If Wild Widgets, Inc., were an all-equity company, it would have a beta of 0.9. The company has a target debt-equity ratio of. 4. The expected return on the market portfolio is 12 percent, and Treasury bills currently yield 4.1 percent. The company has one bond issue outstanding that matures in 20 years and has a coupon rate of 7.2 percent. The bond currently sells for $1,090. The corporate tax rate is 35 percent.

a. What is the company's cost of debt?

b. What is the company's cost of equity?

c. What is the company's weighted average cost of capital?

a. 6.5%

b. 13.06%

c. 10.91%

Explanation:

a.

Cost of debt of a bond is yield to maturity. Yield to maturity is the rate of return that a investor actually receives or a borrows actually pays on a bond. It is long term return or payment which is expressed in annual term.

Formula for yield to maturity is as follow

Yield to maturity = [ C + (F - P) / n ] / [ (F + P) / 2 ]

By placing values in the formula

Assuming the bond face value is $1,000

Yield to maturity = [ (1000x7.2) + (1,000 - $1,090) / 20 ] / [ (1,000 + $1,090) / 2 ]

Yield to maturity = [ $72 + (1,000 - $1,090) / 20 ] / $1,045

Yield to maturity = [ $72 - $4.5 ] / $1,045

Yield to maturity = $67.5 / $1,045

Yield to maturity = 6.5%

So, the cost of Debt is 6.5%

b.

As 0.9 is the unlevered beta, We need Levered beta due to restructuring of capital.

Beta Levered = Beta Unlevered x (1 + (1 - tax rate) x Debt / Equity)

Beta Levered = 0.9 x (1 + (1 - 0.35) x 0.4)

Beta Levered = 1.134

Cost of equity can be calculated using CAPM

CAPM calculated the expected return on an equity investment based on the risk free rate, market premium and risk beta of the investment.

Formula for CAPM is as follow

Expected return = Risk free Rate + Beta (Market premium)

As we know the Risk premium is the difference of market return and risk free rate.

Expected return = Risk free Rate + Beta (Market Return - Risk free Rate)

Ra = Rf + β (Rm - Rf)

Ra = 4.1% + 1.134 (12% - 4.1%)

Ra = 13.06%

Cost of Equity is 13.06%

c.

WACC is the average cost of capital of the firm based on the weightage of the debt and weightage of the equity multiplied to their respective costs.

According to WACC formula

WACC = (Cost of equity x Weightage of equity) + (Cost of debt (1 - t) x Weightage of debt)

Placing the values in formula

If the debt to equity 0.4 the equity value should be 1 and total capital is 1.4 (1 + 0.4)

WACC = (13.06% x 1 / 1.4) + (6.5% (1 - 0.35) x 0.4 / 1.4) = 9.71% + 1.2% = 10.91%

WACC is 10.91%