PROFESSOR: Mr. Konstantinos Kanellopoulos, MSc (L.S.E.), M.B.A.
COURSE: MBA-680-50-SUII13 Corporate Financial Theory
SEMESTER: Summer Session II
Exercises 19 , 23 , 24
(with solutions)
Konstantinos Kanellopoulos
27th August 2013
PART I EXERCISES FROM CHAPTERS 19 , 23 and 24
Exercise 4
The following table is a simplified book balance sheet for Apache Corp. at year-end 2006.
Current assets
2,490.3
$ 3,811.6
Current liabilities
Net property, plant,
21,346.3
2,019.8
Long-term debt
and equipment
Investments and other
471,7
3,619
Deferred taxes
assets
1,666.9
Other liabilities
13,191.0
Shareholders’ equity
Total
$24,308.3
$24,308.3
Total
Here is some further information:
Number of outstanding shares (N)
330.7 million
Price per share (P)
$66.51
Beta
0.98
Treasury bill rate
4.7%
20-year Treasury bond rate
4.8%
Cost of debt
6.3%
Marginal tax rate
35%
a) Calculate Apache’s WACC. Use the capital asset pricing model and the additional
information given above. Make additional assumptions and approximations as necessary.
b) What is Apache’s opportunity cost of capital?
a.
Assume that the expected future Treasury-bill rate is equal to the 20-year
Treasury bond rate (4.8%) less the average historical premium of Treasury bonds
over Treasury bills over the period 1900-2005 (1.3%), so that the risk-free rate (rf)
is 3.5%. Also assume that the market risk premium (rm – rf) is 8%. Then, using
the CAPM, we find rE as follows:
rE = rf + A  [rm – rf] = 3.5% + (0.98  8%) = 11.34%
Market value of equity (E) is equal to: 330.7  $66.51 = $21,994.9 so that:
V = $2,019.8 + $21,994.9 = $24,014.7
D/V = $2,019.8/$24,014.7 = 0.084
E/V = $21,994.9/$24,014.7 = 0.916
WACC = (0.916  11.34%) + (0.084  0.65  6.3%) = 10.73%
b.
Opportunity cost of capital = r = rD  (D/V) + rE  (E/V)
= 6.3%  0.084 + 11.34%  0.916 = 10.92%
2
Exercise 5
Chiara Company management has made the projections shown in the following table. Use this
table as a starting point to value the company as a whole. The WACC for Chiara is 12% and the
long run growth rate after year 5 is 4%. The company has $5 million debt and 865,000 shares
outstanding. What is the value per share?
1.
2.
3.
4.
5.
6.
7.
8.
Sales
Cost of Goods Sold
Other Costs
EBITDA (1 – 2 – 3)
Depreciation and Amortization
EBIT (Pretax profit) (4 – 5)
Tax at 35%
Profit after tax (6 – 7)
9.
10.
Change in working capital
Investment
(change in Gross PP&E)
Latest
year
0
40,123.0
22,879.0
8,025.0
9,219.0
5,678.0
3,541.0
1,239.4
2,301.7
1
36,351.0
21,678.0
6,797.0
7,876.0
5,890.0
1,986.0
695.1
1,290.9
2
30,155.0
17,560.0
5,078.0
7,517.0
5,670.0
1,847.0
646.5
1,200.6
Forecast
3
28,345.0
16,459.0
4,678.0
7,208.0
5,908.0
1,300.0
455.0
845.0
4
29,982.0
15,631.0
4,987.0
9,364.0
6,107.0
3,257.0
1,140.0
2,117.1
5
30,450.0
14,987.0
5,134.0
10,329.0
5,908.0
4,421.0
1,547.4
2,873.7
784.0
-54.0
-342.0
-245.0
127.0
235.0
6,547.0
7,345.0
5,398.0
5,470.0
6,420.0
6,598.0
1.
2.
3.
4.
5.
6.
7.
8.
Sales
Cost of Goods Sold
Other Costs
EBITDA (1 – 2 – 3)
Depreciation and Amortization
EBIT (Pretax profit) (4 – 5)
Tax at 35%
Profit after tax (6 – 7)
9.
10.
Change in working capital
Investment
(change in Gross PP&E)
Free Cash Flow (8 + 5 – 9 – 10)
11.
PV Free cash flow, years 1-4
PV Horizon value
PV of company
Latest
year
0
40,123.0
22,879.0
8,025.0
9,219.0
5,678.0
3,541.0
1,239.4
2,301.7
1
36,351.0
21,678.0
6,797.0
7,876.0
5,890.0
1,986.0
695.1
1,290.9
2
30,155.0
17,560.0
5,078.0
7,517.0
5,670.0
1,847.0
646.5
1,200.6
Forecast
3
28,345.0
16,459.0
4,678.0
7,208.0
5,908.0
1,300.0
455.0
845.0
4
29,982.0
15,631.0
4,987.0
9,364.0
6,107.0
3,257.0
1,140.0
2,117.1
5
30,450.0
14,987.0
5,134.0
10,329.0
5,908.0
4,421.0
1,547.4
2,873.7
784.0
-54.0
-342.0
-245.0
127.0
235.0
6,547.0
648.7
7,345.0
-110.1
5,398.0
1,814.6
5,470.0
1,528.0
6,420.0
1,677.1
6,598.0
1,948.7
3,501.6
15,480.0
18,981.7
Horizon value in year 4
24,358.1
The total value of the equity is: $18,981.7 – $5,000 = $13,981.7
Value per share = $13,981.7/865 = $16.16
3
Exercise 6
Company X has borrowed $150 maturing this year and $50 maturing in 10 years. Company Y has
borrowed $200 maturing in five years. In both cases asset value is $140. Sketch a scenario in
which X does not default but Y does.
