#:________________
SECTION:_____
FIRST STUDENT NAME:________________________
LAST NAME: ______________________
UNIVERSITY AT BUFFALO
MGF405 ADVANCED CORPORATE FINANCE
Professor: Sahn W. Huh
SAMPLE MIDTERM II (TYPE A): Suggested Solution
April
SECTION I (1.5 point x 10 = 15 points): Choose only one of the 5 choices and clearly circle the
letter in each question. No credit will be given based on scratch work in or between lines without
clear marking.
1. As the degree of sensitivity of a project to a single variable rises, the
A. lower the forecasting risk of the project.
B. smaller the range of possible outcomes given a pre-defined range of values for the
input.
C. more attention management should place on accurately forecasting the value of
that variable.
D. lower the maximum potential value of the project.
E. lower the maximum potential loss of the project.
Ans: C
2. Which of the following statements is/are correct concerning the accounting break-even point?
I. The net income is equal to zero at the accounting break-even point.
II. The net present value is equal to zero at the accounting break-even point.
III. The quantity sold at the accounting break-even point is equal to the total fixed costs
plus depreciation divided by the contribution margin.
IV. The quantity sold at the accounting break-even point is equal to the total fixed costs divided
by the contribution margin.
A. I and III only
B. I and IV only
C. II and III only
D. II and IV only
E. I, II, and IV only
Ans: A
3. Including the option to expand in your project analysis will tend to
A. extend the duration of a project but not affect the project's net present value.
B. increase the cash flows of a project but decrease the project's net present value.
C. increase the net present value of a project.
D. decrease the net present value of a project.
E. have no effect on either a project's cash flows or its net present value.
Ans: C
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4. In the financial break-even analysis, the EAC is used to
A. determine the opportunity cost of investment.
B. allocate depreciation over the life of the project.
C. allocate the initial investment over the life of the project.
D. determine the contribution margin to fixed costs.
E. None of the above.
Ans: C
5. The relationship between nominal rates, real rates, and inflation is known as the
A. Miller and Modigliani theorem.
B. Fisher effect.
C. Gordon growth model.
D. term structure of interest rates.
E. interest rate risk premium.
Ans: B
6. Which of the following statements is/are true?
(i)
If the coupon rate of a bond is higher than the yield to maturity, the bond sells at a
discount.
(ii)
When interest rates increase, the prices of bonds will also increase because investors
buying bonds at that time will receive higher yield.
A. (i)
B. (ii)
C. both (i) and (ii)
D. none of the above
E. insufficient information
Ans: D
7. You find that yesterday the bid price of a 20-year Treasury bond was quoted as Bid 135:22
in the WSJ. Assume that the face value of the bond is $1,000. What was the actual bid price of
the Treasury bond (in dollars) yesterday?
A.
B.
C.
D.
E.
$135.22
$1,356.88
$1,350.22
$1,352.20
insufficient information
Ans: B
8. The total number of shares outstanding in UBCorp is 20,000 shares, 4 directors will be elected,
and 7 candidates run for the BOD seats in the cumulative voting. How many shares will
guarantee a seat in the board of UBCorp?
A. 10,000 shares
B. 10,001 shares
C. 4,000 shares
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D. 4,001 shares
E. 2,501 shares
Ans: D
9. A US firm plans to raise debt capital in Tokyo (Japan) by issuing bonds which will be
denominated in the Japanese Yen. These bonds can be referred to as:
A.
B.
C.
D.
E.
Eurobonds
Foreign bonds, specifically Samurai bonds
Foreign bonds, specifically Yankee bonds
Eurobonds, specifically Samurai bonds
Eurobonds, specifically Yankee bonds
Ans: B
10. The formula for calculating beta is given by the dividing the ___________ of the stock return
with the market portfolio return by the ___________ of the market portfolio return.
A. variance; covariance
B. covariance; variance
C. standard deviation; variance
D. expected return; variance
E. expected return; covariance
Ans: B
3
SECTION II (85 points): Whenever necessary, show the equations or expressions leading to the
final answer. Note that in some questions no partial credit (NPC) is available. In multiple choice
questions, choose only one of the 5 choices and clearly circle the letter. In the final answers,
show dollar amounts rounded up to a cent (e.g., $25.38) and other numbers rounded up to 4
decimal places (e.g., 2.3857).
1. (15 points) Your company has developed a new product called M. If M is successful, the PV of
the payoff at the time M is brought to the market is $30,000. If M fails, the PV of the payoff is
$10,000. If M goes directly to the market, there is a 50% chance of success. Alternatively, you
can delay the launch by one year and spend $2,000 now to test-market the product. Testmarketing will improve M next year and thus increase the probability of success to 85%. The
discount rate is 12%. You should decide which strategy is better.
