Question

Use the information below to determine the firms cost of debt, cost of equity, and WACC.  Use market values to determine the weights.

- The expected return on the market portfolio is 11% and the risk-free rate is 3%.  The firm’s beta is 1.6.

- The firm has most recently paid a dividend of $2. Dividends are expected to grow at a rate of 3% per year, indefinitely.

- The firm has 1.5 million shares of common stock outstanding.

The firm has two bond issues outstanding:

1) 10,000 bonds with 5% coupon, 6% YTM, and face value of $1000 that mature in 8 years

2) 50,000 bonds with 3% coupon, 4% YTM, and face value of $1000 that mature in 12 years.

The firm’s average tax rate is 30%.

Answer 1

Cost of Equity (by CAPM) = Risk free Rate + Beta * (Expected Market Return – Risk Free rate)

Cost of Equity = 3% + 1.6 * (11% - 3%) = 15.8%

In order to calculate the current share price, we would use constant growth dividend discount model.

D₁= 2 * 1.03 (3% growth per year mentioned in question), K_e = Discount Rate = Cost of Equity we calculated, g = 3%

Price of Share = (2 * 1.03)/(0.158 – 0.03) = $16.09

Market Cap of Company (or total market value of equity) = 16.09 * 1,500,000 = $ 24,135,000

Now, we need to calculate the current trading price of two bonds. Current price of bonds is basically the present value of all cashflows associated with the bonds (coupons and maturity value)

For Bond 1, C= 50, i = 6%, M = 1000, n = 8

On sustituting these values, we get Price of bond 1 = $937.90. Hence total value of this debt = $9,379,020.62

For Bond 1, C= 30, i = 4%, M = 1000, n = 12

On sustituting these values, we get Price of bond 2 = $906.15. Hence total value of this debt = $9,061,492.62

Now that we have market value of three issuances, let us calculate weights for them

Weight of common stock = 24135000/(24135000+9379020.62+9061492.62) = 56.7%

Weight of bond issue 1 = 9379020.62/(24135000+9379020.62+9061492.62) = 22.0%

Weight of bond issue 2 = 9061492.62/(24135000+9379020.62+9061492.62) = 21.3%

WACC = (56.7%*15.8%) + (22% * 6% * (1 - 30%)) + (21.3% * 4% * (1 - 30%)) = 8.96% + 0.93% + 0.60% = 10.48%