Corporate Finance
Break-even EBIT (with and without taxes)
1. Alpha Company is looking at two different capital structures, one an all-equity firm and the other a leveraged firm with $2,000,000 of debt financing at 8% interest. The all-equity firm will have a value of $4,000,000 and 400,000 shares outstanding. The leveraged firm will have 200,000 shares outstanding.
a. Find the break-even EBIT for Alpha Company using EPS if there are no corporate taxes
b. Find the break-even EBIT for Alpha Company using EPS if the corporate tax rate is 30%
c. What do you notice about these two break-even EBITs for Alpha Company?
Answer: a. Interest expense = $2,000,000(0.08) = $160,000
BE = (EBIT/400,000) = (EBIT - $160,000)/200,000
200,000 EBIT = 400,000 EBIT - $64,000,000,000
EBIT = $320,000
b. Interest expense = $2,000,000 (0.08) (1 - 0.3) = $112,000
BE = (EBIT/400,000) = (EBIT - $112,000)/200,000
200,000 EBIT = 400,000 EBIT - $44,800,000,000
EBIT = $224,000
c. The addition of a tax rate introduces a tax shield, lowering interest expense and decreasing tax expense. The lower break-even point suggests that for a greater range of EBITs, debt should be utilized.
Break-even EBIT (with taxes)
2. Beta, Gamma, and Delta companies are similar in every way except for their capital structures. Beta is an all-equity firm with $3,600,000 of value and 100,000 shares outstanding. Gamma is a levered firm with the same value as Beta but $1,080,000 in debt at 9% and 70,000 shares outstanding. Delta is a levered firm with $2,160,000 in debt at 12% and 40,000 shares outstanding. What is the break-even EBITs for Beta and Gamma, Beta and Delta, and Gamma and Delta companies if the corporate tax rate is 40% for all three companies?
Answer: 1. Beta and Gamma:
Interest expense = $1,080,000 (0.09) (1 - 0.4) = $58,320
BE = (EBIT/100,000) = (EBIT - $58,320)/70,000
70,000 EBIT = 100,000 EBIT - $5,832,000,000
EBIT = $194,400
2. Beta and Delta:
Interest expense = $2,160,000(.12) (1 - 0.4) = $155,520
BE = (EBIT/100,000) = (EBIT - $155,520)/40,000
40,000 EBIT = 100,000 EBIT - $15,552,000,000
EBIT = $259,200
3. Delta and Gamma:
Interest expense (Delta) = $155,520; Interest expense (Gamma) = $58,320
BE = (EBIT - $58,320)/70,000 = (EBIT - $155,520)/40,000
40,000 EBIT - $2,332,800,000 = 70,000 EBIT - $10,886,400,000
EBIT = $285,120
Finding the WACC
3. Monica is the CFO of Cooking for Friends (CFF) and uses the pecking order hypothesis philosophy when she raises capital for company projects. Currently, she can borrow up to $400,000 from her bank at a rate of 8.5%, float a bond for $750,000 at a rate of 9.25%, or issue additional stock for $1,300,000 at a cost of 17%. What is the WACC for CFF if Monica chooses to invest:
a. $1,000,000 in new projects
b. $2,000,000 in new projects
c. $3,000,000 in new projects
Answer: a. WACC = [($400,000/$1,000,000) 8.5%] + [($600,000/$1,000,000) 9.25%] = 8.95%
b. WACC = [($400,000/$2,000,000) 8.5%] + [($750,000/$2,000,000) 9.25%]
+ [($850,000/$2,000,000)17%] = 12.39375%
c. Can only borrow up to $2,450,000. WACC = [($400,000/$2,450,000) 8.5%] + [($750,000/$2,450,000) 9.25%] + [($1,300,000/$2,450,000) 17%] = 13.239769%
Monica has insufficient resources to raise $3,000,000 in capital.
Finding the WACC
4. Chandler has been hired by Cooking for Friends to raise capital for the company. Chandler increases the funding available from the bank to $900,000, but with a new rate of 8.75%. Using the data in Problem 3, determine what the new WACC is for borrowing $1,000,000, $2,000,000, and $3,000,000.
