Question

Tartan Industries currently has total capital equal to $8 million, has zero debt, is in the 40% federal-plus-state tax bracket, has a net income of $4 million, and distributes 40% of its earnings as dividends. Net income is expected to grow at a constant rate of 4% per year, 130,000 shares of stock are outstanding, and the current WACC is 13.40%.

The company is considering a recapitalization where it will issue $2 million in debt and use the proceeds to repurchase stock. Investment bankers have estimated that if the company goes through with the recapitalization, its before-tax cost of debt will be 11% and its cost of equity will rise to 16.5%.

1. What is the stock's current price per share (before the recapitalization)? Round your answer to the nearest cent. Do not round intermediate steps.
   $
2. Assuming that the company maintains the same payout ratio, what will be its stock price following the recapitalization? Assume that shares are repurchased at the price calculated in part a. Round your answer to the nearest cent. Do not round intermediate steps.
   $

Answer 1

a. stock's current price = current dividend per share*(1+constant dividend growth rate)/(WACC - constant dividend growth rate)

earnings and dividends will grow at same constant growth rate of 4%.

current dividend per share = (Net income*dividend payout ratio)/no. of shares outstanding

current dividend per share = ($4,000,000*40%)/130,000 = $1,600,000‬/130,000 = $12.30769230769231

stock's current price = $12.30769230769231*(1+0.04)/(0.1340 - 0.04) = $12.30769230769231*1.04/0.094‬ = $12.8‬/0.094 = $136.17

b. After recapitalization, WACC will change because firm's capital structure will have one more source of financing i.e. debt.

New WACC = weight of debt*after-tax cost of debt + weight of equity*cost of equity

total capital of the firm will remain the same at $8 million but its composition will change. earlier it was 100% equity but now it will have both equity and debt. we have to calculate weight of debt an equity as % of total capital. new debt is $2 million. so, new equity will be $8 million - $2 million = $6 million.

weight of debt = $2 million/$8 million = 0.25‬

weight of equity = $6 million/$8 million = 0.75‬

before-tax cost of debt is given as 11% and cost of equity as 16.5%.

after-tax cost of debt = before-tax cost of debt*(1-tax rate) = 11%*(1-0.40) = 11%*0.60 = 6.6‬%

New WACC = 0.25*6.6% + 0.75*16.5% = 1.65% + 12.375‬% = 14.025%

now we calculate new no. of shares outstanding. shares will be repurchased at $136.17 price per share calculated in part a.

new no. of shares outstanding = existing no. of shares - new shares purchased

new no. of shares outstanding = 130,000 - $2,000,000/$136.17 = 130,000 - 14,688 = 115,312

firm value = current dividend*(1+constant dividend growth rate)/(New WACC - constant dividend growth rate)

firm value = $1,600,000*1.04/(0.14025 - 0.04) = $1,664,000‬/0.10025‬ = $16,598,503.74064838‬

equity value = firm value - value of debt = $16,598,503.74064838‬ - $2,000,000 = $14,598,503.74064838‬

stock price after recapitalization = equity value/new no. of shares outstanding = $14,598,503.74064838‬/115,312 = $126.60