in time
- Cash Flows are equal: CF1=CF2=CF3…
- Cash Flows occur at the beginning of the payment period
- Cash Flows are finite in number
-
The value of Annuity due should be (1 + r) x Ordinary Annuity, since the money gains
interest for one extra month.
Types of Loans
Pure discount – interest and principal are paid at maturity.
o Borrower receives money and repays a lump sum in the future
o Makes no interim interest payment
Interest only – interest is paid periodically, and the principal is paid at maturity.
o Constant periodic interest paid at a certain rate
o Eg. $1000 borrowed at 10%, $100 monthly payments until $1000 repaid
Amortized loan – equal payments are made. Each includes partial interest and principal.
o Loan is paid off by making regular principal reductions
o Each payment is partial interest and partial principal
o Most common consumer loan
o Takes form of Ordinary Annuity or Annuity Due (equal CFs, fixed t period)
Amortization Table
Example: loan of $20,000 with 12% interest paid in equal payments over 3 years
- Using ordinary annuity formula for PVA we find each payment C = $8326.98
Year
1
Beg. Balance
Loan size
Repayment
C from PVA
2
3
Total
prior end balance
“
“
∑repayments
Interest charged
Beg. Balance x
interest rate
Principal paid
Repayment –
interest charged
∑repayments –
loan size
Loan size
End Balance
Beg. Balance –
principal paid
0
Bonds
Basic Properties
- A bond is a security that is issued with a borrowing agreement between company
and investor.
- Usually carry more favourable financing terms than equivalent bank loan
- Issuer can add special features that can’t be added on bank loans
- Expires at a set date
A bond indenture is the contract between the issuer and investor. It protects the
bondholders and provides legal security if principal payments are missed.
Bonds may be classified as to:
1. Level of Security
o
Collateralized: secured by a physical asset
o
Debentures: unsecured, but secured in Aus and NZ
2. Level of Seniority
o
Senior
o
Junior – subordinated to senior bonds in case of bankruptcy or default
o
Subordinated class – must give preference to other specified creditors
Bond Issuers
Governments (to finance deficits)
o
Treasury bills (maturity < 52 weeks)
o
Treasury notes (maturity 1-10 years)
o
Treasury bonds (maturity > 10 years)
Local government (relating to town or city)
Companies (to finance investment)
o
Large multinational, smaller national and banks
Famous Individuals eg. Bowie Bonds
Differing Bonds
Bonds can differ in…
1.
Conditions of borrowing
o
YTM
o
Years to maturity
o
Coupon rate/frequency of payments
2.
Coupon rate
o
Fixed
o
Floating-rate (non-examinable in 114)
3.
Interest and non-interest paying
o
Coupon bond
o
Pure discount bond
Coupon Bond
Face Value is paid to the seller of the bond
Fixed regular coupon payments occur periodically
Face Value is returned at the bond’s maturity
Combination of:
Combination of Ordinary Annuity from coupon: (C / YTM) x (1-(1/1+YTM)t)
Principal from single cash flow: Face Value / (1+YTM)t
The Bond price = Present Value of both ordinary annuity and single cash flow
(r is Yield to Maturity, t is number of coupon payments – may be adjusted for compounding)
Zero Coupon Bonds – have no coupon payments.
Bonds can be traded in the secondary market – called “Over-the-counter” (OTC). Buyers and
sellers are connected by a dealer. Dealers earn money by selling bonds for more than they
bought them. Bond prices and interest rates are inversely related. When interest rates rise,
bond prices fall, and vice versa. This is because bonds with out-of-date lower coupon rates
require a lower price to attract buyers.
If YTM = coupon rate: bonds trade at par (face value), called par-value bonds
If YTM > coupon rate: bonds trade at a discount to par, called discount bonds
If YTM < coupon rate: bonds trade at a premium to par, called premium bonds
-
Prices of longer-term bonds tend to be more sensitive to interest rate change than
prices of short-term bonds.
Prices of bonds with higher coupon rates are less sensitive to interest rate changes
than those with lower coupon rates.
