FIN331.101
Fall 2010 Exam
Dr. Rhee
NAME__________________ ID#__________________
1.
Which of followings is NOT the characteristics of a perpetuity?
a. A perpetuity continues for a fixed time period.
b. Value of a perpetuity can be calculated as “PMT/i”
c. In a perpetuity, returns are earned in the form of a series of cash flows.
d. A perpetuity is a constant infinite stream of identical cash flows.
e. Real estate and preferred stock are effectively perpetuities.
Answer: a
2.
If a security of $17,200 is worth $20,390 three years in the future and assuming that no withdrawals or
deposits are made, what is the implied interest rate that the investor expects to earn on the security?
a. 4.19%
b. 5.84%
c. 6.78%
d. 7.82%
e. 8.24%
Answer: b
N = 3, PV = -17,200, FV = 20,390 ⇨ I = 5.8%
3.
You’ve decided to buy a house that is valued at $1 million. You have $500,000 as a down payment on the
house and you take out a mortgage for the rest. Your bank is offering you a 30-year standard mortgage at a
fixed nominal rate of 9% or a 15-year mortgage at a fixed nominal rate of 9%. How much larger must your
monthly payment would be?
a. $1,048.22
b. $1,205.45
c. $1,519.92
d. $1,729.56
e. $1,836.69
Answer: a
30-year: N = 360, I = 9/12, PV = 500,000 ⇨ PMT = $4,023.11
15-year: N = 180, I = 9/12, PV = 500,000 ⇨ PMT = $5,071.33
Therefore, difference is $1,048.22
4.
How long will it take for you to pay off $1,000 charged on your credit card, if you plan to make the
minimum payment of $15 per month and the credit card charges 24% per annum?
a. 10 years
b. 12 years
c. 15 years
d. 17 years
e. You may not be able to pay off the debt
Answer: e
If you use a financial calculator, you may get an error message because $15 of monthly payment is too
small to pay back $1,000 at 24% per annum. In other words, it takes almost forever to pay back $1,000 at
24% per annum with monthly payment of $15.
5.
Which of the following investments would have the lowest present value? 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 end 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 beginning of every year for the next 10 years (a total of 10 payments).
Answer: d
A is smaller than E and B is smaller than C because the money comes in later. A is smaller than B
because a larger annuity is received later. So, now the choice comes down to eithe r A or D. Since all
of D is received at the end, this is the logical choice. We could also do these calculations to answer
the question:
A
B
C
D
E
6.
$1,536.14
$1,573.63
$1,650.44
$963.86
$1,689.76
EFF%
10.00%
NOM% 9.76%
10
Smallest
250
125
125
2500
250
Which of the following statements is CORRECT?
a.
b.
The cash flows for an ordinary annuity all occur at the beginning of the periods.
If a series of unequal cash flows occurs at regular intervals, such as once a year, then the series is by
definition an annuity.
c. The cash flows for an annuity due must all occur at the beginning of the periods.
d. The cash flows for an annuity may vary from period to period, but they must occur at regular intervals,
such as once a year or once a month.
e. If some cash flows occur at the beginning of the periods while others occur at the ends, then we have
what the textbook defines as a variable annuity.
Answer: c
7.
You observed an upward-sloping normal yield curve. Which of following statement is the MOST correct?
a.
b.
c.
Pure expectation theory must be correct.
There is a positive maturity risk premium.
If the pure expectation theory is correct, future (short-term) rates are expected to be higher than current
(short-term) rates.
d. Inflation must be expected to change in the future.
e. Default risk premium or liquidity premium must be increasing in the future.
Answer: c
8.
