FIN331.004
Fall 2010 Exam
Dr. Rhee
NAME__________________ ID#__________________
1.
How long does it take to triple your investment at 6% per year?
a. 7.2 years
b. 10.2 years
c. 12.9 years
d. 14.6 years
e. 18.9 years
Answer: e
I=6, PV=-1, FV=3 => N=18.85, 18.9 years
2.
If an investment of $87,250 is earning 5% interest rate compounded annually, how long will it take for this
investment to reach a value of $99,750 if no additional withdrawals or no deposits are being made during
the period?
a. 2.47 years
b. 2.52 years
c. 2.74 years
d. 2.61 years
e. 2.83 years
Answer: c
PV = -87,250, I = 5, FV = 99,750 ⇨ N = 2.74 years
3.
Keanu’s financial planner suggested once he crosses a threshold of $4,991,331 in savings, he will have
enough money for retirement. Keanu has nothing saved for his retirement yet, so he has to start depositing
$85,000 in retirement fund at a fixed rate of 12.00% at the end of each year. How long will it take for
Keanu to retire?
a. 15.64 years
b. 18.40 years
c. 23.00 years
d. 24.84 years
e. Keanu will not be able to retire
Answer: b
I = 12, PMT = 85,000, FV = 4,991,331 ⇨ N = 18.40 years
4.
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 more interest
will you pay if you took out a 30-year mortgage instead of a 15-year mortgage?
a. $535,480.20
b. $631,866.64
c. $685,414.66
d. $738,962.68
e. $876,543.21
Answer: a
30-year: N = 360, I = 9/12, PV = 500,000 ⇨ PMT = $4,023.11
Total payments = $4,023.11 * 360 = $1,448,319.6, Principal = $500,000 ⇨ Interest = $948,319.6
15-year: N = 180, I = 9/12, PV = 500,000 ⇨ PMT = $5,071.33
Total payments = $5,071.33 * 180 = $912,839.4, Principal = $500,000 ⇨ Interest = $412,839.4
Therefore, difference is $535,480.20
5.
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
6.
$4,382.79
$4,081.59
$4,280.81
$2,500.00
$3,984.36
Largest
EFF%
10.00%
NOM% 9.76%
10
250
125
125
2500
250
Which of the following statements is CORRECT?
a.
b.
c.
d.
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, then the series is an annuity.
The cash flows for an annuity due must all occur at the ends of the periods.
The cash flows for an annuity must all be equal, and 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: d
7.
Charles Townsend Agency issues 15-year, AA-rated bonds. What is the yield on these bonds? Disregard
cross-product terms, i.e., if average is necessary, use the arithmetic average.
Relationship between bond ratings and DRP
Rating
Default Risk Premium
U.S. Treasury
AAA
0.60%
AA
0.80%
A
1.05%
BBB
1.45%
Real risk-free rate (r*) = 2.8% (expected to remain constant)
Inflation rate = 5%/yr for each of next five years, 4% thereafter
MRP = 0.1*(t – 1)%, t is the security’s maturity, LP = 0.55%
a. 5.55%
b. 8.48%
c. 9.33%
d. 9.88%
e. 10.12%
Answer: d
IP15 = [(5 * 5%) + (10 * 4%)]/15 = 4.33%
MRP15 = 0.1 * (t – 1)% = 0.1 * (15 – 1)% = 1.40%
rk = r* + IP + DRP+ LP + MRP = 2.8% + 4.33% + 0.80% + 0.55% + 1.40% = 9.88%
8.
There are three factors that can affect the shape of the Treasury yield curve (r*, IP t, and MRPt) and five
factors that can affect the shape of corporate yield curve (r*, IPt, and MRPt, DRPt, and LPt). Suppose the
real risk-free rate and inflation rate are expected to remain at their current level throughout the foreseeable
future. Consider all factors that affect the yield curve. Which of following U.S. Treasury yield curve can
take?
a. Inverted yield curve
b. Upward-sloping yield curve
c. Humped yield curve
d. Downward-sloping yield curve
e. None of above
Answer: b
If the real risk-free rate and inflation rate are expected to be constant, upward-sloping yield curve or flat
yield curve are likely to happen.
9.
The yield on a one-year Treasury security is 5.84%, and two-year Treasury security has a 7.88% yield.
