Question

Question 5 (This question is from the Week 10 Tutorial) Big Water Ltd currently has the following capital structure: Debt: $4,500,000 paying 9.5% coupon bonds outstanding with 12 years to maturity, an annual before-tax yield to maturity of 8% on a new issue. The bonds currently sell for $1,113 per $1,000 face value. Ordinary Shares: 65,000 shares outstanding currently selling for $75 per share. The company just paid a $6.50 dividend per share and is experiencing a 6% growth rate in dividends, which it expects to continue indefinitely.

(Note - The firm's marginal tax rate is 30%.) Required:

a) Calculate the current total market value of the company.

b) Calculate the capital structure of the company.

c) Calculate the weighted average cost of capital (WACC) for the firm.

Answer 1

Answer:

a) $9,883,500

b) 50.68% Debt 49.32% Equity

c) 10.33%

.

Step-by-step explanation

a) Current total market value of the company

Total market value = Market value of debt + market value of equity

= (Number of bonds x current price per bond) + (Number of shares x current price per share)

= ((4,500,000/1,000) x 1,113) + (65,000 x 75)

= 5,008,500 + 4,875,000

= 9,883,500

Thus total market value of the company is $9,883,500.

.

b) Capital structure of the company:

In order to calculate the proportion of debt, divide the market value of debt by the market value of the total company. Similarly proportion of equity is calculated by dividing the market value of equity by market value of total company.

Debt = Market Value of debt/Market Value of the total company

= 5,008,500/9,883,500

= 0.5068 or 50.68%

.

Equity = Market Value of shares/Market value of the total company

= 4,875,000/9,883,500

= 0.4932 or 49.32%

.

Thus the capital structure of the company is:

Debt: 50.68%

Equity: 49.32%

.

c) WACC of the firm.

WACC = [Weight of equity x Cost of equity] + [Weight of debt x Cost of Debt x (1-T)]

We have the following information:

Weight of Equity = 49.32% = 0.4932

Weight of Debt = 50.68% = 0.5068

T = Tax rate = 30% = 0.30

Cost of debt = 8% (Yield to maturity)

Cost of equity = ?

WACC = ?

Let's workout cost of equity first in order to calculate WACC.

Cost of Equity:

We can simple apply Dividend Growth Model (Gordon growth model):

P = D0(1 + g)/(r - g)

We have the following information from the question:

P = Price = 75

D0 = Dividend just paid = 6.50

g = growth = 6% = 0.06

r = cost of equity = ?

.

We can put the values in the above equation and solve for r.

P = D0(1 + g)/(r - g)

75 = 6.50(1.06)/(r - 0.06)

75 = 6.89/(r - 0.06)

We can rearrange the equation as:

r - 0.06 = 6.89/75

r - 0.06 = 0.0919

r = 0.092 + 0.06

r = 0.152 = 15.20%

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We can now put the values in the WACC equation and calculate WACC:

WACC = [Weight of equity x Cost of equity] + [Weight of debt x Cost of Debt x (1-T)]

= [0.4932 x 0.1520] + [0.5068 x 0.08 x (1 - 0.30)]

= [0.0749664] + [0.0283808]

= 0.1033472 = 10.33472% or 10.33% (rounded to two decimal places)

.

Thus WACC of the firm is 10.33%.