Inflation Risk
- Inflation decreases purchasing power of a dollar over time
- Inflation decreases real wealth if it is not invested to earn interest
- If it is invested, inflation reduces the bond coupon rate to a lower real rate of return
rreal =
1 + rnominal
1 + inflation
eg. 5.5% nominal rate and inflation of 1% p.a. rreal = 1.055 / 1.01 = 1.045 (2 dp)
Default Risk
This is the risk that a company is unable to keep up its promises (goes bust). It depends on:
Company’s capacity to generate cash flows
Volatility in cash flows
Fixed commitments relative to cash flows
To compensate for default risk, high-risk bond sellers will generally offer higher yields.
Rating agencies grade the default risk of a company, AAA being safest and D being the
riskiest.
Yield Curve
Bonds of different maturity usually have different yields. The term structure is the
relationship between maturity and yield, all else held constant.
Normal Yield Curve
The cumulative effect of three economic factors determines the level and shape of the yield
curve:
1.
Cyclical movements in real interest rates
2.
Expected rate of inflation
3.
Interest rate risk (usually int. rate risk adds upward bias)
Inverted Yield Curve
The inversion of the yield curve is driven by inflation. Without reaching inflation targets,
prices don’t grow, and the curve is inverted.
Equity
- Ownership interest in the company’s profit in proportion to the number of shares
owned. Profits may or may not be distributed as dividends
- Residual claim on company’s cash flows – you get everything left after
bondholders are paid
- Infinite life
- Management control (shareholders have voting rights of board members,
decisions)
- A share is a potentially long-lived investment
Preference shares (hybrid):
1. Like debt, preferred shares require a fixed dollar payment – preferred dividends
2. Like debt, no management control
3. Like equity, preference shares have an infinite life
4. Intermediate priority to receive firm assets: ranks behind bonds and ahead of
shares
Nowadays, shares are traded electronically in a second-hand market. Investors buy and sell
through share brokers. The broker submits the order to the stock exchange (eg. NZX) on the
investor’s behalf.
Share Intrinsic Value
-
Buying shares gives ownership in a corporation
Valuing shares requires valuing a sequence of cash flows
Cash flows to shares are dividends
Cash flows to shares are uncertain in both magnitude and timing
Cash flows to shares are often riskier than cash flows to bonds
Valuing Perpetual Preference Shares
1.
Determine cash flow stream
o Constant cash flows
o Perpetual
è
Ordinary perpetuity
2.
Choose appropriate discount rate
3.
Evaluate PV of expected dividend
PV = C/r = intrinsic preference share value (C is dividend payment and r is discount rate)
If market price < share intrinsic value, share is undervalued
If market price > share intrinsic value, share is overvalued
Valuing Shares with Growing Dividends
- Dividend grows by constant rate
- Perpetual cash flows
à growing perpetuity
[ C t +1 can be found by C0 x (1 + g) ]
Example:
At t = 1, dividend payment is $5. Grows by a growth rate of g = 4% p.a. The discount rate
(expected rate of return) is 18% p.a.
PV0 = C1 / (r-g) = 5 / (0.18 – 0.04) = $35.71
Valuing Shares with Changing Cash Flows
- The point at which cash flows grow at a constant rate perpetually is identified
- Solve for the value growing perpetuity, using this point as Ct+1
- Find the lump sum present value of all remaining cash flows, including the PV of
the growing perpetuity
Example:
Growing perpetuity after t = 3
P2 = D3 / r-g = 3 / 0.15-0.06 = 33.3333333
PV0 = D1 / (1+r)t + D2 / (1+r)t + P2 / (1+r)t = 1/1.151 + 2/1.152 + 33.3333333/1.152
PV0 = $27.59
Investment Analysis I
Investment Decisions qualify as projects:
Expansion project: Major strategic decisions to enter new areas of business
or new markets
New Product project: Decision on new ventures within existing businesses or
markets
Replacement project: Decision to replace existing assets with new assets
Projects can be classified as:
Independent – a project whose acceptance or rejection does not depend on other projects
Mutually exclusive – projects in which acceptance of one project excludes the others from
consideration
Poor: Payback Rule
The payback on a project is a measure of how quickly the cash flows generated by the
project cover the initial investment.
Payback Decision Rule (independent project):
Accept project if the payback period is less or equal to some pre-set limit (e.g. two years)
Payback Decision Rule (mutually exclusive projects):
Accept project with shortest payback period
The limitation of the payback rule is that it ignores cash flows beyond the payback period.
An advantage of the payback rule is that short-term projects are favoured as liquidity is
generated quickly.
