Question

Gamma Medical Company is currently an un-levered firm with a beta of 1.3925. Government of Canada T-bills are yielding 3% and the market risk premium is 8%. You expect the company will be able to earn the required rate of return forever on an expected before tax earnings of $800,000 per year.

Assume that the tax rate is 40% and there is no cost for the risk of default.

a) Calculate the required rate of return for the un-levered firm.

b) Calculate the market value of the firm using proposition I.

c) Calculate the WACC for the firm using proposition II. No calculation required. (1 mark)

d) The current market interest rate for any debt issued by the company is 5%. If the firm issues $750,000 in debt, calculate the total value of the firm, cost of equity, and the WACC

e) The current market interest rate for any debt issued by the company is 5%. If the firm issues $2,000,000 in debt, what would you expect to happen to the total value of the firm, cost of equity and the WACC? Briefly explain. No calculations required.

Answer 1

Answer a:

For calculating the required rate of return for the un-levered firm

We use CAPM formula

R_a = R_f + _a*(R_m -R_f)

R_a = Return on stock/portfolio a

_a = Beta of stock/portfolio a

R_f = Risk free rate of return

R_m = Return on market portfolio

R_m - R_f = market risk premium

So,

Required rate of return = 3 + 1.3925*(8)

Required rate of return = 14.14%

Answer b:

We have expected before tax earnings = $800,000 per year, Which will be able to earn the required rate of return forever.

Profit after tax = $800,000 *(1-40%) = $480,000

So, market value of firm = $480,000 /14.14%

Market value of firm = $3,394,625

Answer c:

For un levered company WACC = required return on equity

WACC = 14/14%

Answer d:

The current market interest rate for any debt issued by the company is 5%. If the firm issues $750,000 in debt

Now company will pay interest of (5%*750,000=) $37,500

So Profit before tax = $800,000 - $37,500 = $762,500

So profit after tax = $762,500 * (1-40%) = $457,500

Now for there is no cost for the risk of default

Now for levered beta we have formula

Levered beta = Unlevered beta (1+ (1-t) (Debt/Equity))

R_a = R_f + Levered beta*(R_m -R_f)

R_a = R_f + [Unlevered beta (1+ (1-t) (Debt/Equity))]*(R_m -R_f)

R_a = R_f + [Unlevered beta (1+ (1-t) (Debt/(PAT/ (R_a/100)))]*(R_m -R_f)

R_a = 3 + [1.3925* (1+ (1-40%)* (750,000/(457,500/ R_a)))]*8

R_a = 3 + [11.14* (1+ 0.00984* R_a)]

R_a = 3 + 11.14+ 0.10962* R_a

R_a = 15.88%

i.e. cost of equity = 15.88%

Value of equity = 457,500/15.88%

Value of equity = $2,880,982

Total value of the firm = Value of debt + value of equity

Total value of the firm = 2,880,982 + 750,000

Total value of the firm = $3,630,982

WACC = 15.88*(2,880,982/3,630,982) + (1-40%) *(750,000/3,630,982)*5

WACC = 12.6 + 0.62

WACC = 13.24%

Answer e:

Now if the firm issues $2,000,000 in debt which is very significant following things happen

1. Cost of equity : as the leverage is more the levered beta will be more so the cost of equity will increase
2. WACC: as cost of debt and tax rate is constant, as cost of equity increasing WACC is also increasing
3. Total value of firm: as profit before interest and tax (which is available for both debt and equity holder) is constant and WACC is increasing, total value of firm will decrease (as WACC is discounting factor)