Problem Set III Solutions
Capital Structure, Financing, and Financial Distress
1.
Let number of shares before repurchase be x. Thus earnings of the firm are thus $6x and the
market value of the firm is $40x. After repurchase, the market value of the firm remains at
$40x. However to repurchase 0.25x of shares (leaving 0.75x shares outstanding), $10x (25%
of firm) of debt is issued. The yield on that debt is 6%. Thus annual interest is 0.06*10x =
0.6x. Hence earnings of the firm after interest payments at the new capital structure = 6x –
0.6x = 5.4x. Now earnings per share = 5.4x/0.75x = $7.20.
2.
Since the company is reducing the scale, WACC is the appropriate discount rate. To calculate
WACC, first determine the cost of equity with CAPM = .06 + 1.2(.14  .06) = 0.156. The cost
of debt (after tax) = .08*(1  .3) = 0.056. The debttoequity ratio is 2/3. That is the proportion
of debt of total assets is 0.4 and that of equity is 0.6. Thus WACC = 0.4*.056 + 0.6*0.156
= .116 or 11.6%. The amount at which you can sell the P&E (after tax) = $5 million – ($5 
$4)*0.3 million = $4.7 Million. Annual sales reduce by $1.5 million, costs reduce by $1
million, and depreciation reduces by $0.2 million ($4 million/20).
Thus
∆
CFAT = (1.5 – (1) – (0.2))(10.3) + (0.2) = $0.41 million
NPV of selling = 4.7 –0.41*
20
116
.
A
= $1,559,105.36
Hence reduce the production.
3.
All numbers in this problem are in millions.
Step 1: Assuming all equity
The debttoequity ratio of the industry (a proxy for the pure play firm) is .5 and industry
equity beta is 1.5. Beta of assets:
1.09
.75
*
.5
1
1.5
)
T
1
(
*
E
D
1
E
A
=
+
=

+
β
=
β
Using CAPM E(R) for project = .06 + 1.09 *(.12  .06) = 12.55%
The incremental annual cash flows
∆
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