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%.

Please show all steps clearly. Thank you.

Answer 1

Cost of equity using CAPM model = risk free rate + beta ( expected market return - risk free rate)

cost of equity = 0.03 + 1.6 ( 0.11 - 0.03)

cost of equity = 0.158 or 15.8%

Share price = D1 / ( k -g)

Share price = [2 ( 1 + 0.03) / ( 0.158 - 0.03)

Share price = 2.06 / 0.128

Share price = $16.1

Market value of common stock = 1,500,000 * 16.1 = $24,150,000

Bond 1:

Face value = 1000

number of periods = 8

Rate = 6%

Coupon = 0.05 * 1000 = 50

Bond price = 50 * [1 - [1 / ( 1 + 0.06)⁸]] / 0.06 + 1000 / ( 1 + 0.06)⁸

Bond price = 50 * [1 - 0.627412]] / 0.06 + 627.412371

Bond price = 50 * 6.2098 + 627.412371

Bond price = $937.9

Bond 2:

Face value = 1000

number of periods = 12

Rate = 4%

Coupon = 0.03 * 1000 = 30

Bond price = 30 * [1 - [1 / ( 1 + 0.04)¹²]] / 0.04 + 1000 / ( 1 + 0.04)¹²

Bond price = 30 * [1 - 0.624597]] / 0.04 + 624.59705

Bond price = 30 * 9.385074 + 624.59705

Bond price = $906.5

Market value of bond 1 = 10,000 * 937.9 = $9,379,000

Market value of bond 2 = 50,000 * 906.5 = $45,325,000

Total market value of bond =  9,379,000 + 45,325,000 = 54,704,000

Weight of bond 1 = 9,379,000 / 54,704,000 = 0.17145

Weight of bond 2 = 45,325,000 / 54,704,000 = 0.82855

Weighted average before tax cost of debt = 0.17145 ( 0.06) + 0.82855 ( 0.04)

Weighted average before tax cost of debt = 0.010287 + 0.033142

Weighted average before tax cost of debt = 0.043429

Weighted average after tax cost of debt = 0.043429 ( 1 - 0.3)

Weighted average after tax cost of debt = 0.0304 or 3.04%

Total market value of capital structure = 24,150,000 + 54,704,000 = $78,854,000

Weight of common stock = 24,150,000 / 78,854,000 = 0.306262

Weight of debt = 54,704,000 / 78,854,000 = 0.693738

WACC = weight of equity * cost of equity + weight of debt * cost of debt

WACC = 0.306262 * 0.158 + 0.693738 * 0.0304

WACC = 0.048389 + 0.02109

WACC = 0.069479 or 6.9479%