What will be the debttoequity ratio after Reliable Gearing restructuring?
Reliable Gearing currently is allequity financed. It has 10,000 shares of equity outstanding, selling at $100 a share. The firm is considering a capital restructuring. The lowdebt plan calls for a debt issue of $200,000 with the proceeds used to buy back stock. The high debt plan would exchange $400,000 of debt for equity. The debt will pay an interest rate of 10%. The firm pays no taxes.
a. What will be the debttoequity ratio after each possible restructuring?
b. If earnings before interest and tax (EBIT) will be either $90,000 or $130,000, what will earnings per share be for each financing mix for both possible values of EBIT? If both scenarios are equally likely, what is expected (i.e., average) EPS under each financing mix? Is the highdebt mix preferable?
c. Suppose that EBIT is $100,000. What is EPS under each financing mix? Why are they the same in this particular case?
a. Market value of firm is $100 ´ 10,000 = $1,000,000.
With the lowdebt plan, equity falls by $200,000, so D/E = $200,000/$800,000 = .25, and 8,000 shares remain outstanding.
With the highdebt plan, equity falls by $400,000, so D/E = $400,000/$600,000 = .67, and 6,000 shares remain outstanding.
b. Lowdebt plan
EBIT $ 90,000 $130,000
Interest 20,000 20,000
Equity Earnings 70,000 110,000
EPS [Earnings/8000] $ 8.75 $ 13.75
Expected EPS = ($8.75 + $13.75)/2 = $11.25
Highdebt plan
EBIT $ 90,000 $130,000
Interest 40,000 40,000
Equity Earnings 50,000 90,000
EPS [Earnings/6000] $ 8.33 $ 15.00
Expected EPS = (8.33 + 15)/2 = $11.67
Although the highdebt plan results in higher expected EPS, it is not necessarily preferable, since it also entails greater risk. The higher risk shows up in the fact that EPS for the highdebt plan is lower than EPS for the lowdebt plan when EBIT is lower but higher when EBIT is higher.
c. Lowdebt plan Highdebt plan
EBIT $100,000 $100,000
Interest 20,000 40,000
Equity Earnings 80,000 60,000
EPS $ 10.00 $ 10.00
EPS is the same for both plans because EBIT is 10% of assets, equal to the rate the firm pays on its debt. When rassets = rdebt, EPS is unaffected by leverage.
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Astromet is financed entirely by common stock and has a beta of 1.0. The firm pays no taxes. The stock has a priceearnings multiple of 10 and is priced to offer a 10% expected return. The company decides to repurchase half the common stocks and substitute an equal value of debt. If the debt yields a riskfree 5%, calculate
a. The beta of the common stock after the refinancing.
b. The required return on the common stock before the refinancing.
c. The required return on the common stock after the refinancing.
d. The required return on the debt.
e. The expected return on the company after the refinancing.
Answers:
a. Since the debt is riskfree, βd=0.
In addition, no tax ==> Tc= 0
Buyback half the common stocks ==> D=1, E=1, V= 2
βe=βu+(βuβd)*(D/E)*(1Tc)= 1+(10)*(1/1)*(10) = 2
or βa(=1)= (E/V)βe + (D/V)βd ==> βe= 2
b. Ru=10% (from the question)
c. Re=Ru+(RuRd)*(D/E)=10%+(10%5%)*(1/1)=15%
d. Rd=5% (from the question)
e. r(wacc)=(1/2)*5%*(10)+(1/2)*15%=10%
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5) The market value of United Frypan Company is $160 (total firm value). Its book values are below and the market value of debt equals the book value of debt. Assume that Modigliani and Miller’s theory with corporate taxes holds (i.e. consider only the influence of corporate taxes). There is no growth and the $40 of debt is expected to be permanent (i.e they will not borrow or repay this debt). Also, assume a 40% corporate tax rate. (20 points)
Net Working Capital $ 20 Debt $ 40
Fixed Assets 80 Equity 60
Total $100 Total $100
a) Calculate how much of the firm’s market value is accounted for by the debtgenerated corporate tax shield? Show the value of the unlevered firm.
b) Assume that in part a, you determined that debt adds $20 of value to the firm and that the unlevered firm is worth $140. Calculate the market value of UF’s equity if the firm borrows an additional $30 and uses the proceeds to repurchase stock?
c) Again, assume that in part a, you determined that debt adds $20 of value to the firm and that the unlevered firm is worth $140. Now suppose that Congress passes a law eliminating the deductibility of interest for tax purposes after a grace period of five years (i.e. the firm can deduct interest from taxable income for 2 more years). Assuming everything else equal, the firm has the capital structure from part a, and an 8% cost of debt; calculate the new value of the firm.
5) The market value of United Frypan Company is $160 (total firm value). Its book values are below and the market value of debt equals the book value of debt. Assume that Modigliani and Miller’s theory with corporate taxes holds (i.e. consider only the influence of corporate taxes). There is no growth and the $40 of debt is expected to be permanent (i.e they will not borrow or repay this debt). Also, assume a 40% corporate tax rate.
Net Working Capital $ 20 Debt $ 40
Fixed Assets 80 Equity 60
Total $100 Total $100
a) Calculate how much of the firm’s market value is accounted for by the debtgenerated corporate tax shield? Show the value of the unlevered firm.
Value of tax shield = 40*.4=16
Value of unlevered firm = 16016=144
b) Assume that in part a, you determined that debt adds $20 of value to the firm and that the unlevered firm is worth $140. Calculate the market value of UF’s equity if the firm borrows an additional $30 and uses the proceeds to repurchase stock?
Value of Tax Shield = (30+40).4=28
V of the levered firm =140+28=168
Value of equity =16870=98 (where 70 is the amount of debt the firm)
Or
Value of Tax Shield = 20+(30).4=32
V of the levered firm =140+32=172
Value of equity =17270=102 (where 70 is the amount of debt the firm)
c) Again, assume that in part a, you determined that debt adds $20 of value to the firm and that the unlevered firm is worth $140. Now suppose that Congress passes a law eliminating the deductibility of interest for tax purposes after a grace period of five years (i.e. the firm can deduct interest from taxable income for 2 more years). Assuming everything else equal, the firm has the capital structure from part a, and an 8% cost of debt; calculate the new value of the firm.
Using the equation Debt * the tax rate is appropriate if the tax shield is a perpetuity. Here the tax shield provides benefit for only 2 years. So, you must calculate the interest tax shield and discount it for year 1 and 2.
V(L)=140 + (40*.08*.4)/1.08+(40*.08*.4)/1.082 =142 .......
