Towson University
Department of Finance
Fin331
Dr. M. Rhee
2010 Spring
NAME:
ID#:
1.
If the interest is compounded quarterly with 8% APR, which of the following statements is CORRECT?
a. The periodic rate of interest is 2% and the effective rate of interest is 4%.
b. The periodic rate of interest is 8% and the effective rate of interest is greater than 8%.
c. The periodic rate of interest is 4% and the effective rate of interest is less than 8%.
d. The periodic rate of interest is 2% and the effective rate of interest is greater than 8%.
e. The periodic rate of interest is 8% and the effective rate of interest is also 8%.
Answer: d
2.
What is the coefficient of variation for security a?
Probability
35%
40%
25%
Boom
Average
Recession
Ra(State=?)
0.30
0.10
--0.15
Rb(State=?)
0.06
0.06
-0.05
a. 1.00
b. 1.25
c. 1.36
d. 1.73
e. 1.90
Answer: d
Boom
Average
Recession
Probability Ra (state=?) Pi*Ri Ra-E(Ra) {Ra-E(Ra)}^2 [{Ra-E(Ra)}^2]*Pi
35%
0.30 0.1050
0.2005
0.040200
0.014070
40%
0.08 0.0320 -0.0195
0.000380
0.000152
25%
-0.15 -0.0375 -0.2495
0.062250
0.015563
E(Ra)
0.0995
Variance
0.029785
Standard deviation (σ) = Square root (Variance; σ^2)) =
Coefficient of variation = σ / E(Ra) =
3.
0.1726
1.7345
You plan to save $6,400 per year, beginning immediately. You will make 4 deposits in an account that
pays 5.7% interest. How much will you have 4 years from today?
a. $22,980.31
b. $22,685.69
c. $26,221.12
d. $29,461.93
e. $31,524.26
Answer: d
BEGIN Mode
N
I/YR
4
5.7%
Alternative setup:
0
1
2
3
4
PV
PMT
FV
4.
$0.00
-$6,400
$29,461.93
$6,400
$6,400
$6,400
$6,400
NFV = $29,461.93
Which of the following investments would have the highest future value at the end of 10 years? Assume
that the effective annual rate for all investments is the same and is greater than zero.
a.
b.
Investment A pays $250 at the beginning of every year for the next 10 years (a total of 10 payments).
Investment B pays $125 at the end of every 6-month period for the next 10 years (a total of 20
payments).
c. Investment C pays $125 at the beginning of every 6-month period for the next 10 years (a total of 20
payments).
d. Investment D pays $2,500 at the end of 10 years (just one payment).
e. Investment E pays $250 at the end of every year for the next 10 years (a total of 10 payments).
Answer: a
A dominates B because it provides the same total amount, but it comes faster, hence it can earn more
interest over the 10 years. A also dominates C and E for the same reason, and it dominates D because
with D no interest whatever is earned. We could also do these calculations to answer the question:
A
B
C
D
E
5.
FV
$4,382.79
$4,081.59
$4,280.81
$2,500.00
$3,984.36
Largest
Interest
EFF%
10.00%
NOM% 9.76%
# PMT
10
Each PMT
-250
-125
-125
-2500
-250
Your uncle has $300,000 invested at 7.5%, and he now wants to retire. He wants to withdraw $35,000 at
the end of each year, starting at the end of this year. He also wants to have $25,000 left to give you when
he ceases to withdraw funds from the account. For how many years can he make the $35,000 withdrawals
and still have $25,000 left in the end?
a. 13.48
b. 14.96
c. 15.71
d. 16.49
e. 17.32
Answer: a
I/Y
PV
PMT
FV
N
6.
7.50%
-$300,000
$35,000
$25,000
13.48
Suppose you just won the state lottery, and you have a choice between receiving $2,550,000 today or a 20year annuity of $250,000, with the first payment coming one year from today. What rate of return is built
into the annuity? Disregard taxes.
a. 7.12%
b. 7.49%
c. 7.87%
d. 8.26%
e. 8.67%
Answer: b
N
PV
PMT
FV
I/YR
7.
20
$2,550,000
-$250,000
$0.00
7.49%
Which indenture provision may affect the price of the bond differently?
a. convertibility
b. sinking fund
c. call
d. restrictions on dividends
e. collateral
Answer: c
Investors do not like a call provision => they want to pay less or expect a higher return. What about other
indenture provisions? All others are advantageous to investors
8.
Suppose 1-year Treasury bonds yield 4.00% while 2-year T-bonds yield 4.80%. Assuming the pure
expectations theory is correct, what is the yield on a 1-year T-bond expected to be one year from now?
a. 5.61%
b. 5.72%
c. 6.22%
d. 5.44%
e. 6.11%
Answer: a
r1-year
4.00%
r2-year
4.80%
r1-year 1 year from now
X in the equation (1.04)(1 + X) = (1.048)2 = 1.0983
X = (1.048)2/(1.040) − 1.0 = r1-year in 1 year
5.61%
9.
