Question

Problem 1 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. 1.      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. 2.      Assuming that the tax rate is 40% and now, there is a cost for the risk of default. Use the following table to answer these questions: Value of Debt RD Beta EBIT 800,000 0 5.0% 1.3925 Tax Rate 40% 250,000 5.5% 1.483015 T-bill Rate 3.0% 500,000 6% 1.542274 TSX 11.0% 750,000 6.5% 1.607016 1,000,000 7.0% 1.678038 1,250,000 9.0% 1.756303 1,500,000 11.0% 1.842075 1,750,000 13.0% 1.939488 2,000,000 15.0% 2.047619 a)             Calculate the required rate of return for the un-levered firm. b)             Calculate the market value of the un-levered firm using proposition I. c)             Calculate the WACC for an un-levered firm using proposition II. No calculation required (1 mark) 2 d)             Using the information from the table, calculate the value of the firm (proposition I), cost of equity, and the WACC (proposition II) of the firm if the firm issues $500,000 of debt. (6 marks) e)             Using the information from the table, 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

1)

a)

Required rate of return for unlevered firm = T-bill yield + beta*market risk premium

= 3% + 1.3925*8% = 14.14%

b)

Market value of firm = operating income/required rate of return

operating income = $800,000

Market value of un-levered firm = operating income*(1-T)/required rate of return  = 800,000*(1-0.40)/0.1414

= $3,394,625.177

c)

WACC = (proportion of debt in capital structure * expected return on debt) + (proportion of equity in capital structure * expected return on equity )

since the firm is unlevered , proportion of debt = 0

WACC = expected return on equity = 14.14% ( calculated in part a)

d)

value of debt = $750,000

interest rate = 5% = 0.05

Total value of firm = value of unlevered firm + tax rate* (market value of debt)

= 3,394,625.177 + 0.40*(750,000)

= $3,694,625.177

Beta of levered firm = Beta of unlevered firm*(1+(1-T)*(D/E))

T = tax rate = 0.40

D = market value of debt = 750,000

E = market value of equity = 3,394,625.177

D + E = 3,394,625.177 + 750,000 = 4,144,625.177

Beta of unlevered firm = 1.3925

Beta of levered firm = 1.3925*(1+0.60*(750000/3,394,625.177)) = 1.3925*(1+0.0795375)

= 1.57709

Cost of equity = T-bill yield + beta of levered firm*market risk premium

= 3% + 1.57709*8 = 15.61672%

WACC = [D/(D+E)]*Expected return on debt*(1-T)  + [E/(D+E)]* expected return on equity

= [750,000/4,144,625.177]*5*0.60 + [3,394,625.177/4,144,625.177]*15.61672

= 0.542871768 + 12.7907612 = 13.333632%