Question

Arch Metals Corp. has 60% debt and 40% equity on its balance sheet.

a.) Solve for Arch’s cost of debt if the company has a 2% probability of default, a Loss Given Default of 55%, the risk-free rate is 2.75% and an expected marginal tax rate of 33%

. b.) Solve for Arch’s cost of equity if it has an equity beta of 1.25 and the market risk premium is 5%.

c.) Solve for Arch’s weighted average cost of capital (WACC）

Answer 1

Given about Arch Metals Corp,

a). Probability of default PD = 2%

Loss goven default LGD = 55%

Risk free rate Rf = 2.75%

=> company's cost of debt can be calculated using formula,

Cost of debt Kd = (1+Rf)/((1-PD) + PD*(1-LGD)) -1 = 1.0275/((1-.02) + 0.02*(1-0.55)) -1 = 3.89%

b), equity beta = 1.25

Market risk premium MRP = 5%

So, cost of equity of company using CAPM model is Rf + Beta*MRP

=> Cost of equity Ke = 2.75 + 1.25*5 = 9%

c). Weight of debt Wd = 60%

Weight of equity We = 40%

Tax rate T = 33%

So, WACC of the company = Wd*Kd*(1-T) + We*Ke = 0.6*3.89*(1-0.33) + 0.4*9 = 5.16%

So, WACC of Arch Metal Corp = 5.16%