Faculteit Bedrijf, Bestuur en Technologie
Afdeling Financieel Management en Bedrijfseconomie
Kenmerk: FMBE 03.100/br
Datum: 27 november 2003
Exam
Corporate Finance (186010)
(Vermogensmarkten en Ondernemingsfinanciering)
Date:
November 27, 2003
Time:
13:30 – 17:00
Place:
CC 1
Teacher:
B. Roorda
Questions may be answered in Dutch or English
The exam consists of 5 questions
The points are distributed is as follows:
Question 1
Question 2
Question 3
Question 4
Question 5
15 points
15 points
20 points
20 points
30 points
NB: The final grade for the course also depends on your grade for the
compulsary group assignments
Question 1 [15 points]
a. Determine the price of a 10-year annuity paying $10 each year with opportunity cost of capital
10%. Also determine its annuity factor.
b. A growth stock with market capitalization rate of 20%, has 40% of its value from growth
opportunities. Determine its price/earnings ratio (current price / earnings per share).
c. The total value of firm L is 100 ($million). The dividend policy of the firm is a 5% dividend yield;
its debt policy is to be 75% equity financed. Investors expect a 16% return on stocks of firm L,
and ask 4% interest on firm L’s debt. What constant expected growth rate of the firm is in line
with these figures (assuming no new equity will be issued)? What then are the expected earnings
in year 1 and in year 5?
Question 2 [15 points]
A company considers to undertake a 2-year project that requires an initial investment (at t=0) of 1.5 (all
cash flows in $million). Expected (after-tax) revenues are 0.25 in year 1 (at t=1) and 1.6 in year two (at
t=2). The company’s cost of capital is 12%, and its cost of debt is 6%. The company is 50% equity
financed. The risk-free rate is 4%. Assume that the project is a carbon copy of the firm.
a. Explain, in two or three sentences, this last assumption. Determine the Net Present Value (NPV)
of the project. Is the project acceptable according to the NPV-rule?
So far we ignored tax deductions. Suppose the effective tax rate is 35%.
b. Determine the (after-tax) Weighted Average Cost of Capital (WACC) for the project, and adapt
your calculation of NPV in part a on the basis of this WACC value.
Alternatively, one could determine the present value of the project’s tax shield directly, and then compute
the Adjusted Present Value (APV) of the project. The outcome will depend on the level of debt assigned
to the project.
c. Explain in one or two sentences the difference between the ‘debt rebalanced’ financing rule and
the ‘debt fixed’ financing rule. Which one corresponds best to (after-tax) WACC calculations?
d. The project’s debt level is set equal to 0.75 in year 0, and 0.71 in year 1. Is this in line with the
‘debt fixed’ rule? Compute the corresponding present value of the tax shield, and compare this to
your answer in part b. Is the project acceptable according to the Adjusted Present Value (APV)–
rule?
Question 3 [20 points]
The following table shows some estimates of the risk of stock A, stock B, and the AEX. The listed
volatility is the standard deviation of the asset return over next year. Assume CAPM theory holds with
AEX as market portfolio.
stock A
stock B
AEX
current price
(euro)
15
7.50
333
volatility
-60%
30%
correlation of stock returns
with AEX returns
0.20
---
Beta of
Equity
0.4
---
a. Complete the table, i.e, reconstruct the 5 figures that are not given in the table.
expected
return
10%
20%
16%
b. Determine a portfolio (pf) in stock A and B with the same level of systematic risk as in the AEX.
What is the unique variance of pf, assuming that the correlation between returns of stock A and B
is 0.3? Is pf efficient?
c. What is the certainty equivalent of selling stock B at the end of the year?
