Final Exam Review I Soln.
Chapter 2
1. What is the PV of a security that will pay $8,000 in 20 years if securities of equal risk
pay 8% annually?
FV=
I/Y=
N=
PMT=
CPT PV=
2. Credit card issuers must by law print their annual percentage rate on their monthly
statements. A common APR is 18%, with interest paid monthly. What is the effective rate
on such a loan?
(19.56)
3. Suppose you borrowed $30,000 on a student loan at a rate of 8% and must now repay it
in three equal installments at the end of each of the next three years. How large would
your payments be, how much of the first payment would represent interest, how much
would be principal, and what would your ending balance be after the first year?
(11,641.01; 2,400; 9,241.01; 20,758.99)
4. Find the future values of these ordinary annuities compounding occurs once a year.
a. $400 per year for 10 years at 10 %
b. $200 per year for 5 years at 5%
c. $400 per year for 5 years at 0%
d. Reword parts a and b, assuming that they are annuities due
Random
1. If EBIT = $850,000; DEP = $220,000; AMORT = 0; and the firm is financed 100%
by Equity, and the tax rate = 40%. Find NI, NCF = ? OCF = ?
EBIT
Interest
EBT
Taxes (40%)
NI
$850,000
0
$850,000
$340,000
$510,000
NCF = NI + Depreciation & Amortization
NCF = $510,000 + 220,000 = $730,000
OCF = NOPAT + Depreciation & Amortization
NOPAT = EBIT (1-Tax rate)
NOPAT = $850,000 X .6 = $510,000
OCF = $510,000 + 220,000 = $730,000
*b/c NCF = OCF: firm is 100% equity financed
Chapter 6
1. The real risk-free rate is 3 percent. Inflation is expected to be 3 percent this year, 4
percent next year, and then 3.5 percent thereafter. The maturity risk premium is estimated
to be 0.05 X (t-1)%, where t = number of years to maturity. What is the yield on a 7-year
Treasury note?
r = r* + IP + MRP + DRP + LP.
r* = 0.03.
IP = [0.03 + 0.04 + (5)(0.035)]/7 = 0.035.
MRP = 0.0005(6) = 0.003.
DRP = 0.
LP = 0.
rT7 = 0.03 + 0.035 + 0.003 = 0.068 = 6.8%.
2. An investor in Treasury securities expects inflation to be 2.5 percent in Year 1, 3.2
percent in Year 2, and 3.6 percent each year thereafter. Assume that the real risk-free rate
is 2.75 percent, and that this rate will remain constant. Three-year Treasury securities
yield 6.25 percent, while 5-year Treasury securities yield 6.80 percent. What is the
difference in the maturity risk premiums (MRPs) on the two securities (MRP5 – MRP3)?
First, calculate the inflation premiums for the next three and five years, respectively.
IP3 = (2.5% + 3.2% + 3.6%)/3 = 3.1%
IP5 = (2.5% + 3.2% + 3.6% + 3.6% + 3.6%)/5 = 3.3%.
The real risk-free rate is given as 2.75%.
Since the default and liquidity premiums are zero on Treasury bonds, we can now
solve for the maturity risk premium.
6.25% = 2.75% + 3.1% + MRP3; MRP3 = 0.4%.
6.8% = 2.75% + 3.3% + MRP5; MRP5 = 0.75%.
MRP5 – MRP3 = 0.75% – 0.40% = 0.35%.
Chapter 7
1. A bond has a $1,000 par value, 10 years to maturity, a 7 percent annual coupon, and
sells for $985
a. What is its current yield?
b. What is its yield to maturity?
c. Assume that the YTM remains constant for the next 3 years. What will the price
be 3-years from today?
VB = $985; M = $1,000; Int = 0.07 ´ $1,000 = $70.
a. Current yield = Annual interest/Current price of bond
= $70/$985.00
= 7.11%.
b. N = 10; PV = -985; PMT = 70; FV = 1000; YTM = ?
Solve for I/YR = YTM = 7.2157%  7.22%.
c. N = 7; I/YR = 7.2157; PMT = 70; FV = 1000; PV = ?
Solve for VB = PV = $988.46.
2. Six years ago, the Singleton Company issues 20-year bonds with a 14 percent annual
coupon at their $1,000 par value. The bonds had a 9 percent call premium, with 5 years of
call protection. Today, Singleton called the bonds. Compute the realized rate of return for
an investor who purchased the bonds when they were issued and held them until they
were called.
The rate of return is approximately 15.03%, found with a calculator using the following
inputs:
N = 6; PV = -1000; PMT = 140; FV = 1090; I/YR = ? Solve for I/YR = 15.03%.
3. An 8 percent semiannual coupon bond matures in 5 years. The bond has a face value of
$1,000 and a current yield of 8.21 percent. What are the bond’s price and YTM?
The problem asks you to solve for the YTM and Price, given the following facts:
N = 5 2 = 10, PMT = 80/2 = 40, and FV = 1000. In order to solve for I/YR we need PV.
However, you are also given that the current yield is equal to 8.21%. Given this
information, we can find PV (Price).
Current yield = Annual interest/Current price
0.0821 = $80/PV
PV = $80/0.0821 = $974.42.
Now, solve for the YTM with a financial calculator:
N = 10, PV = -974.42, PMT = 40, and FV = 1000. Solve for I/YR = YTM = 4.32%.