1) (6 pts) Strategy A is to directly go to the market now without test-marketing. What is the NPV
of this strategy?
Sol 1) In the CF diagram, at t=0 you have $30,000 (with a prob. of 0.5) or
$10,000 (with a prob. of 0.5),
but nothing at t=1. Thus,
NPV = 30,000 x (0.5) + 10,000 x (0.5)
= $20,000
2) (6 pts) Strategy B is to test-market at t=0, and then go to the market next year. What is the
NPV of Strategy B?
Sol 2) In the CF diagram, at t=0 you have a cost of $2,000, and
at t=1 you have $30,000 (with a prob. of 0.85) or
$10,000 (with a prob. of 0.15)
Thus, NPV = -2,000 + [30,000 x (0.85) + 10,000 x (0.15)]/(1.12)
= $22,107.14
3) (3 pts) Based on the above information, which strategy should be chosen?
Sol 3) Strategy B because its NPV is higher.
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2. (19 points) Consider a coupon bond with a coupon rate of 10%. The par value is $1000 and the
bond has 20 years to maturity. The yield to maturity is 8%.
1) (a) (5 pts: NPC) The coupon interest is paid annually. Show the equation for computing the
price of the bond.
Sol (a) m=1 (=k), CR=0.1, FV=1000, annual coupon=100, n=20, i=0.08. Draw a CF diagram.
, or 100
, or
.
.
.
= 100
.
.
.
,
.
.
.
.
.
100
.
.
(b) (2 pts) What is the price of the bond (P0)?: A) 1,196.36 B) 1,916.36 C) 1,169.36
D) 1,619.36 E) 1,916.63
Sol: A. P0 = 981.81 + 214.55 = 1,196.36
2) The coupon interest is paid annually. The value of this bond at the end of year 1 (at t=1)
consists two of components. (a) (1 pts) What is the accrued coupon interest at t=1?
Sol 2) (a) At t=1, you will have a coupon interest of 100.
(b) (5 pts: NPC) Show the equation to find the PV (evaluated at t=1) of the remaining CFs from
the bond (i.e., P1).
Sol (b) You will receive coupon interest from t=2 to t=20 as well as the FV=1000 at t=20. So you
can evaluate all these CFs at t=1, i.e., get P1. Because one year has passed, note that at t=1 only
19 years are left over (n=19). Thus, use your another diagram,
.
.
.
= 100
or = 100
.
.
.
or
.
.
100
.
.
.
.
.
(c) (1 pts) What is the value of the bond at t=1 [i.e., V1 = (Coupon Interest at t=1) + P1]?
A) 1,293.07 B) 1,292.07 C) 1,929.07 D) 1,392.07 E) 1,192.07
Sol: B. V1 = (coupon interest accrues at t=1) + P1 = 100 + (960.36 + 231.71) = 1,292.07
3) The coupon interest is paid semi-annually. (a) (3 pts: NPC) Show the equation for computing
the price of the bond.
Sol 1) (a) m=2 (=k), CR=0.1, FV=1000, annual coupon=100, semi-annual coupon = 100/2 = 50,
n=20, i=0.08. Draw a CF diagram.
, or =50
, or
.
.
.
.
= 50
.
.
.
.
,
.
.
.
50
.
.
(b) (2 pts) What is the price of the bond (P0)? A) 1,297.93 B) 1,719.93 C) 1,197.93 D) 1,917.93
E) 1,297.39
Sol (b): C. P0 = 989.64 + 208.29 = 1,197.93
5
3. (19 points) BBI has an outstanding 30-year maturity bond with a 9% coupon rate that can be
called in one year. The bond makes annual coupon payments. The call premium is set at $130
(including the coupon interest of $90 accrued at t=1) over the par value. The face (par) value of
the bond is $1,000. There is a 40% chance that the interest rate in one year will be 13%, and a
60% chance that the interest rate will be 8%. The current interest rate is 10%. To obtain the price
of BBIs callable bond, answer the following questions.
1) Suppose that the interest rate increases to 13% in a year. (a) (5 pts: NPC) In this case, what is
the probable value of the bond at the end of year 1 (at t=1)? (b) (2 pts) Will BBI call the bond at
t=1? Why or why not? (c) (1 pts) Based on the available information, what is the actual value of
the bond to the bondholder at t=1?
Sol 1) (a) If i=0.1 => i=0.13 at t=1, the probable value of the bond at t=1 will be the coupon
interest of 90, plus P1 (the present value of the coupon interest to be received from t=2 to t=30
(29 years left) plus FV, evaluated at t=1). So with CR=0.09 and i=0.13,
= (coupon interest at t=1) + P1 = 90 +
.
= 90 + 90
.
.
.
.
.
.
.
= 90 + 90
.
.
