Question

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A firm has issued 5,000 10 year zero coupon bonds outstanding (par value 1,000) with a...

A firm has issued 5,000 10 year zero coupon bonds outstanding (par value 1,000) with a YTM of 4%. It has 100,000 common shares outstanding. The stock has a Beta of 1.1. The risk free rate is 2%, and the market return is 8%. The firm is expected to pay a 2.00 dividend and has a growth rate of 3%. If the firm tax rate is 20%, what is the company’s WACC?

Expert Solution

Answer-

Given

Debt proportion in capital structure

Number of bonds issued = 5000
Par value of bonds = FV = 1000
Number of years to maturity = N = 10
Coupon payment = PMT = $ 0 [ Zero coupon bond]
YTM = I/Y = 4 %

Present Value = PV = ?

PV = 675.564

Therefore the present value or market price = $ 675.564

The total value of bonds = Market value x number of bonds
The total value of bonds = $ 675.564 x 5000

The total value of bonds ( Debt) = $ 3377820

Equity proportion in capital structure

Number of shares outstansding = 100000
Expected Dividend ( D1) = $ 2
Growth rate = g = 3 %

Cost of equity (r)

r = Risk free rate + Beta x (Market return - Risk free rate )

Risk free rate = 2 %
Beta = 1.1
Maerket return = 8 %
Substituting the values we get

r = 2 % + 1.1 x ( 8 % - 2 % )

r = 2 % + 1.1 x 6 %
r = 2 % + 6.6 %
r = 8.6 %

Therefore cost of equity r = 8.6 %

Value of stock ( V) = D1 / r - g
Substituting the values we get

V = $ 2 / ( 8.6 % - 3 % )
V = $ 2 / (0.086 - 0.03)

V = $ 2 / 0.056
V = $ 35.7143

Value of stock = V = $ 35.71428

Total Equity value = Value of stock x number of shares outstanding
Total Equity value = $ 35.71428 x 100000 = $ 3571428

Wt of equity in capital structure = Equity / ( Equity + Debt)

Wt of equity in capital structure = $ 3571428 / ( $ 3571428 + $ 3377820 )

Wt of equity in capital structure = $ 3571428 / $ 6949248

Wt of equity in capital structure = 0.5139

Wt of debt in capital structure = 1 - 0.5139 = 0.4861

After tax Cost of debt = YTM x ( 1 - Tax rate)
Tax rate = 20 %

After tax Cost of debt = 4 % x ( 1 - 20 %)

After tax Cost of debt = 4 % x ( 1 -0.20) = 4 % x 0.80 = 3.20 %

WACC

WACC = Wt of equity x cost of equity + Wt of debt x After tax cost of debt

WACC = 0.5139 x 8.6 % + 0.4861 x 3.2 %

WACC = 4.4195 % + 1.5555 %

WACC = 5.975 %

Therefore the Company's WACC = 5.975 %

jeff jeffy answered 1 year ago

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