Question 4 [20 points]
Are the following statements correct? Motivate your answers.
a. The firms H and L only differ in fanancial structure; firm H is 80% debt financed, firm L for 40%,
both at the risk free interest rate of 5%. According to the Modigliani-Miller (MM) theory, $1
invested in firm H , and, alternatively, borrowing $2 and investing $3 in equity of firm L, will
produce identical cashflows.
b. An assets sells for $8, and a company offers to stockholders the right to buy one new share for $7,
for every 7 shares that they currently hold. Ignoring taxes, this right is worth more than $0.85.
c. According to the pecking order theory, issuing debt is preferred over issuing equity, so companies
maximize leverage.
d. Investing an equal amount into two projects always has an internal rate of return (IRR) equal to
the average IRR of both projects.
e. The dividend policy of a company, which is based on Lintner’s model, is to payout dividend in
year t equal to 10% of the earnings per share in year t plus 60% of the dividend in year t-1. This
implies that their target ratio is 25%.
Question 5 [30 points]
Company ABC has the following (stylized) balance sheet, in million $.
Current Assets
Plant and Equipment
Total Assets
40
85
125
Debt:
Equity
Firm Value
75
50
125
The opportunity cost of capital of investing in ABC’s assets is given by r = 15%. Costs of debt are given
by rD = 7%. The corporate tax rate (TC) is equal to 35%.
a. Determine the cost of equity ( rE) and the (‘after tax’) weighted average cost of capital (WACC) of
the firm.
The company considers replacing $25 million of equity by long term debt. Because of increased leverage,
the cost of debt is set to 8%.
b. Compute the WACC under this new capital structure.
c. Make a sketch of WACC as function of leverage (D/E) that is in line with the given information.
d. Analysts estimate that the new financial structure will cause an increase of costs of financial
distress, and that the cost of capital will increase correspondingly to 16%. Is the new capital
structure an improvement according to the trade-off theory?
[end of the exam]
Answers Exam Corporate Finance November 27 2003
Question 1
a. C  [1/r – 1/(r(1+r)t)] = 10  [1/0.1 – 1/0.1(1.110)] = 10  [10 – 3.855] = 10  6.145 = 61.45.
Annuity factor is 6.145. cf BM p39
b. P0 = EPS/r + PVGO = EPS/0.20 + 0.4 P0; so EPS = 0.12 P0, hence ratio is 1/0.12 = 8.33
c. From data for equity we have: g = r - DIV1 / P0 = 16%-5% = 11%. This must also be the growth rate of
the firm if the D/E ratio is kept fixed (and no new equity is issued) [for more background: cf. CQ 16.2;
p837 (not part of exam)]. Expected earnings in year 1 are 13 (as rA = 0.25  4% + 0.75  16% = 13%);
alternatively: for interest: 0.25  100  4% = 1, for dividends 0.75  100  5% = 3.75, for growth 0.75 
100  11% = 8.25 from retained earnings (the rest of growth is by extending debt with 0.25  100  11%
= 2.75). In year 5: expected growthrate of everything is 11% annually, so expected earnings year 5 =
1.114  earnings year 1 = 19.735.
Question 2
a. Carbon copy: see book. NPV(@ 12%) = -1.5 + 0.25/1.121 + 1.6 /1.122 = -0.0012755.
b. rE = rA + D/E (rA – rD) = 18%; WACC = (1-0.35)  0.5  6% + 0.5  18% = 10.95%.
NPV(@WACC) = 0.025093.
c. See book
d. Debt fixed: set at 50% of project’s value. Year 0: 0.5  PV = 0.5  (1.5 – 0.00128) (cf part a) = 0.749.
