Williamson, Inc., has a debt-to-equity ratio of 2.53. The firm’s weighted averag

Question

Williamson, Inc., has a debt-to-equity ratio of 2.53. The firm’s weighted average cost of capital is 10 percent, and its pretax cost of debt is 6 percent. Williamson is subject to a corporate tax rate of 35 percent.

What is Williamson’s cost of equity capital?

What is Williamson’s unlevered cost of equity capital?

What would Williamson’s weighted average cost of capital be if the firm’s debt-to-equity ratio were .65 and 1.65

What is Williamson’s cost of equity capital?

What is Williamson’s unlevered cost of equity capital?

What would Williamson’s weighted average cost of capital be if the firm’s debt-to-equity ratio were .65 and 1.65

Explanation / Answer

Answer)

Given in question =

Debt to equity = 2.53

WACC = 10%

Cost of debt = 6% (Pre tax)

Tax rate = 35%

WACC = Weight of equity * Cost of equity + Weight of debt*cost of debt*(1-tax rate)

We do not have the company’s debt-to-value ratio orthe equity-to-value ratio, but we can calculate eitherfrom the debt-to-equity ratio. With the given debt-equity ratio, we know the company has 2.5 dollarsof debt for every dollar of equity. Since we onlyneed the ratio of debt-to-value and equity-to-value,we can say

Debt B/B+S = 2.53/2.53+1 = 0.716714

Equity = 1/ (2.53+1) = 0.283286

0.10 = (0.716714) * 0.06*(1-0.35) + 0.283286*Cost of equity

Cost of equity = 0.25433 or 25.43%

we have to use Modigliani-Miller Proposition II with corporate taxes to find the unlevered cost of equity

rs= r0+ (B/S)( r0– rB)(1 – tC)

0.2543= ro + 2.53 *(ro - 0.06) *(1-0.35), where ro is the unlevered cost of equity

0.2543 = ro + (2.53ro -0.06*2.53 ) *0.65

0.2543 = ro + 1.6445ro - 0.09867

0.2543 + 0.09867 = ro + 1.6445 ro

0.353 = 2.6445*ro

ro = 0.133485 or 13.34%

If Debt / equity is 0.65

weight of debt =0.65 /(0.65+1) = 0.3939

weight of equity = 1-0.3939 = 0.606061

Cost of levered equity = ro + B/S *(ro-rb)*(1-tc)

Cost of levered equity = 0.133485 + 0.65*(0.13345-0.06)*(1-0.35)

Cost of levered equity = 0.164532

WACC = 0.606061*(0.164532) +0.3939 * (0.06) *(1-0.35)

WACC = 0.11508

Now when debt / equity = 1.65

Weight of debt =1.65/(1.65+1) =0.622642

Weight of equity = 1-0.622642 = 0.377358

Cost of levered equity

rS= r0+ (B/S)( r0– rB)(1 – tC)

= 0.133485 +1.65 (0.133485-0.06)*(1-0.35)

=0.212297

WACC = 0.212297 * 0.377358 + 0.06*(1-0.35)*(0.622642)

WACC = 0.104395 OR 10.43%

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