Question

3G is an all-equity firm with 200,000 shares outstanding, has $2,000,000 of EBIT, which is expected to remain constant in the future. The company pays out all of its earnings, so earnings per share (EPS) equal dividends per shares (DPS). Its tax rate is 40%.
The company is considering issuing $5,000,000 of 10.0% bonds and using the proceeds to repurchase stock. The risk-free rate is 6.5%, the market risk premium is 5.0%, and the beta is currently 0.90, but the CFO believes beta would rise to 1.10 if the recapitalization occurs.

Assuming that the shares can be repurchased at the price that existed prior to the recapitalization, what would the price be following the recapitalization?

Answer 1

Before the Recapitalization:

rS = rRF + _old(RP_m) = 6.5% + (0.9 x 5%) = 6.5% + 4.5% = 11%

DPS = EPS = [EBIT x (1 - t)] / Shares = [$2,000,000 x (1 - 0.40)] / 200,000 = $1,200,000 / 200,000 = $6

P0 = DPS / rS = $6 / 0.11 = $54.55

Shares Repurchased = Bonds Issued / P0 = $5,000,000 / $54.55 = 91,667 shares

After the Recapitalization:

rS = rRF + _new(RP_m) = 6.5% + (1.1 x 5%) = 6.5% + 5.5% = 12%

DPS = EPS = [{EBIT - (rD x Bonds)} x (1 - t)] / Shares

= [{$2,000,000 - (0.10 x $5,000,000)} x (1 - 0.40)] / (200,000 - 91,667)

= $900,000 / 108,333 = $8.31

P0 = DPS / rS = $8.31 / 0.12 = $69.23