Suppose the interest rate on a 1-year T-bond is 5.0% and that on a 2-year T-bond is 7.0%. Assuming the
pure expectations theory is correct, what is the market's forecast for 1-year rates 1 year from now?
a. 7.36%
b. 7.75%
c. 8.16%
d. 8.59%
e. 9.04%
Answer: e
(1 + 0Rn)n = (1 + 0R1) * (1 + 1R2) * (1 + 2R3) * … * (1 + nRn-1) * [1 + E(n-1Rn)]
(1 + 0R2)2 = (1 + 0R1) * [1 + E(1R2)] ⇨ (1.07)2 = (1.05) * [1 + E(1R2)]
⇨ E(1R2) = (1.07)2 / (1.05) – 1 = 9.04%
9.
Assume a scenario in which there is no maturity risk premium (MRP = 0) and the real risk-free rate is
expected to remain constant, and the yield curve is likely to be normal for the next 10 years. Is inflation
expected to increase, decrease, or stay the same over the next 10 years?
a. Stay the same
b. Decrease
c. Increase
d. Increase at first and then decrease
e. None of above
Answer: c
10.
Crockett Corporation's 5-year bonds yield 6.65%, and 5-year T-bonds yield 4.75%. The real risk-free rate
is r* = 3.60%, the default risk premium for Crockett's bonds is DRP = 1.00% versus zero for T-bonds, the
liquidity premium on Crockett's bonds is LP = 0.90% versus zero for T-bonds, and the maturity risk
premium for all bonds is found with the formula MRP = (t – 1) × 0.1%, where t = number of years to
maturity. What inflation premium (IP) is built into 5-year bond yields?
a. 0.68%
b. 0.75%
c. 0.83%
d. 0.91%
e. 1.00%
Answer: b
Basic equation: r = r* + IP + MRP + DRP + LP
rCrockett
Not needed in this problem
6.35%
LP
Not needed in this problem
0.90%
DRP
Not needed in this problem
1.00%
rT-bond
Required data
4.75%
r* Required data
3.60%
Years to maturity Required data
5
MRP = (t – 1) × (0.1) =
0.40%
IP = rT-bond − r* − MRP
0.75%
11.
You have 2 options to buy a membership. One is to pay $5,000 upfront today and the other one is to pay
$500 each year starting today. If the prevailing discount rate is 8%, how many years do you remain as a
member before the $500 annual payment becomes more expensive than the one-time membership?
a. 14.5 years
b. 17.5 years
c. 18.5 years
d. 19.5 years
e. 21.5 years
Answer: b
Set it BGN, then I=8, PV=-5000, PMT=500 => N=17.54, 18 after rounding. Alternatively, you can take a
difference between the two payment ($4,500), then I=8%, PV=-4500, PMT=500 => N=16.54. Since your
membership last for one more year after the current membership fee is paid, your membership ends in
17.54 years.
12.
What is the bond contract feature that allows the issuer to redeem bonds under specified terms prior to
maturity and when issuers more likely to redeem the outstanding bonds issue?
a.
b.
c.
Deferred call,
Sinking fund provision,
Indenture,
when interest rates are higher than when the bonds are issued
when interest rates are higher than when the bonds are issued
whenever the buyer wants the issuer to redeem the outstanding bonds
d. Call provision,
e. Put provision,
Answer: d
13.
when interest rates are lower than when the bonds are issued
when interest rates are lower than when the bonds are issued
Roen is planning to invest in five-year 15% annual coupon bonds with a face value of $1,000 each.
Calculate number to fill the blanks in the table and identify which one is the discount bond if the market is
at equilibrium.
Bond
Bond A
Bond B
Bond C
Discount Rate
10.00%
15.00%
(3)
Bond Value
$1,189.54
(2)
$954.58
Current Yield
(1)
15.00%
15.71%
a. 10.00%,
$988.76, 14.47%, bond A
b. 11.00%, $1,000.00, 15.71%, bond B
c. 12.61%, $1,000.00, 16.40%, bond C
d. 13.24%, $1,100.00, 16.00%, bond A
e. 14.00%, $1,250.00, 16.40%, bond B
Answer: c
(1) CY = Annual Coupon PMT / Price of a Bond = $150 / $1,189.54 = 12.61%
(2) Discount rate = coupon rate. Therefore bond value = $1,000
(3) N = 5, PV = -954.58, PMT = 150, FV = 1,000 ⇨ I = 16.40%
Discount bond = bond C
14.