Good: Internal rate of return (IRR)
The internal rate of the return is the rate of return such that the project breaks even. The
rate of flows such as ordinary annuity, lump sum etc. can be calculated with formulae. The
NPV = 0 where the IRR is the discount rate in the formula.
IRR Decision Rule (independent project):
Accept a project if its IRR is greater than the hurdle (cost of capital) rate
IRR Decision Rule (mutually exclusive projects):
Among projects where IRR > hurdle rate, accept the one with highest IRR
The limitation of the IRR rule is that it only works easily for conventional cash flows. The
advantage is that it produces an internal percentage rather than an absolute value.
Best: Net present value (NPV)
This is when the PV of all cash flows are calculated for t = 0, then initial cost is subtracted. It
includes the value of free cash flows (next topic).
NPV Decision Rule (independent project):
Accept a project if NPV > 0
NPV Decision Rule (mutually exclusive projects):
Accept project with the greatest NPV
The limitation of the NPV rule is that it produces an absolute rather than a percentage
measure of returns, which makes some managers uncomfortable. The NPV rule is
advantageous as it accounts for the time value of money and is a direct measure of value
creation, consistent with maximising business value.
è
NPV is also used if there is no unique IRR. This arises in nonconventional cash flows, where there is more than one change in sign (+/-) of the
cash flows.
NPV and IRR adjust for time value of money and riskiness of a project, while the payback
rule does not.
Investment Analysis II – Free Cash Flows
Free cash flows are those which are over and above that required to maintain the assets of
the project (or business). FCF are available to be paid to the suppliers of capital. FCF are
unleveraged, meaning they are calculated without regard to how the firm is financed.
Why is FCF calculated?
1.
The accrual system leads to revenues being recognised when a sale is
agreed/made, rather than when money changes hands
2.
Expenses are recognised when they are incurred, even if cash has not been
paid
3.
Capital expenditures (eg. plant, property) are calculated across the asset’s
useful life
The free cash flow is made up of: FCF = OCF – ΔNWC – CAPEX + tax effect
Free cash flows are calculated for each year of the project/business life
CAPEX
Capital expenditure is the original cost of investment in property, plant, equipment or other
long-term assets. CAPEX reduces FCF. CAPEX can be categorised into two main groups:
Purchase cost of new assets
Installation cost of new assets
Most capital expenditures depreciate. Depreciation charges are intended to represent the
wear and tear over the asset life. The straight line depreciation method is used to find this
value. Depreciation expense (per year) =
cost of the asset + installation costs
useful life of the asset
We generally don’t depreciate land, because it is assumed to have an unlimited useful life.
Tax Effect
Tax effect typically comes in the terminal salvage value of CAPEX. Assets that are no longer
needed for a project often have resale value. Whenever the asset is sold at a market price
(salvage value) that is different from the written value (book value), taxes must be
paid/received.
Book value = CAPEX – accumulated depreciation
After tax salvage value = salvage – tax rate*(salvage – book value)
a)
b)
c)
salvage value < book value => Company experiences losses
salvage value > book value => Company will make gains
salvage value = book value => No effect
Change in Net Working Capital
Working capital is the difference between non-cash current assets and non-debt current
liabilities, at a given time. ΔNWCt = NWCt – NWCt-1
Example: Project has 3 years, initial inventory level of $20,000, maintained through t=1, 2,
drawn down to $0 in year 3 as the project closes. There are no liabilities.
Year:
0
1
2
3
Level of NWC
20,000
20,000
20,000
0
NWCt – NWCt-1 20,000 - 0
20,000 - 20,000 20,000 - 20,000 0 - 20,000
ΔNWCt
20,000
0
0
-20,000
Operating Cash Flow
OFC is cash generated from normal operations of business:
o
Revenues (P x Q)
o
– variable costs (– VC x Q)
= gross profit
o
– fixed costs
o
– depreciation (not paid as tax)
= EBIT (“operating income”)
o
– taxes (EBIT x tax rate)
= EBIAT (“net income”)
o
+ depreciation (after taxes paid)
= OCF
This calculation is carried out for each year. Depreciation is subtracted then added again at
the end as a depreciation tax shield.
Other FCF Effects
1.
Sunk Cost – any expenditure that has already been incurred and cannot
be recovered. When analysing a project, sunk costs should not be considered as they
are not incremental.
2.
