Question

1. You are trying to determine the WACC for White Sox. It has the following characteristics. (12 points)

1. Discount rate of 10%.   The company had pre-tax net income of $50mm last year and paid taxes of $10mm.
2. White Sox has $900mm of total liabilities, $100mm of accounts payable, and $650mm of debt.
3. The company has 120mm shares authorized, 17mm shares issued, and 7mm shares of treasury stock.   The stock traded at $65 per share two years ago and now trades at $97.87 per share.
4. A 10-year senior bond was issued 1 year ago. It is priced at 97 today. The coupon rate is 6% paid semi-annually. Use the YTM on this bond as a proxy for the pre-tax cost of total debt.
5. The company pays a dividend of $.75 per share per quarter. Twelve years ago, the dividend was $0.30 per share. The ten-year treasury rate is 2%. The company’s Beta is 1.5 and the market return for equities is 8%.

Cost of Equity – CAPM
Cost of Equity – Gordon Growth
Pre-tax cost of debt
After-tax cost of debt
Total Capital
WACC (use average of CAPM and GGM for cost of equity)

Answer 1

i) Cost of equity (using capm) = Rf + Beta * (Rm - Rf)

Here,

Rf (risk free rate) = 2% or 0.02

Rm (market return) = 8% or 0.08

Beta = 1.5

Now,

Cost of equity = 0.02 + 1.5 * (0.08 - 0.02)

Cost of equity = 0.02 + 0.09

Cost of equity = 0.11 or 11%

ii) Cost of equity (Gordon growth model) = (D1 / P) + g

Here,

P (Price) = $97.87

a) g (growth rate) = (End value dividend / Start value dividend)^1/n - 1

n = 12 years

g = ($0.75 / $0.30)^1/12 - 1

g = ($2.5)^1/12 - 1

g = 1.0794 (refer note) - 1

g = 0.0794 or 7.94%

b) D1 (Expected dividend) = Current dividend + g

D 1 = $0.75 + ($0.75 * 0.0794)

D1 = $0.81

Here, $0.75 is assumed as current dividend.

Now put the values into formula,

Cost of equity = ($0.81 / $97.87) + 0.0794

Cost of equity = 0.0083 + 0.0794

Cost of equity = 0.0877 or 8.77%

Note : Steps to calculate 1/n root

Step 1 : Take 2.5 & press √ (root) sign 12 times

Step 2 : Deduct 1 (one) to result of step 1 , divide by n (ie. 12) and then add back 1 (one).

Step 3 : Press * (multiply) and = (equals to) sign

Step 4 : Repeat step 4 again 11 times

iii) a) Pre tax cost of debt = YTM

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

Here,

P (Par value) = $100 (assumed)

M (Market price) = $97

n (years remaining to maturity) = 9 years (10 year - 1 year ago)

Coupon = Par value * Coupon rate * 6/12 months

Coupon = $100 * 6% * 6/12 months = $3

Now,

YTM = ($3 + (($100 - $97)/9)) / (($100 + $97)/2)

YTM = ($3 + $0.33) / $98.50

YTM = $3.33 / $98.50

YTM (semi annual) = 0.0338

YTM (annually) = (1 + YTM semi annual)^n - 1

Here, n (no. Of compounding per year) = 2

YTM annually = (1 + 0.0338)^2 - 1

YTM = 0.0687 or 6.87%

b) After-tax cost of debt = YTM annual * (1 - Tax rate)

Here, tax rate = Tax / Before tax income

Tax rate = $10 mm / $50 mm

Tax rate = 0.20 or 20%

Now,

After tax cost of debt = 0.0687 * (1 - 0.20)

After tax cost of debt = 0.0550 or 5.50%

iv) Debt = 650 mm

Equity = (17 mm shares + 7mm treasury stock )* $97.87 per share

Equity = $2348.88 mm

Total capital = Debt + Equity

Total capital = $650 mm + $2,348.88 mm

Total capital = $2,998.88 mm

Weight of debt = Debt / Capital

Weight of debt = $650 mm / $2,998.88 mm = 0.22

Weight of equity = Equity / Capital

Weight of equity = $2,348.88 mm / $2,998.88 = 0.78

v) Average of cost of equity of CAPM & GGM = (Cost of equity using CAPM + Cost of equity using GGM) / 2

Average cost of equity = (0.11 + 0.0877) / 2

Average cost of equity = 0.0989 or 9.89%

vi) WACC = (Weight of debt * Cost of debt) + (Weight of equity * Cost of equity)

Using above details,

WACC = (0.22 * 0.055) + (0.78 * 0.0989)

WACC = 0.0121 + 0.0771

WACC = 0.0892 or 8.92%