Suppose the securities do not have a maturity risk premium, what is the market’s estimate of the one-year
Treasury rate one year from now?
a. 8.118%
b. 9.55%
c. 9.92%
d. 11.354%
e. 12.129%
Answer: b
From (1 + 0Rn)n = (1 + 0R1) * (1 + 1R2) * (1 + 2R3) * … * (1 + nRn-1) * [1 + E(n-1Rn)],
(1 + 0R2 – MRP)2 = (1 + 0R1) * [1 + E(1R2)] ⇨ (1 + 0.0788 – 0.002)2 = (1.0584) * [1 + E(1R2)]
⇨ E(1R2) = (1.0768)2 / (1.0584) – 1 = 9.55%
10.
Koy Corporation's 5-year bonds yield 12.50%, and 5-year T-bonds yield 5.15%. The real risk-free rate is
r* = 3.0%, the inflation premium for 5-year bonds is IP = 1.75%, the liquidity premium for Koy's bonds is
LP = 0.75% 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 is the default risk premium (DRP) on
Koy's bonds?
a. 5.94%
b. 6.60%
c. 7.26%
d. 7.99%
e. 8.78%
Answer: b
Basic equation: r = r* + IP + MRP + DRP + LP
Years to maturity
r*
In both bonds, so not needed in this problem
MRP In both bonds, so not needed in this problem
IP
In both bonds, so not needed in this problem
rKoy
rT-bond
LP
Included in corp. only
DRP = rKoy – rT-bond – LP
5
3.00%
0.40%
1.75%
12.50%
5.15%
0.75%
6.60%
11.
Assume that interest rates on 20-year Treasury and corporate bonds are as follows:
T-bond = 7.72%
AAA = 8.72%
A = 9.64%
BBB = 10.18%
The differences in these rates were probably caused primarily by:
a. Tax effects
b. Default risk differences
c. Maturity risk differences
d. Inflation differences
e. Real risk-free rate differences
Answer: b
12.
In July 2009, Hungary successfully issued 1 billion euros in bonds. The transaction was managed by
Citigroup. Who is the issuer and what is the category of bonds issued?
a. Citigroup,
b. The bank of Budapest,
c. The Hungarian government,
d. The New York Citibank,
e. The Hungarian government,
Answer: c
Corporate bonds
Municipal bonds
Foreign government bonds
Sinking bonds
T-bonds
13.
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 premium bond if the market is
at equilibrium.
Bond
Discount Rate
Bond Value
Current Yield
Bond A
(1)
$1,189.54
12.61%
Bond B
15.00%
(2)
15.00%
Bond C
16.40%
$954.58
(3)
a.
9.00%,
$988.76, 14.47%, bond A
b. 10.00%, $1,000.00, 15.71%, bond A
c. 11.00%, $1,100.00, 15.92%, bond B
d. 12.24%, $1,000.00, 16.00%, bond B
e. 10.00%, $1,250.00, 16.12%, bond C
Answer: b
(1) N = 5, PV = -1,189.54, PMT = 150, FV = 1,000 ⇨ I = 10.00%
(2) Discount rate = coupon rate. Therefore bond value = $1,000
(3) CY = Annual Coupon PMT / Price of a Bond = $150 / $954.58 = 15.71%
Premium bond = bond A
14.
Assume that a $1 million par value, semiannual coupon U.S. Treasury note with five years to maturity has a
coupon rate of 6%. The YTM of the bond is 11.00%. What is the value of the T-note?
a. $511,282.39
b. $689,825.45
c. $973,871.22
d. $811,559.35
e. $987,654.32
Answer: d
N = 10, I = 11.00/2, PMT = 1million * 6% / 2, FV = 1 million ⇨ PV = -811,559.35
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 not trading at discount.
Company
Coupon
Maturity
Last Price
Last Yield
EST
Spread
UST
(Years)
EST
Volume
(1000s)
01-01Schubert, Inc. 8.125%
$82.25
11.11%
6.20
2015
Chapman,
01-019.625%
$80.48
12.05%
7.15
Inc.
2035
01-01Rust, Inc.
4.500%
5.62%
1.37
2010
Murphy &
01-015.375%
$101.02
5.14%
0.89
Co.
2010
01-01Pickman, Inc. 7.750%
$93.11
8.80%
3.89
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.
10
72,070
30
65,275
5
59,277
5
57,465
10
56,305
a. $88.27,
Rust, Inc.
b. $95.23,
Murhpy & Co.
c. $95.18,
Murhpy & Co.
d. $100.40,
Pickman, Inc.
e. $102.80,
Schubert, Inc.
Answer: c
N = 10, I = 2.81, PMT = 2.25, FV = 100 ⇨ PV = -95.18
16.
