Question

Magic Inc. has 1 billion of BBB-rated debt with a yield to maturity of 5%. BBBrated debt has a default rate of 5% and the expected loss rate in the event of default is 40%. Magic Inc’s stocks have a market value of 1 billion and a beta of 1. Assume the risk-free rate is 0%, the expected market risk premium is 10%, and corporate tax rate is 30%.

a. What is the firm’s cost of debt?

b. What is the firm’s cost of equity?

c. What is the firm’s weighted cost of capital?

d. Now you want to use the FFC model to calculate the equity cost of capital. You have estimated factor betas and factor returns below. Calculate the equity cost of capital using the FFC factor specification.

Factor Portfolio. Factor betas Average yearly returns

MKT - rf 1   10%

SMB -0.3    20%

HML -0.1 20%

PR1YR 0.1 70%

Answer 1

b) What is the firm Cost of Equity?

Ans: As per the data provided in the question

Beta=1

Risk free rate = 0%

Market risk premium=10%

According to the CAPM the required rate of return on equity is calculated by

ke = Rf + (Rm - Rf) B

Rf = Risk free rate

(Rm - Rf )= Market risk premium

B = Beta

Ke = 0 + 0.10*1

Ke =0.10

Ke = 10%

So the Cost of Equity is 10%

a) What is the firm cost of debt?

Ans: Cost of debt is the return that a company provide to is debt holder & creditor.

According to the data provided in the question YTM=5%

So, the cost of debt=5%

C) What is firm Weighted Cost of Capita?

Ans: Considering Weighted cost of capital as Weighted Average Cost of Capital.

Therefore,

WACC(Ko) = Ke(E / (E+D)) + Kd(1-T)(D / (E+D))

Where

Ke = Cost of Equity

E= Market Value of Equity

D= Market value of Debt

Kd = Cost of Debt

Ko = 0.10 * (1000000000 /(1000000000+1000000000)) + 0.05 * (1- 0.30) * (1000000000 / ( 1000000000 + 1000000000))

Ko = (0.10 * 0.5) + (0.05 * 0.7 * 0.5)

Ko= 0.05 + 0.0175

Ko= 0.0675

Ko= 6.75%

So The Weighted Cost of capital is 6.75%