Question

Your company’s balance sheet currently shows the following:

            Debt                  $750 million

            Equity             $1250 million

            Total Assets    $2,000 million

      Bonds have a par value of $1000, 9 years to maturity and have a coupon rate of 5.9% paid semiannually. Other bonds with similar characteristics and risk currently have a yield to maturity of 6.58%. Price of a bond is $954.36. The book value of common stock price is $50 per share. The current stock price is $22 per share in the market. Beta for your stock is 1.19 and the current risk-free return and market return are 3% and 10%, respectively. The tax rate is 35%.

1. Find the market value and cost of debt.
2. Find the market value and cost of equity.
3. Calculate the weighted average cost of capital using market values.
4. Calculate the weighted average cost of capital using book values.
5. Explain the advantages and disadvantages of each weighting method.
6. Calculate the cost of equity if your book value capital structure changes to 60% debt and 40% equity. Explain in detail why the cost of equity changed the way it did.

Answer 1

a. market value of debt = no. of bonds outstanding*price per bond

no. of bonds outstanding = book value of debt/par value of bond = $750,000,000/$1,000 = 750,000‬

market value of debt = 750,000‬*$954.36 = $715,770,000‬

Cost of debt is the yield to maturity of the bonds. Other bonds with similar characteristics and risk currently have a yield to maturity of 6.58%. so, cost of debt is 6.58%.

b. market value of equity = no. of shares outstanding*current price per share

no. of shares outstanding = book value of equity/book value per share of common stock

no. of shares outstanding = $1,250,000,000‬/$50 = 25,000,000‬

market value of equity = 25,000,000‬*$22 = $550,000,000‬

cost of equity = risk-free rate + stock's beta*(market return - risk-free rate) = 3% + 1.19*(10% - 3%) = 3% + 1.19*7% = 3% + 8.33‬% = 11.33‬%

c. weighted average cost of capital = market weight of debt*after-tax cost of debt + market weight of equity*cost of equity

market weight of debt = market value of debt/total market value of capital

market weight of equity = market value of equity/total market value of capital

total market value of capital = market value of debt + market value of equity = $715,770,000‬ + $550,000,000‬ = $1,265,770,000‬

market weight of debt = $715,770,000/$1,265,770,000‬‬ = 0.57

market weight of equity = $550,000,000‬/$1,265,770,000‬‬ = 0.43

after-tax cost of debt = cost of debt*(1-tax rate) = 6.58%*(1-0.35) = 6.58%*0.65 = 4.277‬%

weighted average cost of capital = 0.57*4.277% + 0.43*11.33% = 2.43789‬‬% + 4.8719‬% = 7.31%

d. weighted average cost of capital = book weight of debt*after-tax cost of debt + book weight of equity*cost of equity

book weight of debt = book value of debt/total book value of capital

book weight of equity = book value of equity/total book value of capital

total book value of capital = book value of debt + book value of equity = $750,000,000‬ + $1,250,000,000‬ = $2,000,000,000

book weight of debt = $750,000,000/$2,000,000,000‬ = 0.375

market weight of equity = $1,250,000,000‬/$2,000,000,000‬ = 0.625

after-tax cost of debt = cost of debt*(1-tax rate) = 6.58%*(1-0.35) = 6.58%*0.65 = 4.277‬%

weighted average cost of capital = 0.375*4.277% + 0.625*11.33% = 1.603875% + 7.08125‬% = 8.69%