Williamson, Inc. has a debt-toequity ratio of 2.44. The firm\'s weighted average

Question

Williamson, Inc. has a debt-toequity ratio of 2.44. The firm's weighted average cost of capital is 9%. and its pretax cost of debt is 7%. Williamson is subject to a corporate tax rate of 40%.

A) What is Williamson's cost of equity capital? Round to 2 decimal places. Do not round intermediate calculations.

B) What is Williamson's unlevered cost of equity capital? Round to 2 decimal places. Do not round intermediate calculations.

C) What would Williamson's weighted average cost of capital be if the firm's debt-to-equity ratio were .60 and 1.75? Round to 2 decimal places. Do not round intermediate calculations.

Explanation / Answer

Solution:

A) Calculation of cost of equity capital:

A firm’s weighted average cost of capital is equal to:

RWACC= [B/ (B+S)](1 tC)RB+ [S/ (B+S)]RS

We do not have the company’s debt-to-value ratio or the equity-to-value ratio, but we can calculate either from the debt-to-equity ratio. With the given debt-equity ratio, we know the company has 2.44 dollars of debt for every dollar of equity. Since we only need the ratio of debt-to-value and equity-to-value, we can say:

B/ (B+S) = 2.44 / (2.44 + 1) = 0.7093

S/ (B+S) = 1 / (2.44 + 1) = 0.2907

We can now use the weighted average cost of capital equation to find the cost of equity, which is:

0.09 = (0.7093)(1 – 0.40)(.07) + (0.2907)(RS)

RS= 0.2071

= 20.71%

B) Calculation of unlevered cost of equity capital:

We can use Modigliani-Miller Proposition II with corporate taxes to find the unlevered cost of equity. Doing so, we find:

RS = R0 + (B/S)(R0RB)(1 tC)

0.2071 = R0 + (2.44)(R0 – 0.07)(1 – 0.40)

R0= 0.0900

= 9%

C) Calculation of weighted average cost of capital be if the firm's debt-to-equity ratio were .60 and 1.75:

We first need to find the debt-to-value ratio and the equity-to-value ratio. We can then use the cost of levered equity equation with taxes, and finally the weighted average cost of capital equation. So:

If debt-equity = .60

B/ (B+S) = .60 / (.60 + 1) = 0.375

S/ (B+S) = 1 / (.60 + 1) = 0.625

The cost of levered equity will be:

RS=R0+ (B/S)(R0RB)(1 tC)

RS = 0.09 + (0.60)(0.09 .07)(1 .40)

RS= .0972

= 9.72%

And the weighted average cost of capital will be:

RWACC = [B/ (B+S)](1 tC)RB+ [S/ (B+S)]RS

RWACC = (0.375)(1 .40)(.07) + (0.625)(0.0972)

RWACC = 0.0765

= 7.65%

If debt-equity = 1.75

B/ (B+S) = 1.75 / (1.75 + 1) = 0.6364

S/ (B+S) = 1 / (1.75 + 1) = 0.3636

The cost of levered equity will be:

RS=R0+ (B/S)(R0RB)(1 tC)

RS = 0.09 + (1.75)(0.09 .07)(1 .40)

RS= 0.111

= 11.1%

And the weighted average cost of capital will be:

RWACC = [B/ (B+S)](1 tC)RB+ [S/ (B+S)]RS

RWACC = (0.6364)(1 .40)(.07) + (0.3636)(0.111)

RWACC = 0.0671

= 6.71%

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.