Answer: a. WACC = [($900,000/$1,000,000) 8.75%] + [($100,000/$1,000,000) 9.25%] = 8.8%
b. WACC = [($900,000/$2,000,000) 8.75%] + [($750,000/$2,000,000) 9.25%]
+ [($350,000/$2,000,000) 17%] = 10.38125%
c. WACC = [($900,000/$3,000,000) 8.75%] + [($750,000/$3,000,000) 9.25%]
+ [($1,300,000/$3,000,000) 17%] = 12.304167%—Insufficient resources to raise $3,000,000. Can only borrow up to $2,950,000
Modigliani and Miller’s World of No Taxes
5. Air America is looking at changing its capital structure from an all-equity firm to a leveraged firm with 50% debt and 50% equity. Air America is a not-for-profit company and therefore pays no taxes. If the required rate on the assets (RA) of Air America is 20%, what is the current required cost of equity? What is the new required cost of equity if the cost of debt is 10%?
Answer: RE = RA + (RA - RD) ´ (D/E)
Current required cost of equity: 0.20 + (0.20 - 0.10) (0) = 0.20 or 20%
New required cost of equity: 0.20 + (0.20 - 0.10) (0.5/0.5) = 0.30 or 30%
6. Roxy Broadcasting, Inc. is currently a low-leveraged firm with a debt-to-equity ratio of 1/3. The company wants to increase its leverage to 3/1 for debt-to-equity. If the current return on assets is 14% and the cost of debt is 11%, what is the current and new cost of equity if Roxy operates in a world of no taxes?
Answer: RE = RA + (RA - RD) ´ (D/E)
Current cost of equity: 0.14 + (0.14 - 0.11) (1/3) = 0.15 or 15%
New cost of equity: 0.14 + (0.14 - 0.11) (3/1) = 0.23 or 23%
Modigliani and Miller’s world of taxes
7. Air America from Problem 5 has lost its not-for-profit status, and the corporate tax rate is now 35%. If Air America’s value was $5,000,000 as an all-equity firm, what is its value under a 50/50 debt-equity ratio? Assume that the $5,000,000 is the after-tax value of the unlevered firm.
Answer: $5,000,000 after tax value: $5,000,000/0.65 = $7,692,307.70 implied before-tax value
At 50% debt amount of new bond issues = $7,692,307.70 ´ (0.5) = $3,846,153.8
Equity value after tax with new structure = $3,846,153.8 ´ (1 - 0 .35) = $2,500,000
New equity wealth after tax = $2,500,000 + $3,846,153.8 = $6,346,153.8
Or this problem can be solved by adding the current equity wealth unlevered to the tax shield.
VL = VE + (D ´ TC)
$5,000,000 + ($3,846,153.80 ´ 0.35) = $6,346,153.8
8. Roxy Broadcasting in Problem 6 was originally an all-equity firm with a value of $25,000,000. Roxy now pays taxes at a 40% rate. What is the value of Roxy under the 1-to-3 debt-to-equity capital structure? Under the 3-to-1 capital structure?
Answer:
| | All-Equity | 25/75 | 75/25 |
| Total Company | $25,000,000 | $25,000,000 | $25,000,000 |
| Debt Sold (a) | $ 0 | $ 6,250,000 | $18,750,000 |
| Gov’t Slice | $10,000,000 | $ 7,500,000 | $ 2,500,000 |
| Equity Slice (b) | $15,000,000 | $11,250,000 | $ 3,750,000 |
| Equity Wealth |
|
|
|
| Equity Increase | | $ 2,500,000 | $ 7,500,000 |
| Tax Shield | $ 0 | $ 2,500,000 | $ 7,500,000 |
Once again this problem can be solved by adding the tax shield to the current after tax equity value without debt.