Duff Brewing Co. has 9% annual coupon bonds that are callable and have 18 years left until maturity. The
bonds have a par value of $1,000 and their current market price is $1,190.35. However, Duff Brewing Co.
may call the bonds in 8 years at a call price of $1,060. What are the YTM and YTC, respectively? Also, if
Duff Brewing Co. issues new bonds today, what coupon rate must the bonds to be issued at par?
YTM
YTC
Coupon Rate
a. 6.09%,
5.47%,
6.09%
b. 7.09%,
6.47%,
7.09%
c. 8.09%,
7.47%,
7.47%
d. 8.92%,
8.82%,
8.82%
e. 9.23%,
9.32%,
9.32%
Answer: b
YTM: N = 18, PV = -1,109.35, PMT = 90, FV = 1,000 ⇨ I = 7.09%
YTC: N = 18, PV = -1,109.35, PMT = 90, FV = 1,060 ⇨ I = 6.47%
The YTM of existing bonds reflects the rate of return required by investors, thus same as current YTM.
15.
The following bond list is from the business section of a newspaper on January 1, 2005 (all are semi-annual
bonds). Prices are stated relative to the par value of $100. Calculate what number should be in the blank
and indicate which bond is trading at premium.
Company
Coupon
Schubert, Inc.
8.125%
Chapman,
Inc.
9.625%
Rust, Inc.
4.500%
Murphy &
Co.
5.375%
Maturity
01-012015
01-012035
01-012010
01-012010
Last Price
Last Yield
EST
Spread
UST
(Years)
EST
Volume
(1000s)
$82.25
11.11%
6.20
10
72,070
$80.48
12.05%
7.15
30
65,275
$95.18
5.62%
1.37
5
59,277
$101.02
5.14%
0.89
5
57,465
01-01$93.11
3.89
10
2015
Last Price & Last Yield: bond’s price and YTM at the end of trading.
EST Spread: bond’s spread above the relevant U.S. Treasury benchmark (percentage).
UST: relevant maturity of U.S. Treasury benchmark for each bond.
EST Volume: # of bonds traded during the day.
Pickman, Inc.
7.750%
a. 4.40%,
b. 6.40%,
c. 8.80%,
d. 10.40%,
e. 12.80%,
Answer: c
Murhpy & Co.
Rust, Inc.
Murhpy & Co.
Pickman, Inc.
Schubert, Inc.
56,305
Pickman Inc.’s relevant UST maturity is 10 years, which is same as Schubert, Inc.’s maturity. Since
EST Spread of Schubert, Inc. is 6.20%, UST yield is 11.11% - 6.20% = 4.91%. Thus, 4.91% + 3.89%
(spread of Pickman, Inc.) = 8.80%
ii) N = 20, PV = -93.11, PMT = 3.875, FV = 100 ⇨ I = 4.40 * 2 = 8.80%
i)
16.
A 15-year bond with a face value of $1,000 currently sells for $850. Which of the following statements is
CORRECT?
a. The bond’s coupon rate exceeds its current yield.
b. The bond’s current yield exceeds its yield to maturity.
c. The bond’s yield to maturity is greater than its coupon rate.
d. The bond’s current yield is equal to its coupon rate.
e. If the yield to maturity stays constant until the bond matures, the bond’s price will remain at $850.
Answer: c
17.
Taussig Corp.'s bonds currently sell for $1,150. They have a 6.35% annual coupon rate and a 20-year
maturity, but they can be called in 5 years at $1,067.50. Assume that no costs other than the call premium
would be incurred to call and refund the bonds, and also assume that the yield curve is horizontal, with
rates expected to remain at current levels on into the future. Under these conditions, what rate of return
should an investor expect to earn if he or she purchases these bonds?
a. 3.42%
b. 3.60%
c. 3.79%
d. 3.99%
e. 4.20%
Answer: e
If the coupon rate exceeds the YTM, then it is likely that the bonds will be called and replaced with
new, lower coupon bonds. In that case, the YTC will be earned. Otherwise, one should expect to earn
the YTM.