Year 1: 0.5  1.6/1.12 =0.714. Indeed in line with ‘debt fixed’ rule. Interest level: 6%  0.75 = 0.045 in
year 1, 6%  0.71 (or 0.75) = 0.0426. Tax deduction: TC  interest, so $15.750 (year 1) and $14.910 in
year 2. PV(tax shield) = 15.750/1.06 + 14.910/1.062 = 14.858 + 13.270 = 28.128 . Induced value of tax
shield in part b: 25.093 + 1.276 = 26.369. Quite close. [Extra: with debt rebalanced perhaps closer? Same
expected cash flows, discount tax shield year 2 by 1/(1+rD)  1/(1+rA), gives PV(tax shield) =
15.750/1.06 + 14.910/(1.06  1.12) = 14.858 + 12558 = 27416, indeed closer. Perfect replication of
WACC result: more mathematics]
Question 3
a. In AEX row: beta=1, correlation =1;
For stock A: A = AM  A / M , hence 0.4 = 0.2  A / 0.3, so A = 60%.
For stock B: first B from the Security Market Line (SML): rB = rf + B (rM – rf), with rM = rAEX =16%,
and rf = 6% (from fact that stock A and AEX are at SML). So B = 0.14 / 0.10 = 1.4. Correlation BM
from B = BM  B / M , hence BM = 0.3  1.4 / 0.6 = 0.7.
b. Same , hence 60% in stock A, and 40% in stock B; (in terms of numbers of stocks: 1 stock A : euro
15, hence euro 15  0.40/0.60 = euro 10 in stock B; or: 3 stock A and 4 stock B). Rpf = 0.6  RA + 0.4 
RB , hence pf2 =0.42 A2 + 0.62 B2 + 2  0.4  0.6 AB A B = 0.242 + 0.362 + 0.1728AB = 0.1872 +
0.05184 = 0.23904. So unique variance is 0.23904 – 0.302 = 0.14904. Not efficient (compare with AEX).
c. Expected value: 1.20  7.50 = 9. Certainty equivalent (CEQ) satisfies: 9/1.20 = CEQ/1.06. So CEQ = 9
 1.06 / 1.20 = 7.95.
Question 4.
a. No: : Let V denote the value of the firms. 1$ in firm H = 0.80$ in debt of H, and 0.20$ in equity of H,
which is 0.20/(0.20V)  equity value; the other investment has $3 in equity of L, which is fraction
3/(0.6V), hence larger part of (uncertain) profit, hence cannot be the same.
(Yes, if you took $1 in firm H as “1$ in equity of firm H”, cf. exam Nov 2002. Then $1 in equity of H
yields cash flow (1/0.2V)  (profit – interest) = (1/0.2V)  (profit – 0.8 V rD) = 5/V  profit – 0.20. The
other investement gives (3/0.6V) (profit – interest) – 2  rD = (3/0.6V)  (profit – 0.4  V  rD) = 5/V 
profit – 0.10 – 0.10.
b. Yes: Value after issue: (7  8 + 7)/8 = 7.875; value is 0.875.
c. No, internal financing (in effect increasing equity) preferred over debt.
d. No; easy to find counterexample.
e. Yes. Rewrite in Lintner’s form: DIVt = 0.10  EPSt + 0.60 DIVt-1 = DIVt-1 + adj rate  (target ratio 
EPSt – DIVt-1). So adjustment rate is 0.40, and target rate is 0.10/0.40 = 0.25.
Question 5
a. rE = rA + D/E (rA – rD) = 0.15 + 75/50  (0.15-0.07) = 27%.
WACC = (1-0.35)  75/125  7% + 50/125  27% = 0.65  4.2% + 10.8% = 13.53%.
b. r = 15% independent of leveraging. MM proposition II gives rEnew = rA + D/E  (rA - rDnew ) = 15% + 4
 7% = 43%. Hence WACC = (1-0.35)  0.8  8% + 0.2  43% = 0.65  6.4% + 8.6 % = 12.76%.
c. book
d. Same computations, now with rAnew = 16%, give now rEnew = 16% + 4  8% = 48%. Hence WACC =
(1-0.35)  0.8  8% + 0.2  48% = 0.65  6.4% + 9.6 % = 13.76% (In fact immediate: WACC also +1%).
Not an improvement. (moreover, how about costs of transition to new capital structure?).
[end of answers]