VE = $25,000,000 (1 - 0.4) = $15,000,000
VL = VE + (D ´ TC)
a. $15,000,000 + ($6,250,000 ´ 0.4) = $17,500,000
b. $15,000,000 + ($18,750,000 ´ 0.4) = $22,500,000
Size of tax shield
9. Using the information from Problems 5 and 7 on Air America, determine the size of the tax shield with a corporate tax rate of 15%, 25%, 35%, and 45% if Air America’s capital structure is 50/50 debt-to-equity.
Answer: Before-tax firm value all-equity = $7,692,307.70; after-tax value = $5m; tax rate = 35% (This is assumed to be the value of the firm).
New debt issues with 50% debt = $7,692,307.70 ´ (0.5) = $3,846,153.8
Tax shield = (D ´ TC)
a. TC @ 15% ($3,846,153.8 ´ 0.15) = $576,923.08
b. TC @ 25% ($3,846,153.8 ´ 0.25) = $961,538.46
c. TC @ 35% ($3,846,153.8 ´ 0.35) = $1,346,153.80
d. TC @ 45% ($3,846,153.8 ´ 0.45) = $1,730,769.20
10. Using the information from Problems 6 and 8 on Roxy Broadcasting, determine the size of the tax shield with a corporate tax rate of 15%, 25%, 35%, and 45% if Roxy’s capital structure is 1/3 debt-to-equity. Determine the same if the capital structure is 3/1.
Answer: Before-tax firm value with all equity = $25,000,000
New debt issues with 25% debt = $25,000,000 ´ (0.25) = $6,250,000
Tax shield = (D ´ TC)
a. TC @ 15% ($6,250,000 ´ 0.15) = $937,500
b. TC @ 25% ($6,250,000 ´ 0.25) = $1,562,500
c. TC @ 35% ($6,250,000 ´ 0.35) = $2,187,500
d. TC @ 45% ($6,250,000 ´ 0.45) = $2,812,500
New debt issues with 75% debt = $25,000,000 ´ (0.75) = $18,750,000
Tax shield = (D ´ TC)
a. TC @ 15% ($18,750,000 ´ 0.15) = $2,812,500
b. TC @ 25% ($18,750,000 ´ 0.25) = $4,697,500
c. TC @ 35% ($18,750,000 ´ 0.35) = $6,562,500
d. TC @ 45% ($18,750,000 ´ 0.45) = $8,437,500
Equity value in a levered firm
11. Air America has an annual EBIT of $1,000,000, and the WACC in the unlevered firm is 20%. The current tax rate is 35%. Air America will have the same EBIT forever. If the company sells debt for $2,500,000 with a cost of debt of 20%, what is the value of equity in the unlevered and in the levered firm? What is the value of debt in the levered firm? What is the government’s value in the unlevered firm and in the levered firm?
Answer: Present Value of Cash Flow = EBIT/WACC = ($1,000,000/0.20) = $5,000,000
VE = $5,000,000(1 - 0.35) = $3,250,000
VL = VE + (D ´ TC)
$3,250,000 + ($2,500,000 ´ 0.35) = $4,125,000
i.e., (E + D)รจ: $1,625,000 + $2,500,000)
Government’s value:
Unlevered: $5,000,000 ´ 0.35 = $1,750,000
Levered: ($5,000,000 - $2,500,000) ´ 0.35 = $2,500,000 ´ 0.35 = $875,000
12. Roxy Broadcasting has an annual EBIT of $3,500,000 and a WACC of 14%. The current tax rate is 40%. Roxy will have the same EBIT forever. The company currently has debt of $6,250,000 with a cost of debt of 14%. Roxy will sell $12,500,000 more of debt and retire stock with the proceeds. What is the value of equity in the higher-levered firm? What is the government’s value in the higher-levered firm?
Answer: Present Value of Cash Flow = ($3,500,000/0.14) = $25,000,000
VE = $25,000,000 (1 - 0.40) = $15,000,000
VL = VE + (D ´ TC)
$15,000,000 + ($18,750,000 ´ 0.40) = $22,500,000
Equity only slice: $25,000,000 - $18,750,000 = $6,250,000 (1 - 0.40) = $3,750,000
Government’s value: $25,000,000 - $18,750,000 = $6,250,000(0.40) = $2,500,000
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