Question

You have information regarding your firm’s (call it Firm A) common equity:

Market value of equity = $10M.

Current market price per share = $20.

Q(a):- How many shares are outstanding?

Suppose you are given additional information regarding the firm’s equity and market returns:

Standard deviation of equity returns (σA ) = 0.20

Correlation between your firm’s equity returns and market returns (ρA,M ) = 0.76

Standard deviation of market returns (σM ) = 0.175

Market risk premium = 6.25%

Risk free rate = 2.5%

Q(b):- What is your firm’s equity beta?

Q(c):- What is the cost of equity capital?

Lastly, assume you have the following information regarding your firm’s debt:

Market value of bonds = $5M.

Current market price per bond = $785.

Face value = $1000.

I.e., the amount of money returned at maturity by each bond.

Zero-coupon (i.e., the bond only pays out its face value at the maturity date).

Remaining time to maturity = 4 years.

Tax rate = 35%.

Q(d):- What is the after-tax cost of debt?

Q(e):- What is the weighted average cost of capital?

Answer 1

(a)

Shares outstanding = Market capitalization / Market price per share

                                    = $10M / $20

                                   = 500,000 shares outstanding.

 

(b)

equity beta = [(σA )/(σM ) ] * (ρA,M )

                     = 0.2 * 0.76 / 0.175

                     = 1.216

 

(c)

Cost of equity under CAPM = Risk free rate + [ Beta * Market risk premium ]

                                                 = 2.5% + ( 1.216 * 6.25%)

                                                 = 2.5% + 7.90%

                                                 = 10.4%

 

(d)

Yield to maturity of zero coupon Bond = [(F-P)/n ] / (F+P)/2

                                                                      = [($1,000-$785)/4years ] / ($1000+$785)/2

                                                                     = $53.75/$892.5

                                                                     = 6.02%

 

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

                                       = 6.02% * (1-35%)

                                       = 3.91%

 

(e) WACC = 6.98%

WACC = (Cost of equity * Weigh in equity) + (after tax cost of debt * Weight in debt)

 

It is assumed that capital is equally invested in debt and equity.

(No information given about capital mix ratio in given question)

WACC = (0.5 * 10.4%) + (0.5 * 3.91%)

            = 5.2% + 1.96%

           = 6.98%

(a) Shares outstanding = 500,000 shares outstanding.

(b) equity beta = 1.216

(c) Cost of equity under CAPM = 10.4%

(d) Yield to maturity of zero coupon Bond = 6.02%

After tax cost of debt = 3.91%

(e) WACC = 6.98%