However, this is a periodic rate so the nominal YTM = 4.32%(2) = 8.64%.
Chapter 8
1. A stock has a required return of 11%; the risk-free rate is 7%; and the market risk
premium is 4%.
a. What is the stock’s beta?
b. If the market risk premium increased to 6%, what would happen to the stock’s required
rate of return? Assume that the risk-free rate and the beta remain unchanged
a. r = 11%; rRF = 7%; RPM = 4%.
r = rRF + (rM – rRF)b
11% = 7% + 4%b
4% = 4%b
b = 1.
b. rRF = 7%; RPM = 6%; b = 1.
r = rRF + (rM – rRF)b
= 7% + (6%)1
= 13%.
2. An individual has $35,000 invested in a stock with a beta of 0.8 and another $40,000
invested in a stock with a beta of 1.4. If these are the only two investments in her
portfolio, what is her portfolio risk?
Investment
Beta
$35,000
0.8
$40,000
1.4
Total
$75,000
bp = ($35,000/$75,000)(0.8) + ($40,000/$75,000)(1.4) = 1.12.
3. Use the following information for problems 1-3. A stock’s expected return has the
following distribution:
Demand for the
Probability of this
Rate of Return if this
Company’s Products
Demand Occurring
Demand Occurs
Weak
0.1
-50%
Below Average
0.2
-5%
Average
0.4
16%
Above Average
0.2
25%
Strong
0.1
60%
1.
A.
B.
C.
D.
Calculate the stock’s expected return.
10.45%
10.90%
11.40%
11.75%
2.
A.
B.
C.
D.
Calculate the standard deviation.
28.32%
27.53%
27.12%
26.69%
3.
A.
B.
C.
D.
Calculate the stock’s coefficient of variation.
1.34
2.34
3.34
4.34
1. = (0.1)(-50%) + (0.2)(-5%) + (0.4)(16%) + (0.2)(25%) + (0.1)(60%)
= 11.40%.
2. s2 = (-50% – 11.40%)2(0.1) + (-5% – 11.40%)2(0.2) + (16% – 11.40%)2(0.4)
+ (25% – 11.40%)2(0.2) + (60% – 11.40%)2(0.1)
s2 = 712.44; s = 26.69%.
3. CV = 2.34.
Chapter 9
1. Thomas Brothers is expected to pay $0.50 per share dividend at the end of the
year (that is, D1 = $0.50). The dividend is expected to grow at a constant rate of
7% a year. The required rate of return on the stock, Rs, is 15%. What is the
stock’s value per share?
D1 = $0.50; g = 7%; rs = 15%; P(hat) 0 = ?
2. Harrison Clothiers’ stock currently sells for $20 a share. It just paid a dividend of
$1.00 a share (that is, Do = $1.00). The dividend is expected to grow at a constant
rate of 6% a year. What stock price is expected 1 year from now? What is the
required rate of return?
3. Fee Founders has perpetual preferred stock outstanding that sells for $60 per share
and pays a dividend of $5 at the end of each year. What is the required rate of
return?
Chapter 11
1. Project K costs $52,125, and its expected net cash inflows are $12,000 per year
for 8 years, and its WACC is 12 percent. What is the project’s NPV?
11-1 Financial calculator solution: Input CF0 = -52125, CF1-8 = 12000, I/YR = 12, and
then solve for NPV = $7,486.68.
2. Refer to problem 1. What is the project’s IRR?
11-2 Financial calculator solution: Input CF0 = -52125, CF1-8 = 12000, and then solve for
IRR = 16%.
3. Refer to problem 1. What is the project’s MIRR?
11-3 MIRR: PV costs = $52,125.
4. Refer to problem 1. What is the project’s payback?
11-4 Since the cash flows are a constant $12,000, calculate the payback period as:
$52,125/$12,000 = 4.3438, so the payback is about 4 years.
Chapter 12
1. Kennedy air services is now in the final year of a project. The equipment originally
cost $20 million, of which 80% has been depreciated. Kennedy can sell the used
equipment today for $5 mil and its TR is 40%. What is the equipment’s after-tax net
salvage value?
2. Eisenhower communications is trying to estimate the first-year net operating cash flow
(at year 1) for a proposed project. The financial staff has collected the following
information on the project:
Sales revenue
$10 million
Operating costs (excluding depreciation)
$ 7 million
Depreciation
$ 2 million
Interest expense
$ 2 million
The company has a 40 percent tax rate, and its WACC is 10 percent
a. What is the project’s operating cash flow for the first year?
Chapter 13
1. Martin Development Co. is deciding whether to proceed with Project X. The cost
would be $9 million in Year 0. There is a 50% chance that X would be hugely successful
and would generate annual after-tax CF of $6 million per year during years 1, 2 & 3.
However, there is a 50% chance that X would be less successful and would generate only
$1 million per year for the 3 years. If project X would be less successful and would
generate only $1 million per year for the 3 years. If Project X is successful, it would open
the door to another investment, Project Y, that would require a $10 million outlay at the
end of Year 2. Project Y would then be sold to another company at a price of $20 million
at the end of Year 3. Martin’s WAAC is 11%.
a. If the company does not consider real options, what is Project X’s NPV?
b. What is X’s NPV considering the growth option?
c. How valuable is the growth option?