= 90 + 672.31 + 28.89 = $791.20
(b) This is lower than the exercise price of $1,130. So BBI will NOT call the bond.
(c) So $791.20 is the actual value of the bond to bondholders at t=1.
2) Suppose that the interest rate decreases to 8% in a year. (a) (5 pts: NPC) In this case, what is
the probable value of the bond to the bondholder at the end of year 1 (t=1)? (b) (2 pts) Will BBI
call the bond at t=1? Why or why not? (c) (1 pts) Based on the available information, what is the
actual value of the bond to the bondholder at t=1?
Sol 2) (a) If i=0.11 => i=0.08 at t=1, the probable value at t=1 will be the coupon interest of
90, plus P1 (the present value of the coupon interest to be received from t=2 to t=30 (29 years
left) plus FV, evaluated at t=1). So with CR=0.09 and i=0.08,
= (coupon interest amount at t=1) + P1 = 90 +
.
= 90 + 90
.
.
.
= 90 + 90
.
.
.
.
+
.
= 90 + 1,004.26 + 107.33 = $1,201.59
(b) This is higher than the exercise price of $1,130. So the company WILL CALL the bond at
$1,130. (the firm will choose to give out the lower and get back the higher!).
(c) So $1,130 is the actual value of the bond to bondholders at t=1 (not $1,201.59).
3) (a) (2 pts) Given the information above, what is the expected value of the bond to the
bondholder at t=1? (b) (1 pts) Thus, what is the price of the callable bond?
Sol 3) (a) V1 = 791.20 with a probability of 0.4
= 1,130 with a probability of 0.6
Thus, the expected value at t=1 is: E(V1) = (791.20)(0.4) + (1,130)(0.6) = 994.48
(b) Because i=0.1 for the first period, the price (P0) of the callable bond is:
P0 = 994.48/(1.1) = $904.07
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4. (15 points) UBC has 2 million shares of common shares outstanding. The stock sells at $25 per
share. The firms debt is publicly traded and was recently quoted at 95% of the face value. It has
a total face value of $8 million, and its yield to maturity is 11%. The risk-free rate is 6%, and the
market risk premium is 7%. The firms beta is 1.8 and the corporate tax rate is 35%.
1) (5 pts) Calculate the weights for UBCs equity and debt based on their market values.
Sol 1) E = 2M x $25 = $50M
D = $8M x 0.95 = $7.6M
So, xE = E/(E+D) = 50M/(50M+7.6M) = 0.8681
Thus, xD = D/(E+D) (or = 1 xE) = 7.6M/(50M+7.6M) = 0.1319
2) (5 pts) What is the cost of equity capital for UBC?
Sol 2) RF=0.06, (RM RF) = 0.07, and =1.8. To get the cost of equity capital, use
CAPM/SML: RE = RF + (RM RF)
= 0.06 + 1.8(0.07)
= 0.186
3) (5 pts) Given the information above, what is the weighted average cost of capital (RWACC) for
UBC?
Sol 3) RD=0.11, and tC=0.35. Lets get
RWACC xE RE xD RD (1 tc )
E
D
RE
RD (1 tc )
ED
ED
= (0.8681)(0.186) + (0.1319)(0.11)(1 0.35)
= 0.1709
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5. (17 points) AB Corp. (ABC) recently issued new securities to finance a project. The project
cost $15 million and the firm paid a total of $850,000 in flotation costs. The equity issued had a
flotation cost of 7%, whereas the debt issued has a flotation cost of 3%. ABC issued new
securities in the same proportion as its target capital structure (i.e., target debt-equity ratio).
1) (4 pts) Based on the information given above, what is the weighted average flotation cost for
the project?
Sol 1) YNet = $15M, Flotation cost = $0.85M, so YGross = $15M + $0.85M = $15.85M. We can use
the relation: YGross (1 fWAVG) = YNet.
15.85M(1 fWAVG) = 15M => (1 fWAVG) = 0.946372.
Thus,
fWAVG = 0.0536 .(a)
2) (7 pts) Now you like to find ABCs target debt-equity ratio. First, let D/E = u. Then fill out the
following part using all the information available so that the right-hand side of the equation
includes only one unknown (i.e., u).
fWAVG = xEfE + xPfP + xDfD
=
Sol 2) Let D/E = u. Then D = uE. Also, fE = 0.07 and fD = 0.03 are given. Also xP = fP = 0. Thus,
fWAVG =
=
=
0.07
0.03
0.07
0.03 .(b)
3) (6 pts) Given the information in 1) and 2) above, solve out for the target debt-equity ratio (i.e.,
u).
0.07
Sol 3) Let (a) = (b): 0.0536 =
=
.
+
.
0.03
=
.
.
So u=0.6949 (or more precisely 0.6929 if we use more decimal places in (a) above).
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