Question

Assume no taxes.

Current capital structure

Debt: zero. Equity: $200,000, total number of shares: 5,000. EBIT: Normal – $21,000; Expansion – 20% higher; Recession 25% lower.

Proposed capital structure Debt: $50,000. Cost of debt: 8%. Proceeds are used for purchase of equity.
(a) Calculate EPS under each of the three economic scenarios before debt is issued. Calculate the percentage changes in EPS when the economy expands or contracts.

(b) Repeat part (a) with the proposed capital structure.

(c) Suppose the market-to-book ratio is 1. Calculate the ROE.

Answer 1

a) EPS - NI / Number of shares outstanding
Normal EPS	21000/5000	4.20
Expansion EPS	21000(1.20)/5000	5.04
Recession	21000(1-0.25)/5000	3.15
b) Number of outstanding share = 5000*0.75=3750 shares
Normal EPS	(21000-4000)/3750	4.53
Expansion EPS	[21000(1.20)-4000)/3750	5.65
Recession	[21000(0.75)-4000)/3750	3.13
c) Market / Book ratio =1
Total Market = 1 * (200000+21000) = 221000
RoE = 221000 / 5000 = $44.20