MIDTERM EQUATIONS
FINAL EQUATIONS
Common stock portfolio: No
promise you will get your money
back.
T-bill portfolio: Sure to get your
money back from the government,
the price of the t-bill portfolio is
quite stable and predicable.
Long-term bond portfolio: Most
likely to get your money back at
maturity. However, it will be
uncertain, and not easily predicted.
Which bonds have the most interest rate sensitivity/ Interest Perpetuity (growth, recent dividend):
rake risk?
The longer the time to maturity, the greater the interest rate
risk.
The lower the coupon rate, the greater the interest rate
risk
Dividend yield = dividend income / beginning price
Capital gain yield = (ending price – beginning) / beginning price
Annuity due =
NPV Rule:
PV (BENEFITS) – PV(COSTS) bgn
Annuity = end
NPV > 0, ACCEPT
Calculator Setup
For the Casio 9750Gii:
First, make sure to check your default settings
Enter the TVM module
Press shift then setup
For most problems, we want
Payment = End
Date mode = 365
Periods/yr = Annual
Press EXIT when done with default settings
How to solve cash flow problems with the calculator
Zero coupon
bond:
0 pmt
Dollar return = dividend income +capital gain
Percentage return = Dividend yield + capital yield
STOCKS EQU. DEFINTIONS:
P0 = current stock price
P1 = stock price (right
after paying dividend)
rE = Equity cost of capital,
total/required return
3. Set PMT = 0; P/Y =1; C/Y = 1 4.
Enter the values of the three variables you know
5. Press the appropriate function key (F1, F2, F3,
or F5) to solve for the variable you need to find
Note that:
- n = number of periods; use a very large
number for perpetuities (e.g., 9999999999999)
- PV = 0 unless you need to include the initial
cost of the annuity
- PMT = the amount of the equal cash flows
- FV = 0 unless there is an extra payment at
maturity (e.g., repayment of principal
FACE VALUE; at PAR
The timeline must be in 6-month periods. You need to compute
If market interest rate < the coupon rate, bonds sell for
the 6-month required return
more than the face value; at a premium
Preferred stock are stocks that takes priority over
common stock in regards to dividends and in bankruptcy,
often without voting rights. Stock generally does not have
voting rights.
Cumulative preferred stock: is all missed preferred
dividends must be paid before any common dividends
may be paid.
Non-cumulative preferred stock: missed preferred
dividends do not accumulate.
Dividends payments are not considered a business
expense, and therefore are not tax deductible.
Efficient market hypothesis: Implies that securities will be fairly priced, based on
their future cash flows, given all information that is available to inventors.
Three forms of efficient market hypothesis:
Weak form: past information already incorporated In stock price.
Semi-strong form: all public information already incorporated.
Strong form: all information already incorporated.
NPV standard rule for
accepting or
rejecting investment will
maximize
shareholder value.
NPV >0, ACCEPT
Sensitivity analysis:
Shows how the NPV varies as
a single
underlying assumption is
changed/
Independent risk:
Risks that bear no relation to
each other
How to solve compound interest question using the calculator
If market interest rate > the coupon rate, bonds SELL for
Real Bonds have Semi Annual coupons:
It implies that the annual coupon payment is paid in two equal LESS than FACE VALUE; at a discount
installments, every 6 months.
If market interest rate = the coupon rate, bonds sell for
Common stock: ownership shares in a publicly held
corporation, without priority for dividends or in bankruptcy.
Confers rights to any common dividends as well as rights to
vote on election of directors, mergers, and other major
events.
Straight voting means voting for directors during which
stakeholders must vote for each directory.
Cumulative voting means each shareholders total vote
allocation for all directors.
Ticker symbol is a unique abbreviation assigned to a
publicly traded company.
Unit 1 hard:
A firm earns $10 per share after tax and
distributes 40%
earnings.
Corp tax is 25%, personal tax rate on dividend
is 20%, and the personal tax rate on ordinary
Dividend = 10 x 0.4 = $4.00
income is 30%.
Dividend after taxes =
How much net dividend income per share will
4 x (1.-0.2)
each investor receive?
= 3.20
This is for an investment of TVM problem that
has only 1 input of investment instead of a
steady flow of cash to continuously invest, and Note that:
n is the number of periods (N in our formulas)
withdraw (cash inflow or outflow).
I% is the rate of return per period (r in our
formulas)
The procedure for solving these problems is
For PV and FV, recall that a negative sign = cash
1. Enter the TVM module
2. Press F2 for the compound interest function outflow and a positive sign = cash inflow
1. Enter the TVM module
2. Press F3 for the cash flow function
3. If provided, enter the interest rate (ROI)
under I%
4. Scroll down to Csh = List 1 and press F5
5. Enter the cash flow for each period, starting
with today’s cash flow
Enter 0 for periods with no cash flow
Use a negative sign for cash outflows
6. Press the appropriate function key (F1, F2, or
F4) to solve for the variable you need to find
F1 = PV; F2 = ROI; F4 = F
4. Enter the values of the variables you know,
pressing EXE after each one is entered
5. Press the appropriate function key (F1 to F5)
to solve for the variable you are trying to
calculate
Question about semi-annual coupon:
Divide APR by 2,
Multiply n by 2m
Find CPN using equation
Correlation Coefficient:
if p >0, positively correlated, move in the same direction.
If negative, move in opposite. If 0, no relationship.
TVM for Annuities
1. Press shift then setup to check your settings
⧫ Payment = End for an ordinary annuity;
Payment = Bgn for an annuity due
⧫ Press EXIT when done with default settings
2. Enter the TVM module
3. Press F2 for the compound interest function
⧫ Check that P/Y = 1 and C/Y = 1
Question about annual coupon bond:
PMT = annual coupon rate % x face value
Bond is a security sold by governments and corporations
to raise money today.
