Corporate Finance MC PS 6
Uptown Interior Designs is an all-equity firm that has 40,000 shares of stock outstanding. The company has decided to borrow $74,000 to buy out the 2,100 shares of a deceased stockholder. What is the total value of this firm if you ignore taxes?
Firm value = ($74,000 / 2,100) × 40,000 = $1,409,524
The effects of financial leverage depend on the operating earnings of the company. Based on this relationship, assume you graph the EPS and EBI for a firm, while ignoring taxes. Which one of these statements correctly states a relationship illustrated by the graph?
Leverage only provides value above the break-even point.
Johnson Tire Distributors has an unlevered cost of capital of 13 percent, a tax rate of 34 percent, and expected earnings before interest and taxes of $1,800. The company has $3,200 in bonds outstanding that have an 8 percent coupon and pay interest annually. The bonds are selling at par value. What is the cost of equity?
VU = [$1,800 x (1- .34)]/.13 = $9,138.46 VL = $9,138 + (.34 x $3,200) = $10,226.46 VE = $10,226 - $3,200 = $7,026.46 RE = 0.13 + [(0.13 - 0.08) x ($3,200/$7,026.46) x (1 - .34)] = 14.5 percent
Jemisen's firm has expected earnings before interest and taxes of $1,900. Its unlevered cost of capital is 13 percent and its tax rate is 34 percent. The firm has debt with both a book and a face value of $2,900. This debt has an 8 percent coupon and pays interest annually. What is the firm's weighted average cost of capital?
VU = [$1,900 x (1 - .34)]/.13 = $9,646.15 VL = $9,646.15 + (.34 x $2,900) = $10,632.15 VE = $10,632.15 - $2,900 = $7,732.15 RE = 0.13 + (0.13 - 0.08) x ($2,900/$7,732.15) x (1 - 0.34) = 0.142377 WACC = [($7,732.15/$10,632.15) x 0.142377] + [($2,900/$10,632.15) x 0.08 x (1 - 0.34)] = 11.79 percent
MM Proposition II with taxes:
has the same general implications as MM Proposition II without taxes.
In the absence of taxes, the capital structure chosen by a firm doesn't really matter because of:
homemade leverage.
MM Proposition I with taxes states that:
increasing the debt-equity ratio increases firm value.
MM Proposition I with no tax supports the argument that:
it is completely irrelevant how a firm arranges its finances.
MM Proposition I without taxes proposes that:
leverage does not affect the value of the firm.
A firm should select the capital structure which:
maximizes the value of the firm.
According to MM Proposition II with no taxes, the:
required return on equity is a linear function of the firm's debt-equity ratio.
The interest tax shield has no value for a firm when:
the firm is unlevered.
The interest tax shield is a key reason why:
the net cost of debt to a firm is generally less than the cost of equity.
The Backwoods Lumber Co. has a debt-equity ratio of .68. The firm's required return on assets is 11.7 percent and its levered cost of equity is 15.54 percent. What is the pretax cost of debt based on MM Proposition II with no taxes?
RS = .1554 = .117 + .68(.117 - RB) RB = .0605, or 6.05%
The concept of homemade leverage is most associated with:
MM Proposition I with no tax.
Longmont Inc. is a levered firm with a cost of equity of 12 percent and a cost of debt of 6 percent. The required return on the assets is 10 percent. What is the firm's debt-equity ratio if there are no taxes?
RS = .12 = .10 + B/S(.10 - .06) B/S = .50
A firm has a debt-equity ratio of .64, a pretax cost of debt of 8.5 percent, and a required return on assets of 12.6 percent. What is the cost of equity if you ignore taxes?
RS = .126 + .64(.126 - .085) = .1522, or 15.22%
Kelso Electric is debating between a leveraged and an unleveraged capital structure. The all equity capital structure would consist of 19,000 shares of stock. The debt and equity option would consist of 12,000 shares of stock plus $240,000 of debt with an interest rate of 6 percent. What is the break-even level of earnings before interest and taxes between these two options? Ignore taxes.
EBIT/19,000 = [EBIT - ($240,000 x .06)]/12,000 EBIT = $39,085.71
You own 25 percent of Unique Vacations, Inc. You have decided to retire and want to sell your shares in this closely held, all-equity firm. The other shareholders have agreed to have the firm borrow $1.5 million to purchase your 1,000 shares of stock. What is the total value of this firm today if you ignore taxes?
Firm value = $1.5 million / .25 = $6.0 million
Thompson amp; Thomson is an all-equity firm that has 280,000 shares of stock outstanding. The company is in the process of borrowing $2.4 million at 5.5 percent interest to repurchase 75,000 shares of the outstanding stock. What is the value of this firm if you ignore taxes?
Firm value = ($2,400,000 / 75,000) × 280,000 = $8,960,000
The proposition that the value of a levered firm is equal to the value of an unlevered firm is known as:
MM Proposition I with no tax.
The proposition that the cost of equity is a positive linear function of capital structure is called:
MM Proposition II (no taxes).