Which of the following factors would be most likely to lead to an increase in nominal interest rates?
a. Households reduce their consumption and increase their savings.
b. A new technology like the Internet has just been introduced, and it increases investment opportunities.
c. There is a decrease in expected inflation.
d. The economy falls into a recession.
e. The Federal Reserve decides to try to stimulate the economy.
Answer: b
If the new technology were so efficient that it takes an underdeveloped economy from a subsistence
level, where savings are necessarily low and rates high, to a level where people can afford to save, this
might cause interest rates to decline. However, it would take time for this to occur.
10.
You are comparing saving $100 every month for a year vis-à-vis $1,200 at the beginning of the year. How
much extra will you have at the end of the year by saving $ 1,200 at the beginning of the year instead of
saving $100 each month at the end of each month. Use 6% interest rate.
a. $35.51
b. $38.44
c. $60.90
d. $63.90
e. $76.71
Answer: b
BEG, deposit lump-sum
N
1
I
6%
PV
-1200
PMT
0
FV
$1,272.00
Difference =
11.
Ordinary annuity
N
12
I
0.005
PV
0
PMT
-100
FV
$1,233.56
$38.44
The real risk-free rate is 3.05%, inflation is expected to be 2.75% this year, and the maturity risk premium
is zero. IBM stock has a risk premium of 0.9%. What is the equilibrium rate of return on a 1-year Treasury
bond?
a. 5.51%
b. 5.80%
c. 6.09%
d. 6.39%
e. 6.71%
Answer: b
Note: you need to find the yield on 1-year Treasury bond not IBM’s stock
Real risk-free rate, r*
3.05%
Inflation this year
2.75%
1-year bond yield: rRF = r* + IP
5.80%
The theoretically more precise answer is (1 + r*)(1 + I) – 1 = 5.884%
12.
Suppose the real risk-free rate is 3.25%, the average future inflation rate is 4.35%, and a maturity risk
premium of 0.07% per year to maturity applies to both corporate and T-bonds, i.e., MRP = 0.07%(t), where
t is the years to maturity. Suppose also that a liquidity premium of 0.50% and a default risk premium of
0.90% apply to A-rated corporate bonds but not to T-bonds. How much higher would the rate of return be
on a 10-year A-rated corporate bond than on a 5-year Treasury bond?
a. 1.75%
b. 1.84%
c. 1.93%
d. 2.03%
e. 2.13%
Answer: a
Real risk-free rate, r*
IP
MRP, 5-year T-bond
MRP, 10-year corporate
LP
DRP
T-bond yield
A bond yield
Difference
13.
Per year: 0.07%
Per year: 0.07%
Years: 5
Years: 10
rT-bond = r* + IP + MRP + DRP + LP
rCorp = r* + IP + MRP + DRP + LP
3.25%
4.35%
0.35%
0.70%
0.50%
0.90%
7.95%
9.70%
1.75%
Dyl Inc.'s bonds currently sell for $1,180 and have a par value of $1,000. They pay a $65 annual coupon
and have a 15-year maturity, but they can be called in 5 years at $1,100. What is their yield to maturity
(YTM)?
a.
4.79%
b. 3.69%
c. 4.65%
d. 5.08%
e. 4.36%
Answer: a
N
PV
PMT
FV
I/YR
14.
15
-$1,180
$65
$1,000
4.79%
= YTM
Sadik Inc.'s bonds currently sell for $1,270 and have a par value of $1,000. They pay a $105 annual
coupon and have a 15-year maturity, but they can be called in 5 years at $1,100. What is their yield to call
(YTC)?
a. 6.89%
b. 5.89%
c. 5.18%
d. 6.54%
e. 6.30%
Answer: b
N
PV
PMT
FV
I/YR = YTC
15.
5
-$1,270
$105
$1,100
5.89%
Bonds sell at a discount from par value when market rates for similar bonds are
a. Less than the bond’s coupon rate.
b. Greater than the bond’s coupon rate.
c. Equal to the bond’s coupon rate.
d. Both lower than and equal to the bond’s coupon rate.
e. Market rates are irrelevant in determining a bond’s price.
Answer: b
16.
Which of the following bonds would have the greatest percentage increase in value if all interest rates in
the economy fall by 1%?
a. 10-year, zero coupon bond.
b. 20-year, 10% coupon bond.
c. 20-year, 5% coupon bond.
d. 1-year, 10% coupon bond.
e. 20-year, zero coupon bond.
Answer: e
17.
O'Brien Ltd.'s outstanding bonds have a $1,000 par value, and they mature in 25 years. Their nominal yield
to maturity is 9.25%, they pay interest semiannually, and they sell at a price of $975. What is the bond's
nominal coupon interest rate?
a.
b.
c.
d.
7.32%
7.71%
8.12%
8.54%
e. 8.99%
Answer: e
First, use the data provided to find the dollar coupon payment per 6 months, then multiply by 2 to get the
annual coupon, and then divide by the par value to find the coupon rate. One could use the indicated data
and solve for the price. It would be $975, which confirms the rate.