Cannibalization Costs/Erosion – Loss of sales due to new products being
introduced to the market. Eg. iPad sales drop after introduction of iPad Mini.
Reduces FCF
3.
Opportunity Cost – value foregone as a result of an action. The cost of
not choosing the next best alternative. Reduces FCF.
FCF for NPV
For a project with constant revenue/costs, asset life = project life, and NWC changes only in
year 0 and year n, generally:
- FCF0 = -CAPEX – ∆NWC
- FCF0<t<n = OCF
- FCFn = OCF + after-tax salvage - ∆NWC
NPV = I0 (initial investment, FCF0) + ∑ FCFk / (1 + cost of capital)k
Investment Market History
Dollar Returns
Total dollar return = income from investment (eg. dividend or coupon) + capital gain or loss
(due to change in price)
Example: You bought a bond for $950 one year ago. You have received two coupons of $30
each. You can sell the bond for $975 today. What is your total dollar return?
Income = $30 x 2 = $60
Capital gain = Pf – Pi = 975-950 = $25
Total dollar return = 60 + 25 = $85
Only realised if you decide to sell. Limited as it is a dollar value rather than percentage, so is
not scalable.
Holding Period Return
The total return on an asset over a specified holding period. HPR consists of:
1.
Capital appreciation
2.
Cash income
Example: One year ago, you bought a newly-issued 3-year semi-annual coupon bond with a
coupon rate of 8% p.a. at $100 par value. Today is a payment date and you just received a
coupon payment. The YTM today is 9% p.a.
i.
What is your HPR?
ii.
How much of HPR comes from income yield?
iii.
How much comes from capital appreciation?
Coupon payment = $4
P0 = 100
P1(C=4, r=0.09/2, t=4) = $98.21
i.
HPR = ((P1 – P0) / P0) + (CFT / P0) = (98.21-100 / 100) + (2x4 / 100) =
6.21%
ii.
Income yield = 2x4 / 100 = 8%
iii.
Capital appreciation = 98.21-100 / 100 = -1.79%
Example 2: Invested $10 in a stock a month ago. Today it paid a dividend of 50c and you
then sold it for $11. What was your HPR?
HPR = ((P1 – P0) / P0) + (CF1 / P0) = (11-10 / 10) + (0.5 / 10)
= 15%
The limitation of HPR is that it can be volatile year by year, and over a long period of time
gives only a broad performance. The details of the year-by-year performance can’t be seen.
Mean Return
Arithmetic Mean Return: The simple average of returns (often misleading).
RA = (R1 + R2 + R3 … Rt ) / t
Limited because it doesn’t take compounding into account.
Geometric Mean Return: Constant single rate of return that if compounded over multiple
holding periods gives the true rate of growth in wealth.
RG = [(1 + R1) x (1 + R2) … x (1 + Rt)] 1 / t – 1
Return in each year is given by: (end price – start price) / start price
Risk Level with Investment Classes
-
There is a positive relationship between risk and return.
Shares are riskier compared to bonds, very volatile, but greater returns
Expected Return
An expected value is a probability weighted average. Eg. 30% chance of making $800,000,
70% chance of making $400,000. E(profit) = (0.3 x 800,000) + (0.7 x 400,000) = $520,000
Expected return formula:
Risk in finance captures both danger and opportunity.
Variance and Standard Deviation
var = ∑ [pi x (Ri – E(R)2]
sd = √var
Eg. Apple shares have 0.3 probability of 15% return, 0.7 probability of 2% return
E(R) = (0.3 x 0.15) + (0.7 x 0.02) = 0.059 = 5.9%
var = 0.3 x (0.15 – 0.059)2 + 0.7 x (0.02 – 0.059)2
= 0.003549
sd = √0.003549 = 0.0596
Risk Premium
The hurdle rate (r) of NPV is made up of riskless rate + risk premium.
Risk premium is the difference between average return rate and the return of a zero risk
investment. For example:
NZ Assets
Average monthly
Risk premium
return
Cash (T-bills, zero risk) 0.43%
Bonds
0.54%
0.54 – 0.43 = 0.11%
Shares
0.75%
0.75 – 0.43 = 0.32%
Risk and Return
-
How do investors manage their investment risk?
Diversification
Portfolio: a collection of investments
Beta, CAPM and Security Market Line
Diversification
Return of a single asset vs collection of assets:
- Return on a single asset is more
volatile than return on a portfolio
of assets.
