Question

1. You have been asked to analyze the capital structure of Stevenson Steel. The company has supplied you with the following information:

• There are 100 million shares outstanding, trading at $ 10 a share.

• The firm has bond outstanding of $500 million (in market value) in total. Each bond has a coupon rate of 6% with semiannual payment and 10 year maturity. Current price of each bond is quoted at 96.7.

• The beta for the firm currently is 1.04, the risk free rate is 5% and the market risk premium is 5.5%.

• The expected dividend payment for the next year is $0.5/share, and it is expected to grow at 5% every year.

• The tax rate is 40%.

a. Estimate the current equity cost of capital for Stevens Steel. Please use all the possible methods and then take the average as your final estimate.

b. Estimate the current debt cost of capital for Stevens Steel. c. What is the firm’s pretax WACC and aftertax WACC?

e. Now assume that you have computed the optimal debt-to-equity ratio to be 75%. If it moves to the optimal debt level, estimate the new after-tax cost of capital according to MM theory.

Answer 1

a) i) Cost of equity using CAPM method

Cost of equity (CAPM) = Rf + Beta(Rm - Rf)

Here,

Rf (Risk free rate) = 5% or 0.05

Rm - Rf (Risk premium) = 5.5% or 0.055

Beta = 1.04

Now,

Cost of equity (CAPM) = 0.05 + (1.04 * 0.055)

Cost of equity (CAPM) = 0.1072 or 10.72%

ii) Cost of equity using dividend discount model

P = D1 / (Ke - g)

Here,

P (Price of share) = $10 per share

D1 (Expected dividend) = $0.5 per share

Ke (Cost of equity) = ?

g (Growth) = 5% or 0.05

Now, put the values into formula

$10 = $0.5 / (Ke - 0.05)

Ke - 0.05 = $0.5 / $10

Ke - 0.05 = 0.05

Ke = 0.05 + 0.05

Ke (Cost of equity) = 0.10 or 10%

iii) Cost of equity (Taking average of cost of equity as per CAPM & dividend discount model)

Cost of equity (average basis)= (10.72% + 10%)/2

Average cost of equity = 10.35% or 0.1035

b) Cost of debt is YTM (yield to maturity) of bonds

YTM = (Coupon + ((P - M) /n)) / ((P + M) /2)

Here,

Par value (P) assumed = $100

Coupon (semi annual) = Par value * Rate of bond * 6/12 months = $100 * 6% * 6/12 = $3

M (Market value) = $96.70

n (years to maturity -semi annual)= 10 years*2= 20

Now,

YTM = ($3 + (($100 - $96.70)/20)) / (($100 + $96.70)/2)

YTM = ($3 + 0.1650) / $98.35

YTM(semi annual) = $3.1650 / $98.35 = 0.0322 or 3.22%

YTM (Annual cost of debt) = 3.22% * 2 = 6.44%

c) WACC calculations :

Debt = $500 million

Equity = 100 million shares*$10 per share = $1000 million

Total capital = Equity + Debt = $1000 + $500 = $1500 million

Weight of debt = Debt / Total capital = $500/$1500 million = 0.33

Weight of equity = 1 - Weight of debt

Weight of equity = 1 - 0.33 = 0.67

Cost of debt = 6.44% or 0.0644

Cost of equity = 10.35% or 0.1035

Tax rate = 40%

i) WACC (before tax) = (Weight of debt * Cost of debt) + (Weight of equity * Cost of equity)

WACC (before tax) = (0.33 * 0.0644) + (0.67 * 0.1035) = 0.0213 + 0.0694

WACC (before tax) = 0.0907 or 9.07%

ii) WACC (after tax) = (Weight of debt * Cost of debt * (1 - Tax rate)) + (Weight of equity * Cost of equity)

WACC (after tax) = (0.33 * 0.0644 * (1 - 0.40)) + (0.67 * 0.1035)

WACC (after tax) = 0.0128 + 0.0694

WACC (after tax) = 0.0822 or 8.22%

d) Debt equity ratio = Debt / Equity

Let debt = x & equity = 1 - x

Debt equity ratio = 75% or 0.75

Use the formula,

0.75 = x / (1 - x)

0.75 * (1 - x) = x

0.75 - 0.75x = x

0.75 = x + 0.75x

0.75 = 1.75x

x = 0.75 / 1.75

x(Debt weight) = 0.43

Equity weight (1 - x) = 1 - 0.43 = 0.57

Tax rate = 40% or 0.40

Cost of equity = 10.35% or 0.1035

Cost of debt = 6.44% or 0.0644

Now,

WACC (after tax) = (Weight of debt * Cost of debt * (1 - Tax rate)) + (Weight of equity * Cost of equity)

WACC (after tax) = (0.43 * 0.0644 * (1 - 0.40)) + (0.57 * 0.1035)

WACC (after tax) = 0.0166 + 0.0590

WACC (after tax) = 0.0756 or 7.56%