PROFESSOR: Mr. Konstantinos Kanellopoulos, MSc (L.S.E.), M.B.A.
COURSE: MBA-680-50-SUII12 Corporate Financial Theory
SEMESTER: Summer Session II
Exercises 18 , 19 , 23
(with solutions)
Konstantinos Kanellopoulos
14th August 2012
PART I EXERCISES FROM CHAPTERS 18, 19 and 23
Exercise 1
Take a look at the Circular File’s market value balance sheet:
Net working capital
$ 20
$25
Fixed assets
10
5
Total assets
$30
$30
Bonds outstanding
Common stock
Total value
Who gains and who loses from the following maneuvers?
a) Circular scrapes up $5 in cash and pays a cash dividend.
b) Circular halts operations, sells its fixed assets, and converts net working capital into $20
cash. Unfortunately the fixed assets fetch only $6 on the secondhand market. The $26 cash
is invested in Treasury bills.
a) Circular encounters an acceptable investment opportunity, NPV = 0, requiring an
investment of $10. The firm borrows to finance the project. The new debt has the same
security, seniority, etc., as the old.
b) Suppose that the new project has NPV = +$2 and is financed by an issue of preferred stock.
a) The lenders agree to extend the maturity of their loan from one year to two in order to give
Circular a chance to recover.
Solution 1
a.
Stockholders win. Bond value falls since the value of assets securing the bond has fallen.
b.
Bondholder wins if we assume the cash is left invested in Treasury bills. The bondholder is
sure to get $26 plus interest. Stock value is zero because there is no chance that the firm value
can rise above $50.
c.
The bondholders lose. The firm adds assets worth $10 and debt worth $10. This would
increase Circular’s debt ratio, leaving the old bondholders more exposed. The old
bondholders’ loss is the stockholders’ gain.
d.
Both bondholders and stockholders win. They share the (net) increase in firm value. The
bondholders’ position is not eroded by the issue of a junior security. (We assume that the
preferred does not lead to still more game playing and that the new investment does not
make the firm’s assets safer or riskier.)
e.
Bondholders lose because they are at risk for a longer time. Stockholders win.
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Exercise 2
a) Who benefits from the fine print in bond contracts when the firm gets into financial
trouble? Give a one-sentence answer.
b) Who benefits from the fine print when the bonds are issued? Suppose the firm is offered
the choice of issuing (i) a bond with standard restrictions on dividend payout, additional
borrowing, etc., and (ii) a bond with minimal restrictions but much higher interest rate?
Suppose the rates on both (i) and (ii) are fair from the viewpoint of lenders. Which bond
would you expect the firm to issue? Why?
Solution 2
a.
The bondholders benefit. The fine print limits actions that transfer wealth from
the bondholders to the stockholders.
b.
The stockholders benefit. In the absence of fine print, bondholders charge a
higher rate of interest to ensure that they receive a fair deal. The firm would
probably issue the bond with standard restrictions. It is likely that the restrictions
would be less costly than the higher interest rate.
Exercise 3
Most financial managers measure debt ratios from their companies’ book balance sheets.
Financial economists tend to emphasize ratios from market-value balance sheets. Which is the
right measure in principle? Does the trade-off theory propose to explain book or market
leverage? How about the pecking-order theory?
Solution 3
The right measure in principle is the ratio derived from market-value balance sheets. Book
balance sheets represent historical values for debt and equity which can be significantly different
from market values. Any changes in capital structure are made at current market values.
The trade-off theory proposes to explain market leverage. Increases or decreases in debt levels
take place at market values. For example, a decision to reduce the likelihood of financial distress
by retirement of debt means that existing debt is acquired at market value, and that the resulting
decrease in interest tax shields is based on the market value of the retired debt. Similarly, a
decision to increase interest tax shields by increasing debt requires that new debt be issued at
current market prices.
Similarly, the pecking-order theory is based on market values of debt and equity. Internal
financing from reinvested earnings is equity financing based on current market values; the
alternative to increased internal financing is a distribution of earnings to shareholders. Debt
capacity is measured by the current market value of debt because the financial markets view the
amount of existing debt as the payment required to pay off that debt.
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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%
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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
784.0
6,547.0
648.7
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
-54.0
-342.0
-245.0
127.0
235.0
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
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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.
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