- Investors try not to put all their
wealth into one asset
- Don’t put all your eggs in one
basket
Concepts of diversification:
Invest in two or more risky assets, whose values do not always move in the
same direction at the same time
Portfolio: a collection of assets an investor owns
Diversification is about combining risky assets into a portfolio, where the
risks offset to some extent because of low correlations
Weight – percentage of portfolio investment into a specific asset
The aim of diversification is to create a portfolio of different assets and weight them to
maximise return and minimise risk.
Example:
E(R)boom = 0.2 x -0.05 + 0.8 x 0.2 = 0.15
E(R)bust = 0.2 x -0.1 + 0.8 x 0.25 = 0.18
E(Rportfolio) = 0.4 x 0.15 + 0.6 x 0.18 = 16.8%
var = 0.4(0.15 – 0.168)2 + 0.6(0.18 – 0.168)2 = 0.000216
sd = √0.000216 = 0.0147 = 1.47%
As more assets are added to the
portfolio, risk (sd) declines
The rate of decreased risk gets
smaller as more assets are added
No matter how many assets are
in the portfolio, risk will never reach 0.
Diversifiable risk is firm-specific
There is no reward for firmspecific risk, as it can be diversified out
Non-diversifiable risk is known
as market or systematic risk (β), usually
driven by changes in macroeconomic factors
Beta
β is a measure of the non-diversifiable risk for any asset. It is a measure of sensitivity of a
specific stock to the market as a whole.
Expected Return = Risk-free Rate + βx(Expected Return on Market portfolio – Risk-free Rate)
β > 1 – above average risk investment
β = 1 – average risk investment
β < 1 – below average risk investment
β = 0 – riskless investment
The beta of a portfolio is a weighted average of its individual stock betas.
Capital Asset Pricing Model (CAPM)
E(Rshare) = rf + β(Rm – rf)
rf : risk-free rate
Rm : expected return on market portfolio
(Rm – rf) : market risk premium
β(Rm – rf) : stock risk premium
This E(Rshare) is the ‘r’ in NPV calculation for shares.
Cost of Capital
-
Cost of equity
Cost of debt
Capital structure weights
Overall weighted average cost of capital
Cost of Equity
2 methods of solving:
Dividend Growth Model (DGM):
P0 = D1 / (r – g)
r = (D1 / P0) + g
Doesn’t work for companies which don’t pay dividends
If share is overpriced/underpriced, doesn’t work
Assumes steady growth
CAPM:
E(Rshare) = rf + β(Rm – rf)
(cost of equity = risk-free rate + systematic risk of asset x market risk premium)
In equilibrium, these two methods give the same r.
Cost of Debt
The return required by debt investors given the risk of the cash flows that
flow to debt holders
Best estimated by YTM on existing long-term debt
Cost of debt can come from bank loans or bonds.
For bank loans, the cost of debt is the interest rate, r
For bonds, the cost of debt is the YTM
Because of a tax shield from tax-deductible interest, there is an after tax cost of debt. This is
found by: after tax cost of debt = pre-tax cost of debt x (1 – tax rate). This is the cost of debt
entered into NPV calculation. Here, cost of debt is expressed as a percentage rate, eg. the
YTM of a bond.
Cost of Preferred Equity
Preferred dividends are a fixed dividend amount promised to shareholders at regular
interval for an indefinite period of time. The cost of preferred stock is the preferred
dividend yield.
Example: Company issues preferred stocks that pay $0.20 dividend per share. Current share
price is $1.84. What is the cost of perpetual preference equity?
REP = D1 / P0 = 0.2 / 1.84 = 0.1087 = 10.87%
(ordinary perpetuity)
Weighted Average Cost of Capital (WACC)
Assets = Debt + Equity
Book value of debt/equity: largely based on historical measures
Market-value of debt/equity: fair value that is reflective of the current worth of bonds and
shares based on PV of future cash flows
Calculating WACC:
1.
Cost of critical components
o
Cost of Equity – RE = CAPM of shares
o
Cost of Debt – RD = YTM of bonds
2.
Capital structure
o
Equity weight – wE
o
Debt weight – wD
3.
RWACC = [wE x RE] + [wD x RD x (1-t)]
Weights are an expression of market value of the debt or equity / market value of all assets.