The Spartan Co. has an unlevered cost of capital of 11.6 percent, a cost of debt of 7.9 percent, and a tax rate of 35 percent. What is the target debt-equity ratio if the targeted levered cost of equity is 12.6 percent?
RS = .126 = .116 + B/S × (.116 - .079) × (1 - .35) B/S = .42
A firm has a debt-equity ratio of .64, a cost of equity of 13.04 percent, and a cost of debt of 8 percent. The corporate tax rate is 35 percent. What would be the cost of equity if the firm were all-equity financed?
RS = .1304 = R0 + .64(1 - .35) (R0 - .08) R0 = .1156, or 11.56%
Rosita's has a cost of equity of 13.76 percent and a pretax cost of debt of 8.5 percent. The debt-equity ratio is .60 and the tax rate is 34 percent. What is Rosita's unlevered cost of capital?
RS = .1376 = RU + .60 × (1 - .34) × (RU - .085) RU = .1227, or 12.27%
Wild Flowers Express has a debt-equity ratio of .60. The pretax cost of debt is 9 percent while the unlevered cost of capital is 14 percent. What is the cost of equity if the tax rate is 34 percent?
RS = .14 + .60 × (1 - .34) × (.14 - .09) = .1598, or 15.98%
Bigelow has a levered cost of equity of 14.29 percent and a pretax cost of debt of 7.23 percent. The required return on the assets is 11 percent. What is the firm's debt-equity ratio based on MM Proposition II with no taxes?
RS = .1429 = .11 + B/S(.11 - .0723) B/S = .87
A firm has a pretax cost of debt of 7.35 percent and an unlevered cost of capital of 12.8 percent. The tax rate is 34 percent and the levered cost of equity is 15.07 percent. What is the debt-equity ratio?
RS = .1507 = .128 + B/S × (1 - .34) × (.128 - .0735) B/S = .63
A firm has a debt-equity ratio of .48. Its cost of debt is 7 percent and its overall cost of capital is 10.8 percent. What is its cost of equity if there are no taxes or other imperfections?
RWACC = .108 = (.48 / 1.48)(.07) + (1 / 1.48)RS RS = .1262, or 12.62%
A firm has debt of $7,000, equity of $12,000, a cost of debt of 7 percent, a cost of equity of 14 percent, and a tax rate of 30 percent. What is the firm's weighted average cost of capital?
RWACC = {[$12,000 / ($7,000 + 12,000)] × .14} + [$7,000 / ($7,000 + 12,000)] × .07 × (1 - .30) RWACC = .1065, or 10.65%
A firm has debt of $5,000, equity of $16,000, a cost of debt of 8 percent, a cost of equity of 12 percent, and a tax rate of 34 percent. What is the firm's weighted average cost of capital?
RWACC = {[$16,000 / ($5,000 + 16,000)] × .12} + [($5,000 / ($5,000 + 16,000) × .08 × (1 - .34)] RWACC = .1040, or 10.40%
A firm has zero debt in its capital structure and has an overall cost of capital of 10 percent. The firm is considering a new capital structure with 60 percent debt at an interest rate of 8 percent. Assuming there are no taxes or other imperfections, what would be the cost of equity with the new capital structure?
Rs = .10 + .60 / .40(.10 - .08) = .13, or 13%
If a firm is unlevered and has a cost of equity capital of 13.7 percent, what would be the cost of equity if its debt-equity ratio was revised to .4? The expected cost of debt is 7.4 percent and there are no taxes.
Rs = .137 + .4(.137 - .074) = .1622, or 16.22%
A firm has zero debt and an overall cost of capital of 13.8 percent. The firm is considering a new capital structure with 40 percent debt. The interest rate on the debt would be 7.2 percent and the corporate tax rate is 34 percent. What would be the cost of equity with the new capital structure?
Rs = .138 + (.4 / .6)(1 - .34)(.138 - .072) =.1670, or 16.70%
A firm has a debt-equity ratio of .57, and unlevered cost of equity of 14 percent, a levered cost of equity of 15.6 percent, and a tax rate of 34 percent. What is the cost of debt?
Rs = .156 = .14 + .57(1 - .34)(.14 - RB) RB = .0975, or 9.75%
A firm has a debt-equity ratio of 1, a cost of equity of 16 percent, and a cost of debt of 8 percent. If there are no taxes or other imperfections, what is its unlevered cost of equity?
Rs = .16 = r0 + 1(r0 - .08) r0 =.12, or 12%
Aspen's Distributors has a levered cost of equity of 13.84 percent and an unlevered cost of capital of 12.5 percent. The company has $5,000 in debt that is selling at par. The levered value of the firm is $14,600 and the tax rate is 34 percent. What is the pretax cost of debt?
VE = $14,600 - 5,000 = $9,600 RS = .1384 = .125 + ($5,000 / $9,600) × (1 - .34) × (.125 - RB) RB = .0860, or 8.60%
The Dance Studio is currently an all-equity firm that has 22,000 shares of stock outstanding with a market price of $27 a share. The current cost of equity is 12 percent and the tax rate is 35 percent. The firm is considering adding $225,000 of debt with a coupon rate of 6.25 percent to its capital structure. The debt will sell at par. What will be the levered value of the equity?
