Question

You are trying to assess the cost of capital for a small commercial aircraft manufacturer called Jetstream Inc. Unfortunately, Jetstream is a private company so you can not estimate its equity beta using its stock returns. You have, however, collected some information on comparable firms that are publicly traded (see the table below). Assume that Jetstream targets a stable debt to enterprise value ratio (D/(D+E)) of 10% and that its cost of debt is 3.95%.

All firms face a marginal tax rate of 21%, the market risk premium (?[?_?]−?_?) is 5%, and the risk-free rate (?_?) is 3.5%. Additionally, assume that corporate taxes are the only market imperfection.

	D/(D+E)	rD	βE	rE	rU
Lightwing Aircraft Inc.	50%	4.85%	1.8
Gulfstream Jets	45%	4.80%	1.75
Into Thin Air Corp	15%	4.00%	1.3
Turbulence Corp.	55%	4.87%	1.89

1. Using the CAPM calculate the cost of equity for each competing firm. Then, using the Modigliani and Miller formula calculate the unlevered cost of capital for each competing firm. Tabulate your results in a table similar to the one above.
2. Assume that the unlevered cost of capital of Jetstream Inc. is equal to the average unlevered cost of capital of the competing firms, what is Jetstream’s cost of equity? C) What is Jetstream’s WACC?

Answer 1

Computation of cost of equity of all competing firms

Cost of equity as per CAPM = rf + (E[rm] - rf)

First we have to calculate unlevered beta from the given levered beta

For Lightwing Aircraft Inc.

beta levered = 1.8

beta unlevered = beta levered Equity/(Debt(1-t)+Equity)

beta unlevered = 1.8 (0.5/0.895) = 1

Cost of equity = 3.5% + 1(5%) = 8.5%

For Gulfstream Jets

beta levered = 1.75

beta unlevered = 1.75(0.55/.9055) = 1.06

cost of equity = 3.5% + 1.06(5%) = 8.8%

For Into Thin Air Corp

beta levered = 1.3

beta unlevered = 1.3 (0.85/0.9685) = 1.14

cost of equity = 3.5% + 1.14(5%) = 9.2%

For Turbolence Corp

beta levered = 1.89

beta unlevered = 1.89 (0.45/0.8845) = 0.96

cost of equity = 3.5% + 0.96(5%) = 8.3%

Computation of unlevered cost of capital of all four firms

WACC = [rd (1-t) D/total capital] + [re e/total capital]

For Lightwing Aircraft Inc.

WACC = [4.85%(1-0.21)0.5] + [8.5% 0.5] = 6.17%

For Gulfstream Jets

WACC = [4.8%(1-0.21)0.45]+[8.80.55] = 6.55%

For Into Thin Air Corp

WACC = [4%(1-0.21)0.15]+[9.2%0.85] = 8.29%

For Turbolence Corp

WACC = [4.87%(1-0.21)0.55]+[8.3%0.45] = 5.85%

	rE	rU
Lightwing Aircraft Inc.	8.5%	6.17%
Gulfstream Jets	8.8%	6.55%
Into Thin Air Corp	9.2%	8.29%
Turbolence Corp	8.3%	5.85%

Computation of unlevered beta, cost of equity and cost of capital for Jetstream

Average of all four firms unlevered beta = (1+1.06+1.14+0.96)/4 = 1.04

beta levered = beta unlevered (Debt(1-t)+Equity)/Equity

= 1.04 [(0.1 0.79)+0.9]/0.9 = 1.13

Cost of equity = 3.5% + 1.13(5%) = 9.15%

WACC = [3.95%0.790.1]+[9.15%0.9] = 8.55%