The price of a bond decreases
Bond indenture indicates the with increasing interest rate
amounts and dates of all payments to be made.
Maturity
date is the date on which the loan will be paid off.
Treasury bills are issued by national gov.
Bondholders
own the securities, have rights to the cashflows
described and can trade these financial assets
Relative valuation:
Price -Earning ratio
Trailing PE =(P0/EPS0)
Forward PE =(P0/EPS1)
Enterprise value multiples
EV/EBIT
EV/EBITDA
M = number of compounding periods
(c/y) F = number of payments periods
each year (p/y)
P/Y = MONTHLY PAYMENTS OF..
C/Y = COMPOUNDED…
*if given months, do not multiply, only
years
Semi-monthly: yrs x 24
Semi-annually: yrs x 2
Annually: yrs x 1
Quarterly: yrs x 4
Monthly: yrs x 4
Weekly: yrs x 52 Bi-weekly: yrs x 26
Zero coupon bonds are known as pure
discount bonds.
YTM is the discount rate that sets PV of the
promised bond payments equal to the current
market price of a bond.
Term is the remaining time until maturity date.
As time passes, interest rate changes in the
marketplace, but the coupon rate does not
change
Model Limitation:
All three discounted cashflows are sensitive to the assumed long term growth
rate and forecasted short-term growth rates.
Total payout model:
Accounts for share repurchases by the firm in addition to dividends paid out
Discount rate = opportunity cost of capital
Constant dividend (zero growth):
firm will pay a constant dividend
forever, like a preferred stock.
Capital gain is the amount by selling price of an asset exceeds its initial
purchase price.
Capital gain rate is the percentage of the initial price of the asset
Constant dividend growth is
when the firm will increase
dividend by a constant percent
every period.
Lecture 2:
1.If its growth by 10%, multiply everything by 1.10
2. ignore interest expense, short/long term debt
3. subtract cost of sales/expenses/depreciation by revenue to get EBIT
4. keep interest expense the same, then subtract EBIT by interest
expense to get taxable income
5. multiply the tax percentage by taxable income to get taxes
6. subtract taxable income and taxes to get net income
Supernormal growth is not
consistent initially but settles
down to constant growth
eventually.
Efficient markets imply that positive-NPV
trading opportunities will be hard to come
by, especially for most individual investors.
Individual investors display many biases
including overconfidence, disposition
effect, limited attention
Net new financing needed:
1. Additions to equity = net income x retention ratio (1-payout)
2. ending stockholder equity = beginning stockholder equity + addition to equity
3. ending total liabilities = beginning total liabilities + increase in non - debt liabilities
4. ending total liabiltiies and equity = ending total liab + ending stockholder equity
5. net new financing needed = ending asset – ending liab and equity
Advantage of IRR
Knowing a return is intuitively appealing. It is a simple way to communicate the
value of a project to someone who doesn’t know. If the IRR is high enough, you
may not need to estimate a required return
Disadvantage of IRR
May result in multiple answers or no answer with non-conventional cash flows.
May lead to incorrect decisions in comparisons of mutually exclusive investment.
Payback: The time it takes for the clash flows generated by the project to
cover the initial investment in the project.
Project payback > specific cut off, reject project. (3 yrs > 2 yrs).
Advantages: easy to understand, adjusts for uncertainty of later cashflows,
biased to liquidity.
Disadvantages: ignores the time value of money, requires arbitrary cut-off,
biased against long-term projects, such as research developments and new
project.
Volatility
T-bill have the lowest average rate of return, and the lowest level of
volatility.
Stocks have the highest average rate of return, and the highest level
of volatility
Bonds are in the middle
Net new financing needed:
1. Additions to equity = net income x retention ratio (1-payout)
2. ending stockholder equity = beginning stockholder equity + addition to equity
3. ending total liabilities = beginning total liabilities + increase in non - debt liabilities
4. ending total liabiltiies and equity = ending total liab + ending stockholder equity
5. net new financing needed = ending asset – ending liab and equity
Capital budget: list of projects that a company plans to undertake
the next period.
Capital budgeting is the process of analyzing investment
opportunities.
Stand-alone principle allows us to analyze each project in isolation,
by focusing on incremental FCF
Capital cost allowance
(CCA):
A method used for tax
purposes to allocate the
original purchase cost of the
asset. D X T
Incremental earnings
The amount by which a
firm’s earnings are
expected to change as a
result of investment
decision
Market index
Measure of the
investment
performance of
the overall
market.
Unsystematic risk are fluctuations of a stock’s return that are due to company-or
industry specific news (can be avoided by diversifying).
Systematic risk are fluctuations of a stock’s return that are due to market-wide news
representing common risk (cannot be eliminated).
Arithmetic Average Return: The return earned in ana average year over year
multiyear period.
Geometric Average Return: is the average compound return earned per year
over a multiyear period.
Trade credit
The difference between
receivables and payables
that is the net amount of
a firm’s capital consumed
as a result of those credit
transactions
Discounted payback: Accept only projects where the sum of
the discounted cashflows within payback period are greater
or equal to initial investment
Beta is defined as the sensitivity of a stock’s return to the
return of the market
Volatility: The total risk, measured as standard deviation, of
the logarithmic returns.
Real Option: The right to make a particular business
decision, such as capital investment.
Option to delay commitment: The option to time a
particular investment, which is almost always
present.
Abandonment Option: An option for an investor to
cease (come to an end) making investments