Chapter 6
⎡1 - ( 1 + r )-t ⎤
C⎢
⎥
-t
r
⎣
⎦ + F( 1 + r ) ,
Bond value =
where
C = coupon paid each period
r = market rate (required return) per period
t = number of periods
F = face (par) value of the bond
-t
Zero-coupon bond price = F( 1 + r )
(Par Value - Bond Price) ⎤
⎡
+
Coupon
⎢
⎥
Years to Maturity
Estimated YTM = ⎢
⎥
Par Value + 2(Bond Price)
⎢
⎥
⎢⎣
⎥⎦
3
1
F
⎡
⎤t
⎢ Bond Price ⎥ − 1
⎦
YTMzero = ⎣
Current yield = $C / $Bond price
YTM = Current yield + Capital gains (loss) yield
The Fisher Effect is a theoretical relationship between nominal returns, real returns and the expected inflation rate. Let
R be the nominal rate, r the real rate, and h the expected inflation rate; then, (1 + R) = (1 + r)(1 + h).
A reasonable approximation, when expected inflation is relatively low, is R = r + h.
The real rate can be found by deflating the nominal rate by the inflation rate: r = [(1 + R) / (1 + h)] – 1.
Chapter 7
Common Stock Valuation under Supernormal Growth (two-stage growth)
D (1 + g s ) ⎡ ⎛ 1 + g s ⎞
P0 = 0
⎟
⎢1 − ⎜
(R −g s ) ⎢⎣ ⎝ 1 + R ⎠
Ns
⎤ D 0 (1 + g s ) Ns (1 +g n )
(1 + R) − Ns
⎥+
−
R
g
⎥⎦
n
[
]
P0 = Intrinsic or theoretical value of the stock
D0 = The dollar amount of the last actual dividend on the stock
R = Required rate of return on the stock
gn = Expected constant growth rate of the dividends on the stock
gs = Expected supernormal growth rate of the dividends on the stock
Ns = Number of years of initial (supernormal) growth
Cumulative Voting: In general, if there are N directors up for election, then 1/(N + 1) percent of the stock plus one
share will guarantee you a seat.
Chapter 8
Modified Internal Rate of Return
Net Present Value
1) Using the required rate of return as the compounding
rate, find the terminal value (future value) of all of the
cash inflows (positive cash flows) at the end of the project
life.
n
NPV =
t =0
t
Internal Rate of Return
2) Using the required rate of return as the discounting
rate, find the present value at t = 0 of all of the cash
outflows (negative cash flows).
n
NPV = ∑
t =0
CFt
= 0,
(1 + IRR) t
where CFt is the expected net cash flow at period t,
IRR is the internal rate of return on the project, and n is
the project’s life.
3) Compute the MIRR.
⎛ TVinflows ⎞
MIRR = ⎜
⎟
⎝ PVoutflows ⎠
CFt
∑ (1 + r)
(1/n)
−1,
⎛ CFn ⎞
“Lump Sum” case: IRR = ⎜
⎟
⎝ CF0 ⎠
Where n is equal to the life of the project.
Average Accounting Return:
AAR = average net income / average book value
(1/n)
−1
⎛ PVinflows ⎞
Profitability Index: PI = ⎜
⎟
⎝ PVoutflows ⎠
Chapter 11
Portfolio Expected Return
Expected Return
E(R) = (Pr1 x R1) + (Pr2
x
R2) + (Pr3 x R3) + … + (PrT x RT)
E(Rp) = [x1 x E(R1)] + [x2 x E(R2)] + [x3 x E(R3)] + … +
[xn x E(Rn)]
where T is the number of possible states of the economy,
Pr1, Pr2, Pr3, and PrT are the probabilities of the respective where n is the number of assets in the portfolio, x1, x2, x3,
states of the economy, and R1, R2, R3, and RT are the
and xn are the portfolio weights, and E(R1), E(R2), E(R3),
possible rates of return.
and E(Rn) are the expected returns on assets 1 through n.
Risk premium = Expected return – Risk-free rate = E(R) – Rf
n
Var(R) = σ 2 = ∑ p i (R i − E(R)) 2
i =1
Total risk = Nondiversifiable risk + Diversifiable risk =
Systematic risk + Unsystematic risk
Portfolio Beta
βp = (x1 x β1) + (x2 x β2) + (x3 x β3) + … + (xn x βn) ,
where n is the number of assets in the portfolio, x1, x2, x3, and xn are the portfolio weights, and β1, β2, β3, and βn are
the betas of the assets in the portfolio.
Capital Asset Pricing Model
E(Ri) = Rf + [E(RM) – Rf] x βi ,
where E(Ri) and βi are the expected return and beta, respectively, for any asset (i).
Market risk premium = E(RM) - Rf
Chapter 12
Chapter 14
Residual Dividend Approach – A firm which adopts this approach relies primarily on internally generated funds
to finance positive NPV projects. After allocating these funds to all positive NPV projects, the firm pays
dividends only if any residual funds remain.
1. Determine capital budget.
2. Determine target capital structure.
3. Finance investments with a combination of debt and equity in line with the target capital structure, using
additions to retained earnings as the equity component until net income is exhausted, then issue new
shares of stock if necessary.
4. Pay any excess earnings out as dividends
Chapter 16
Operating cycle = inventory period + accounts receivable period
Inventory turnover = Cost of goods sold / average inventory
Inventory period = 365 / inventory turnover
Receivables turnover = credit sales / average receivables
Accounts receivable period = 365 / receivables turnover
Cash cycle = operating cycle – accounts payable period
Payables turnover = Cost of goods sold / average payables
Payables period = 365 / payables turnover
Chapter 17
Total carrying costs = (average inventory)(carrying cost per unit) = (Q/2)(CC)
Total restocking costs = (fixed cost per order)(number of orders) = F(T/Q)
Total costs = carrying costs + restocking costs = (Q/2)(CC) + F(T/Q)
2TF
EOQ =
CC
Cost of credit – the cost of not taking discounts offered (this is a benefit to the company granting credit)
Periodic rate = (discount %) / (100% – discount %)
Number of periods per year = m = 365 / (net credit period – discount period)
APR = m x (periodic rate)
EAR = (1 + periodic rate)m – 1
•