VL = (22,000 × $27) + (.35 × $225,000) = $672,750 VE = $672,750 - 225,000 = $447,750
Anderson's Furniture Outlet has an unlevered cost of capital of 10.3 percent, a tax rate of 34 percent, and expected earnings before interest and taxes of $1,900. The company has $4,000 in bonds outstanding that have an annual coupon of 7 percent. If the bonds are selling at par, what is the cost of equity?
VL = {[$1,900 × (1 - .34)] / .103} + (.34 × $4,000) = $13,534.76 VS = $13,534.76 - 4,000 = $9,534.76 RS = .103 + [($4,000 / $9,534.76) × (1 - .34) × (.103 - .07)] = .1121, or 11.21%
An unlevered firm has a cost of capital of 13.6 percent and earnings before interest and taxes of $138,000. A levered firm with the same operations and assets has both a book value and a face value of debt of $520,000 with an annual coupon of 7 percent. The applicable tax rate is 34 percent. What is the value of the levered firm?
VL = {[$138,000 × (1 - .34)] / .136} + (.34 × $520,000) = $846,505.88
Alexandria's Dance Studio is currently an all-equity firm with earnings before interest and taxes of $338,000 and a cost of equity of 14.2 percent. The tax rate is 34 percent. Alexandria is considering adding $400,000 of debt with a coupon rate of 7 percent to her capital structure. The debt will be sold at par value. What is the levered value of the equity?
VL = {[$338,000 × (1 - .34)] / .142} + (.34 × $400,000) = $1,706,986 VE = $1,706,986 - 400,000 = $1,306,986
Salmon Inc. has debt with both a face and a market value of $227,000. This debt has a coupon rate of 7 percent and pays interest annually. The expected earnings before interest and taxes is $87,200, the tax rate is 35 percent, and the unlevered cost of capital is 12 percent. What is the firm's cost of equity?
VL = {[$87,200 × (1 - .35)] / .12} + (.35 × $227,000) = $551,783.33 VE = $551,783.33 - 227,000 = $324,783.33 Rs = .12 + [($227,000 / $324,783.33) × (1 - .35) × (.12 - .07)] = .1427, or 14.27%
Joe's Leisure Time Sports is an unlevered firm with an aftertax net income of $78,400. The unlevered cost of capital is 11.4 percent and the tax rate is 35 percent. What is the value of this firm?
VU = $78,400 / .114 = $687,719.30
The Montana Hills Co. has expected earnings before interest and taxes of $17,100, an unlevered cost of capital of 12.4 percent, and debt with both a book and face value of $25,000. The debt has an annual 6.2 percent coupon. If the tax rate is 34 percent, what is the value of the firm?
VU = [$17,100 × (1 - .34) ] / .124 = $91,016.13 VL = $91,016.13 + (.34 × $25,000) = $99,516.13
L.A. Clothing has expected earnings before interest and taxes of $2,000, an unlevered cost of capital of 16 percent and a tax rate of 34 percent. The company also has $2,800 of debt that carries a 7 percent coupon. The debt is selling at par value. What is the value of this firm?
VU = [$2,000 x (1 - .34)]/.16 = $8,250.00 VL = $8,250.00 + .34 ($2,800) = $9,202.00
The Winter Wear Company has expected earnings before interest and taxes of $3,800, an unlevered cost of capital of 15.4 percent and a tax rate of 35 percent. The company also has $2,600 of debt with a coupon rate of 5.7 percent. The debt is selling at par value. What is the value of this firm?
VU = [$3,800 ×(1 - .35)] / .154 = $16,038.96 VL = $16,038.96 + (.35 × $2,600) = $16,948.96
MM Proposition II is the proposition that:
a firm's cost of equity capital is a positive linear function of the firm's capital structure.
In an EPS-EBI graphical relationship, the slope of the debt ray is steeper than the equity ray. The debt ray has a lower intercept because:
a fixed interest charge must be paid even at low earnings.
The increase in risk to shareholders when financial leverage is introduced is best evidenced by:
a higher variability of EPS with debt than with all-equity financing.
Which one of the following will tend to increase the benefit of the interest tax shield given a progressive tax rate structure?
a sizeable increase in taxable income
A key underlying assumption of MM Proposition I without taxes is that:
individuals and corporations borrow at the same rate.
The reason that MM Proposition I does not hold in the presence of corporate taxation is because:
levered firms pay less taxes compared with identical unlevered firms.
Bryan invested in Bryco stock when the firm was financed solely with equity. The firm now has a debt-equity ratio of .3. To maintain the same level of leverage he originally had, Bryan needs to:
sell some shares of Bryco stock and loan out the proceeds.
When comparing levered versus unlevered capital structures, leverage works to increase EPS for high levels of EBIT because interest payments on the debt:
stay fixed, leaving more income to be distributed over fewer shares.
MM Proposition I with taxes is based on the concept that:
the value of the firm increases as total debt increases because of the interest tax shield.
MM Proposition I with taxes supports the theory that:
there is a positive linear relationship between the amount of debt in a levered firm and its value.
