Question

Olsen Outfitters Inc. believes that its optimal capital structure consists of 55% common equity and 45% debt, and its tax rate is 40%. Olsen must raise additional capital to fund its upcoming expansion. The firm will have $1 million of retained earnings with a cost of rs = 12%. New common stock in an amount up to $10 million would have a cost of re = 13.5%. Furthermore, Olsen can raise up to $3 million of debt at an interest rate of rd = 11% and an additional $4 million of debt at rd = 15%. The CFO estimates that a proposed expansion would require an investment of $4.2 million. What is the WACC for the last dollar raised to complete the expansion? Round your answer to two decimal places.

Answer 1

We know that WACC = W_dr_d (1-Tax Rate) + W_er_e + W_sr_s

where, W_d = Weight of Debt ,W_e =Weight of Equity & W_s = Weight of retained earnings

cost of retained earnings upto  $1 million (r_s) = 12% = 0.12

cost of common stock upto $10 million (r_e) = 13.5% = 0.135

before tax cost of debt upto $3 million (r_d) = 11% =0.11

before tax cost of debt upto $9 million (r_d) = 15% =0.15

Required investment = $4.2 million & tax rate = 40% = 0.40

Amount of debt required in the Required investment of $4.2 million is = 45% x $4.2 million = $1.89 million

as Amount of debt required is $1.89 million before tax cost of debt is 11%

Amount of equity required in the Required investment of $4.2 million is = 55% x $4.2 million = $2.31 million

as Amount of equity required is $2.31 million which exceeds retained earnings upto  $1 million hence cost of common stock for rest $1.31 million is 13.5%.

W_d = $1.89 million / $4.2 million = 0.45

W_e = ($2.31 million - $1 million) / $4.2 million = 0.3119

W_s = $1 million / $4.2 million = 0.2381

WACC = 0.45 x 11% x(1-40%) + 0.3119 x 13.5% + 0.2381 x 12%

WACC = 0.45 x 0.11 x(1-0.40) + 0.3119 x 0.135 + 0.2381 x 0.12

WACC = 0.45 x 0.11 x0.60 + 0.3119 x 0.135 + 0.2381 x 0.12

WACC = 0.0297 + 0.04210 + 0.02857 = 0.10037 = 10.037%

WACC for the last dollar raised to complete the expansion is 10.037%