Par value = FV
Years × periods/year = N
Periodic rate = YTM/2 = I/YR
Price today = PV
PMT, function of N, I/YR, PV, and FV = semiannual pymt
Annual coupon payment = semiannual payment × 2 =
Coupon rate = Annual coupon payment/Par value = 8.99%
18.
$1,000
50
4.625%
-$975
$44.96
$89.92
Cooley Company's stock has a beta of 1.32, the risk-free rate is 4.25%, and the market risk premium is
5.50%. What is the firm's required rate of return?
a. 10.93%
b. 11.51%
c. 10.13%
d. 8.75%
e. 10.01%
Answer: b
Beta
Risk-free rate
Market risk premium
Required return
19.
1.32
4.25%
5.50%
11.51%
Porter Inc's stock has an expected return of 10.75%, a beta of 1.25, and is in equilibrium. If the risk-free
rate is 5.00%, what is the market risk premium?
a. 5.15%
b. 4.28%
c. 4.32%
d. 4.60%
e. 4.55%
Answer: d
rs = rRF + bStock × RPM
10.75% = 5.00% + 1.25 × RPM
5.75% = RPM × 1.25
4.60%
= RPM
20.
Consider the following information and then calculate the required rate of return for the Global Investment
Fund, which holds 4 stocks. The market’s required rate of return is 9.50%, the risk-free rate is 7.00%, and
the Fund's assets are as follows:
Stock
A
B
C
D
a.
8.91%
Investment
$200,000
$300,000
$500,000
$1,000,000
Beta
1.50
-0.50
1.25
0.75
b. 10.06%
c. 6.77%
d. 8.64%
e. 10.42%
Answer: a
rM
rRF
9.50%
7.00%
Find portfolio beta:
$200,000
$300,000
$500,000
$1,000,000
$2,000,000
Weight
0.100
0.150
0.250
0.500
1.000
Beta
1.50
-0.50
1.25
0.75
Product
0.1500
-0.0750
0.3125
0.3750
0.7625
= portfolio beta
Find RPM = rM − rRF = 2.50%
rs = rRF + b(RPM) = 8.91%
21.
Which of the following statements best describes what you should expect if you randomly select stocks and
add them to your portfolio?
a. Adding more such stocks will reduce the portfolio's unsystematic, or diversifiable, risk.
b. Adding more such stocks will increase the portfolio's expected rate of return.
c. Adding more such stocks will reduce the portfolio's beta coefficient and thus its systematic risk.
d. Adding more such stocks will have no effect on the portfolio's risk.
e. Adding more such stocks will reduce the portfolio's market risk but not its unsystematic risk.
Answer: a
22.
Stock A has a beta of 0.7, whereas Stock B has a beta of 1.3. Portfolio P has 50% invested in both A and
B. Which of the following would occur if the market risk premium increased by 1% but the risk-free rate
remained constant?
a.
b.
c.
d.
The required return on Portfolio P would increase by 1%.
The required return on both stocks would increase by 1%.
The required return on Portfolio P would remain unchanged.
The required return on Stock A would increase by more than 1%, while the return on Stock B would
increase by less than 1%.
e. The required return for Stock A would fall, but the required return for Stock B would increase.
Answer: a
Portfolio beta =0.5*0.7 + 0.5*1.3 = 1.0. From rp = rRF + b(RPM) and b=1.0, 1% increase in RPM
will increase the portfolio’s required return by 1%.
23.
Assume that you manage a $10 million mutual fund that has a beta of 1.05 and a 9.50% required return.
The risk-free rate is 4.20%. You now receive another $5 million, which you invest in stocks with an
average beta of 0.65. What is the required rate of return on the new portfolio? (Hint: You must first find
the market risk premium, then find the new portfolio beta.)
a. 8.83%
b. 9.05%
c. 9.27%
d. 9.51%
e. 9.74%
Answer: a
% of New Port.
Old funds (millions)
New funds (millions)
Total portfolio
Req'd return, old stocks
Risk-free rate
Market risk premium: rP = rRF + b(RPM)
9.5% = 4.2% + 1.05(RPM)
RPM = (9.5% − 4.2%)/1.05 = 5.05%
New portfolio
Old portfolio's beta
New stocks' beta
New portfolio beta
New portfolio required return = rRF + new beta(RPM) =
24.
$10.00
$5.00
$15.00
9.50%
4.20%
5.30%
1.05
0.65
0.9167
8.8270%
If the current one year CD rate is 3% and the best estimate of one year CD which will be available one year
from today is 5%, what is the current two year CD rate with 1% liquidity premium?
a. 4.00%
b. 4.50%
c. 5.00%
d. 5.50%
e. 5.75%
Answer: C
(1 + 0R2 – 0.01)2 = (1.03)1 × (1.05)1
1/2
+ 0.01 – 1 = 4.9952% ≈ 5.00%
0R2 = {(1.03) × (1.05)}
25.
66.67%
33.33%
100.00%
How long approximately does it take to triple your investment at 6% per year?
a. 18.9 years
b. 19.5 years
c. 19.7 years
d. 20.0 years
e. 22.7 years
Answer: a
I=6, PV=-1, FV=3 => N=18.85, 18.9 years