Sometimes a ratio is given eg. 0.5 debt to equity ratio. This means for each unit of equity,
there is 0.5 units of debt, so the weight is not 0.5, but 0.333.
è Weights are in $$ value, eg. 20 shares worth $30, and 2 bonds with $1000 face
value give wE = 20x30 / 2600 = 0.231 and wD = 2x100 / 2600 = 0.769
Example: New Apple product generates cash flows of 5.5M, 6.4M, 7.1M. Initial investment
of 800K. To finance the project, Apple will issue 1000 bonds for $600 each, and 120,000
shares for $100 each. The YTM on the bonds is 1.7% p.a. The expected return on equity is
8.6% p.a. Corporate tax rate is 40%. Using the NPV method, should Apple accept or reject?
NPV = -800,000 + 5.5M/1+RWACC + 6.4M/(1+RWACC)2 + 7.1M/(1+RWACC)3
wE = 120,000x100 / (120,000x100 + 1000x600) = 0.9523
wD = 1000x600 / (120,000x100 + 1000x600) = 0.0477
RWACC = [0.9523 x 0.086] + [0.0477 x 0.017 x (1 - 0.4)] = 0.0824
Sub into NPV gives NPV = $15,342,764.35
NPV > 0 so Apple should accept the project.
Financing Analysis – Capital Structure
Capital Structure – mixture of long-term debt and equity a firm uses.
Debt vs Equity
Pros and Cons of Debt
Advantages:
Tax benefit. Interest expenses on debt are tax deductible. Implication: the
higher the company’s tax rate, the greater the tax benefit.
Added discipline. Borrowing money may force managers to think about the
consequences of the investment decisions a little more carefully. Implication: As the
separation between managers and stockholders goes up, the benefit to debt will go
up.
Disadvantages:
Expected bankruptcy cost. Firms with more stable earnings should borrow
more, for any given level of earnings. Firms with lower bankruptcy costs should
borrow more, for any given level of earnings.
Agency costs. Firms where lenders can monitor/control how their money is
being used should be able to borrow more than firms where this is difficult to do.
Loss of flexibility. Other things remaining equal, the more uncertain a firm is
about its future financing requirements and projects, the less debt the firm will use
for financing current projects.
Debt Interest Tax Shield
Interest is treated as an expense
As interest payment is tax deductible, firm pays less taxes, so firms with more
debt have higher cash flows to bond/share holders
Leverage, therefore, increases the corporate tax rate of a company
Tax savings = debt outstanding x interest rate x tax rate
PV of tax savings is a PV of perpetual “flow” of tax savings
è So PV = tax savings / interest rate
Levered firm value = unlevered firm value + PV of interest tax shield
Optimal Capital Structure
Enterprise Value (EV) = PV of FCFs discounted back at the rWACC
Value of firm = ∑(FCF to firm / (1+rWACC)t)
è If the FCFs are held constant and rWACC is minimised, the firm value is maximised.
When trading off between cost and benefit of debt, firms borrow up until the point where
the tax benefit from an extra dollar offsets exactly costs of default risk.
Dividend Policy
When firms have FCFs, they can choose to:
Retain:
- Invest in new projects
- Increase cash reserves
or Pay Out:
- Pay dividends
- Repurpose shares
Dividend policy refers to a company’s overall policy regarding distributions of value to
shareholders.
Why do companies return cash payments to shareholders?
- Dividends are viewed by managers as a tool for signalling prospects of a sustainable
growth in earnings
- Unable to reinvest intelligently into NPV-positive projects
- Satisfy shareholders
Types of Dividends:
- Regular cash dividend: a regularly occurring cash distribution of corporate earnings
to a firm’s shareholders
- Special dividend: One-time cash distribution of corporate earnings to a firm’s
shareholders, usually stem from exceptional profits in a given period
- Repurchase/buy-back: Company buys some of your stock from you
- Dividend reinvestment programme (DRIP): paid in more shares offer discount shares
Dividend Imputation – aims to reduce double taxation of dividends.
Dividend Payment Timeline
Declaration date – board of directors declares dividends
|
| 2-3 weeks (stock trades cumulative-dividend)
v
ex-dividend date – first day the stock trades without dividends
|
| 2 business days (ex-dividend)
v
Date of record/book closing date – firm prepares list of shareholders entitled to dividends
|
| (ex-dividend)
V
Payment date