If Company X has successfully matched the terms of its assets and liabilities, the
payment of $150 may be reasonably assured while the $50 is considerably smaller and
not due until the distant future. Company Y has a relatively large amount due in an
intermediate time frame. Thus, the risk exposure of Company Y to future events may
be greater than that for Company X.
Exercise 7
What problems are you likely to encounter when using a market-based approach for estimating the
probability that a company will default?
Market-based risk models use comparisons between a firm’s debt level and the market
value of the firm’s assets in order to assess the likelihood of default on the firm’s debt.
The probability of default is a function of the relationship between the amount of debt
and the value of the firm’s assets. Such models require estimates of growth in the value
of the firm’s assets, variability of asset values and the face value and maturity of the
firm’s debt. The value and the variability of the firm’s assets are both difficult to
estimate. Furthermore, a firm with a complex capital structure that includes several
classes of debt can not be equated to a single value to compare to the value of the firm’s
assets.
Exercise 1
Elixir Corporation has just filed for bankruptcy. Elixir is a holding company whose assets consist
of real estate worth $80 million and 100% of the equity of its two operating subsidiaries. It is
financed partly by equity and partly by an issue of $400 million of senior collateral trust bonds
that are just about to mature. Subsidiary A has issued directly $ 320 million of debentures and
$15 million of preferred stock. Subsidiary B has issued $ 180 million of senior debentures and
$60 million of subordinated debentures. A’s assets have a market value of $500 million and B’s
have a value of $220 million. How much will each security holder receive if the assets are sold
and distributed strictly according to precedence?
If the assets are sold and distributed according to strict precedence, the following
distribution will result. In Subsidiary A, the $320 million of debentures will be paid off
and ($500 million – $320 million) = $180 million will be remitted to the parent. In
Subsidiary B, the $180 million of senior debentures will be paid off and ($220 million –
4
$180 million) = $40 million of the $60 million subordinated debentures will be paid. In
the holding company, the real estate will be sold and ($180 million + $80 million) = $260
million will be paid in partial satisfaction of the $400 million senior collateral trust
bonds.
Exercise 2
a) Residential mortgages may stipulate either a fixed rate or a variable rate. As a borrower,
what considerations might cause you to prefer one rather than the other?
b) Why might holders of mortgage pass-through certificates wish the mortgages to have a
floating rate?
15.
a.
Typically, a variable-rate mortgage has a lower interest rate than a comparable
fixed-rate mortgage. Thus, you can buy a bigger house for the same mortgage
payment if you use a variable-rate mortgage. The second consideration is risk.
With a variable-rate mortgage, the borrower assumes the interest rate risk
(although in practice this is mitigated somewhat by the use of caps), whereas,
with a fixed-rate mortgage, the lending institution assumes the risk.
b. If borrowers have an option to prepay on a fixed-rate mortgage, they are likely to do so
when interest rates are low. Of course, this is not the time that lenders want to be repaid
because they do not want to reinvest at the lower rates. On the other hand, the option to
prepay has little value if rates are floating, so floating rate mortgages reduce the reinvestment
risk for holders of mortgage pass-through certificates.
Exercise 3
Dorlcote Milling has outstanding a $1 million 3% mortgage bond maturing in 10 years. The
coupon on any new debt issued by the company is 10%. The finance director, Mr. Tulliver,
cannot decide whether there is a tax benefit to repurchasing the existing bonds in the marketplace
and replacing them with new 10% bonds. What do you think? Does it matter whether bond
investors are taxed?
The existing bonds provide $30,000 per year for 10 years and a payment of $1,000,000 in
the tenth year. Assuming that all bondholders are exempt from income taxes, the market
value of the bonds is:
PV 
$30,000 $30,000
$30,000 $1,000,000



 $569,880
2
1.10
1.10
1.10 10
1.10 10
Thus, the debt could be repurchased with a payment of $569,880 today.
5
From the standpoint of the company, the cash outflows associated with the bonds are
$1,000,000 in the tenth year, and $30,000 per year, less annual tax savings of (0.35 
$30,000) = $10,500. Therefore, the net cash outflow is ($30,000 – $10,500) = $19,500
per year. To calculate the amount of new 10% debt supported by these cash flows,
discount the after-tax cash flows at the after-tax interest rate (6.5%):
PV 
$19,500 $19,500
$19,500 $1,000,000



 $672,908
2
1.065
1.065
1.065 10
1.065 10
In other words, the value of these bonds to the firm is $672,908 and the market value of
the bonds is $569,880. The firm could repurchase the bonds for $569,880 and then issue
$672,908 of new 10% debt that would require cash outflows with a present value equal to
that of the original debt. The firm could also, of course, immediately pocket the
difference ($103,028).
Now suppose that bondholders are subject to personal income taxes. High-income
investors (i.e., those in high income tax brackets) will favor low-coupon bonds and will
bid up the prices of those bonds. If the low coupon bonds are worth more to the highincome investor than they are to Dorlcote, then Dorlcote should not repurchase the bonds.
(Note that, if Dorlcote issued the 3% bonds at face value and then repurchases the bonds
for $569,880, then the company will be liable for taxes on the gain.)
6