Question

Your company’s balance sheet currently shows the following:

Debt $1500 million Equity $2500 million Total Assets $4,000 million

Bonds have a par value of $1000, 8 years to maturity and have a coupon rate of 5.7% paid semiannually.

Other bonds with similar characteristics and risk currently have a yield to maturity of 6.78%.

Price of a bond is $934.15

The book value of common stock price is $45 per share.

The current stock price is $32 per share in the market.

Beta for your stock is 1.15 and the current risk-free return and market return are 3% and 10%, respectively.

The tax rate is 35%.

a) Find the market value and cost of debt and the market value and cost of equity.

b) Calculate the weighted average cost of capital using market values.

c) Calculate the weighted average cost of capital using book values.

d) calculate the cost of equity if your book value capital structure changes to 60% debt and 40% equity. Explain in detail why the cost of equity changed the way it did.

MAKE SURE YOU SOLVE WITH ALL STEPS AND DONT GIVE ME EXCEL SCREENSHOTS

Answer 1

Given Information:

Book Value of Debt = $ 1500 million

Book Value of Equity = $ 2500 million

Capital Employed = $ 4000 million (1500 + 2500)

a(i). Calculation of market value & cost of debt:

Book Value of Debt = $ 1500 million

Par Value of Debt = $ 1000

No. of bonds = $ 1500 million / $ 1000 = 1.5 million bonds

Price per bond = $ 934.15

Market Value of bonds = 1.5 million bonds * $ 934.15 = $ 1401.225 million

Cost of debt =

where C = Coupon payment = $ 1000 * 5.7% / 2 = $ 28.5

t = Tax rate = 35%

RV = Redemption Value = $ 1000

P = Price of the bond = $ 934.15

n = No. of years = 8 years * 2 sem-annual periods = 16 periods

Cost of debt =

Cost of debt = 2.34% per period or 4.68% p.a.

a(ii). Calculation of market value and cost of equity:

Book value of equity = $ 2500 million

Book value of shares = $ 45 per share

No. of shares = $ 2500 million / $ 45 = 55.5556 million shares (approx)

Market price per share = $ 32

Market value of equity = 55.5556 million * $ 32 = $ 1777.78 million

Cost of equity (using capm) = R_f + β_i * (R_m - R_f)

Cost of equity = 3% + 1.15 * (10% - 3%)

Cost of equity = 3% + 1.15 * 7%

Cost of equity = 11.05%

b. Calculation of Weighted Average Cost of Capital (WACC) using market value weights:

WACC = k_d * w_d + k_e * w_e where k_d = cost of debt

w_d = weight of debt

k_e = cost of equity

w_e = weight of debt

k_d = 4.68% (calculated in a(i))

w_d = $ 1401.225 m / ($ 1401.225 m + $ 1777.78 m) = 0.440775

k_e = 11.05% (calculated in a(ii))

w_e = $ 1777.78 m / ($ 1401.225 m + 1777.78 m) = 0.559225

WACC = 4.68% * 0.440775 + 11.05% * 0.559225

WACC = 8.24% (approx)

c. Calculation of Weighted Average Cost of Capital (WACC) using book value weights:

w_d = $ 1500 m / $ 4000 m = 0.375

w_e = $ 2500 m / $ 4000 m = 0.625

WACC = 4.68 * 0.375 + 11.05 * 0.625

WACC = 8.66% (approx)

d. Calculation of cost of equity on change of capital structure:

WACC using book value weights = 8.66% (calculated in c)

New weights: w_d = 60% ; w_e = 40%

WACC = k_d * w_d + k_e * w_e

The cost of debt remains constant at 4.68%

8.66% = 4.68% * 0.6 + k_e * 0.4

k_e = 14.63%

Reason for change in k_e:

The cost of equity increased from 11.05% to 14.63% due to change in capital structure. As the proportion of debt in the overall capital employed increased from 37.5% to 60%, the leverage as well as cost of interest in the company increases.

Interest on debt in a mandatory charge (unlike dividend on equity). It also ranks higher in repayment at the time of liquidation. Hence, a higher proportion of debt increases the risk of non-payment of equity dividend as well as capital repayment to the equity holders.As it increases the expectation of the equity holders, the cost of equity increases.