Al Imam Mohammad Ibn Saud Islamic University (IMSIU)
College of Economics and Administrative Sciences
Department of Finance and Investment
Fin 382: Corporate Finance
Level 6: All branches
(Finance & Investment; Insurance; Business & Banking)
Capital Structure
Exercise 1
(Business risk, financial risk)
Suppose you are given the following information:
Sales
Variable Costs
Fixed Costs
Interest Expense
Taxes @ 50%
45,750,000
22,800,000
9,200,000
1,350,000
6,200,000
Calculate:
1. The break-even point in Saudi Arabian riyals
2. Degree of operating leverage (DOL)
3. Degree of Financial Leverage (DFL)
Solution
1- BEP = 18,339,869.3 SAR
2- DOL= 1.67
3- DFL=1.11
Exercise 2
(Capital structure in perfect capital markets: Modigliani and Miller)
ALYAMAMA Co. is currently an all-equity firm (Unlevered) with an expected return of
12%. The firm expects that the future EBIT will be SAR 276,900 forever and the firm's
tax rate is 35%. Assume that the firm distributes all the net income to the equity
holders. The firm is considering a leveraged recapitalization in which it would borrow
SAR 300,000 and repurchase existing shares. The cost of debt is 10%, Calculate:
1. The value of the firm with leverage.
2. The expected return of equity after recapitalization (firm with leverage)
3. The cost of capital of the firm after recapitalization (firm with leverage)
Solution
-1-
1- VL =1,604,875
2- rL= 12.29%
3- WACC =11.2%
Exercise 3
(Capital structure and the cost of bankruptcy)
ABC Co., an unlevered firm, has expected earnings before interest and taxes of $2
million per year. The firm's tax rate is 40%, and its market value is V = Equity = $12
million. The company is considering the use of debt; The interest rate on debt is 12%.
The firm's analysts have estimated that the present value of any bankruptcy cost is $8
million, and that the probability of bankruptcy will increase with leverage according to
the following schedule:
Value of Debt (D)
2,500,000
5,000,000
7,500,000
8,000,000
9,000,000
10,000,000
12,500,000
Probability of default (pD)
0
0.08
0.205
0.300
0.450
0.525
0.700
1- What is the optimal capital structure when bankruptcy costs are considered?
2- What will the value of the firm be at this optimal capital structure?
Solution
1- Since VL = VU + PV (tax shield) - PV (bankruptcy costs), we should try to find the
debt level which maximizes PV (tax shield) -PV (bankruptcy costs).
The following table shows the present value of the debt tax shield and the present value
of bankruptcy costs and their difference for the different debt levels.
Value of
Debt (D)
2,500,000
5,000,000
7,500,000
8,000,000
9,000,000
10,000,000
12,500,000
Probability
of Failure
(pD)
0
0.08
0.205
0.300
0.450
0.525
0.700
PV (tax
shield)
(0.4×D)
1,000,000
2,000,000
3,000,000
3,200,000
3,600,000
4,000,000
5,000,000
PV (bank
cost)
(PD×8M)
0
640,000
1,640,000
2,400,000
3,600,000
4,200,000
5,600,000
Obviously, the optimal debt level is $5,000,000 or $7,500,000
-2-
Value added
of debt
1,000,000
1,360,000
1,360,000
800,000
0
-200,000
-600,000
2- With this optimal capital structure, the total value of the firm is
VL = VU + value added of debt = 12,000,000 + 1,360,000 = 13,360,000.
Exercise 4
(EPS, ROE)
ABC Corporation has no debt outstanding and a total market value of SAR 140,000. Earnings
before interest and taxes (EBIT) are projected to be SAR 22,000 if economic conditions are
normal. If there is strong expansion in the economy, then EBIT will be 20% higher. If there is a
recession, then EBIT will be 30% lower. ABC Corporation is considering a SAR 56,000 debt issue
with a 6% interest rate. The proceeds will be used to repurchase shares of stock. There are
currently 6000 shares outstanding. Ignore taxes for this problem.
1. Calculate earnings per share (EPS) and return on equity (ROE) under each of the three
economic scenarios after recapitalization.
Solution
EBIT
After recapitalization (With debt)
Recession
Normal
Expansion
15,400
22,000
26,400
3,360
3,360
3,360
Interests
EBT
12,040
18,640
23,040
Taxes
0
0
0
Net
Income
# of
shares
EPS
12,040
18,640
23,040
3,600
3,600
3,600
3.34
5.18
6.40
22.19%
27.43%
ROE
14.33%
Exercise 5 (Levered, Unlevered)
Alfalah, Inc, a prominent consumer products firm, is debating whether or not to convert its
all-equity capital structure to one that is 30 % debt. Currently, there are 1,200 shares
outstanding and the price per share is SAR 90 .EBIT is expected to remain at SAR3,000 per
year forever. The interest rate on new debt is 8%, and there are no taxes.
-3-
1.
Fahad, a shareholder of the firm, owns 100 shares of stock. What is his cash flow
under the current capital structure, assuming the firm has a dividend payout rate of 100
percent!
2.
What will Fahad’s cash flow be under the proposed capital structure of the firm?
Assume that he keeps all 100 of his shares.
3.
Suppose Alfalah does convert, but Fahad prefers the current all-equity capital original
capital structure. Show how he could unlevered his shares of stock to recreate the original
capital structure?
Solution
1-2
I
II
EBIT
3,000
3,000
(INTEREST@ 8%)
0
2,592
EBT
3,000
408
(TAX@0)
0
0
NET INCOME
3,000
408
# OF SHARES
1,200
840
EPS =NI / # OF SHARES
2.500
0.4857
MV
108,000
108,000
Debt
0
32,400
A and B: Fahad's cash flow
250
48.57
3- To undo leverage, investors must loan out money.
The company here borrowed an amount equal to 30% of its value. Fahad can unlevered
the stock by simply loaning out money in the same proportion.
Fahad current wealth = 100 * 90 = SAR9,000
Fahad must sell stocks an amount of 30% of his wealth
= 9,000 * 0.3 = SAR2700 this mean 30 stocks of the 100 he owned. Then, he loans out
the SAR2700 at 8%.
The payoffs calculated in the table below:
# OF SHARES
EPS
Earnings for 70shares
+ interest on 2,700 @ 8%
Fahad's cash flow
-4-
100-30=70
0.4857
34
216
250