A 10-year corporate bond has an annual coupon of 9%. The bond is currently selling at par ($1,000).
Which of the following statements is CORRECT?
a. The bond’s expected capital gains yield is zero.
b. The bond’s yield to maturity is above 9%.
c. The bond’s current yield is above 9%.
d. If the bond’s yield to maturity declines, the bond will sell at a discount.
e. The bond’s current yield is less than its expected capital gains yield.
Answer: a
17.
McCue Inc.'s bonds currently sell for $1,250. They pay a $90 annual coupon, have a 25-year maturity, and
a $1,000 par value, but they can be called in 5 years at $1,050. What is the difference between this bond's
YTM and its YTC?
a. 2.62%
b. 2.88%
c. 3.17%
d. 3.48%
e. 3.83%
Answer: a
If held to maturity:
N = Maturity
Price = PV
PMT
FV = Par
I/YR = YTM
Difference: YTM – YTC =
18.
25
$1,250
$90
$1,000
6.88%
2.62%
Warren holds a small portfolio of 4 stocks as below.
If called in 5 years:
N = Call
PV
PMT
FV = Call Price
I/YR = YTC
5
$1,250
$90
$1,050
4.26%
Stock
Artemis, Inc.
Babish & Co.
Cornell Industries
Danforth Motors
Percentage of Portfolio
20%
30%
35%
15%
Expected Return
8%
14%
12%
3%
Standard Deviation
23%
27%
30%
32%
What is expected return of the portfolio?
a. 7.84%
b. 8.11%
c. 9.68%
d. 10.45%
e. 15.68%
Answer: d
E(rp) = sum(wi * ri) = (0.2 * 0.08) + (0.3 * 0.14) + (0.35 * 0.12) + (0.15 * 0.03) = 0.1045 or 10.45%
19.
Below is investment amount, beta, and standard deviation that Jane holds in her portfolio.
Stock
Rouster Corp.
McLoving Corp.
Burger Queen, Inc.
The Big Three, Inc.
rf = 6%, RPM = 8%
Portfolio Weight
30%
15%
20%
35%
Beta
0.40
1.12
1.60
0.80
Standard Deviation
24.00%
16.00%
11.20%
12.00%
Choose the company (1) contributing the least risk to the portfolio, (2) with the least stand-alone risk if all
the stocks in the portfolio are equally weighted. And calculate (3) required return of the portfolio.
a. Rouster Corp.,
b. McLoving Corp.
c. Burger Queen, Inc.,
d. The Big Three, Inc.,
e. No such company,
Answer: a
Burger Queen, Inc.,
The Big Three, Inc.,
Rouster Corp.,
McLoving Corp,
No such company,
13.10%
14.40%
15.28%
16.72%
18.69%
The least risk to the portfolio = the least beta = Rouster Corp.
The least stand-alone risk = the least standard deviation = Burger Queen, Inc.
rp = rf + RPM*βp
Stock
Investment Beta Standard Deviation
Weight Wi * Beta i
Rouster Corp.
$
2,250
0.40
24.00%
0.30
0.12
McLoving Corp.
$
1,125
1.12
16.00%
0.15
0.168
Burger Queen, Inc. $
1,500
1.60
11.20%
0.20
0.32
The Big Three, Inc. $
2,625
0.80
12.00%
0.35
0.28
Total Investment
$
7,500
Sum = Portfolio Beta
0.888
𝛽𝑝 = ∑(𝑤𝑖 ∗ 𝛽𝑖 ) = 0.888
rp = rf + RPM*βp = 6% + (8% * 0.888) = 13.10%
20.
Data for Dana Industries is shown below. Now Dana acquires some risky assets that cause its beta to
increase by 30%. What is the stock's new required rate of return?
Initial beta
Risk free rate (rs)
1.00
6.20%
Market risk premium, RPM
6.00%
a. 14.00%
b. 14.70%
c. 15.44%
d. 16.21%
e. 17.02%
Answer: a
Old beta:
Old rs = rRF + b(RPM)
RPM
Percentage increase in beta:
Increase in IP:
Find new beta after increase =
Find old rRF: Old rs = rRF+ b(RPM): 10.2% = rRF + 1.0(6.0%): rRF = 10.2% − 6.0% =
Find new rRF: Old rRF + increase in IP =
Find new rs = new rRF + new beta(RPM)
1.00
10.20%
6.00%
30.00%
2.00%
1.30
4.20%
6.20%
14.00%