If held to maturity:
If called:
Par value
$1,000
Par value
$1,000
Coupon
6.35%
Coupon
6.35%
N
20
N
5
Price = PV
$1,150
PV
$1,150
PMT = Par × Coupon
$63.50
PMT
$63.50
FV
$1,000.00
FV
$1,067.50
I/YR = YTM
5.13%
I/YR = YTC
4.20%
Expected rate of return = YTC if Coupon > YTM (Taussing Corp. is likely to call the bonds. Therefore rate
of return is same as YTC). Otherwise, YTM
18.
Bill has below portfolio consists of two stocks; Blue Ocean, Inc. and Red Ocean Corp. He invested 75% in
Blue Ocean, Inc. and the rest in Red Ocean Corp.
Market Condition
Strong
Normal
Weak
Probability
0.20
0.35
0.45
Blue Ocean, Inc.
38%
23%
-30%
Red Ocean Corp.
53%
30%
-38%
Based on the information, calculate expected rate of return of (1) Blue Ocean, Inc., (2) Red Ocean Corp.,
and (3) portfolio.
a. 1.80%,
b. 2.15%,
c. 3.69%,
d. 4.19%,
e. 5.16%,
Answer: b
2.78%,
4.00%,
4.19%,
5.16%,
5.49%,
1.54%
2.61%
3.15%
3.82%
4.42%
Blue Ocean, Inc. Read Ocean Corp.
Market Condition Probability Blue Ocean, Inc. Read Ocean Corp. Prob * E(r)
Prob * E(r)
Strong
0.20
38%
53%
0.076
0.106
Normal
0.35
23%
30%
0.0805
0.105
Weak
0.45
-30%
-38%
-0.135
-0.171
sum = E(ri )
2.15%
4.00%
Expected Return on Portfolio = sum[w i * E(r i )] = (0.75 * 2.15%) + (0.25 * 4.00%) = 2.61%
19.
Below table describes historically realized returns on Towson, Inc.
Stock Return
2005
12.50%
2006
8.50%
2007
15.00%
2008
21.00%
2009
6.50%
Calculate (1) average realized return, and coefficient of variation. (Hint: standard deviation is 5.71%)
a. 12.70%,
b. 25.40%,
c. 31.75%,
d. 39.37%,
e. 40.18%,
Answer: a
0.48
0.55
0.69
0.72
0.84
Average Realized Rate of Return = 𝑟̅ = (∑ 𝑟𝑡 ) / 𝑛
𝑟̅ = (12.50% + 8.50% + 15.00% + 21.00% + 6.50%) / 5 = 12.70%
Standard Deviation
Return
Year
2005
2006
2007
2008
2009
(1)
12.50%
8.50%
15.00%
21.00%
6.50%
Deviation from the
Average Return
(2) = (1) - 12.70%
-0.20%
-4.20%
2.30%
8.30%
-6.20%
Sum
Variance
Standard Dev.
Squared
Deviation
(3) = (2)^2
0.0004%
0.1764%
0.0529%
0.6889%
0.3844%
1.3030%
0.0032575
5.71%
→ sum / (n-1)
→ (Variance)^(1/2)
Coefficient of Variation = Standard Deviation / Expected Return = 5.71% / 12% = 0.48
20.
Limitless Energy, Inc. is considering to issue 8.8% semi-annual coupon bonds with 15 years to maturity.
The bonds are selling at $965.75 with a par value of $1,000. What rate of return are investors expected to
earn?
a. 4.61%
b. 9.24%
c. 9.05%
d. 8.79%
e. 7.90%
Answer: b
YTM calculation. N=15*2=30, PV= -965.75, PMT=(0.088*1000)/2, FV=1000 => I=4.62, 4.62*2=9.24%