Question

Air Tampa has just been incorporated, and its board of directors is grappling with the question of optimal capital structure. The company plans to offer commuter air services between Tampa and smaller surrounding cities. Air Tampa believes it would have the same business risk as Jaxair, which is an airline that has been around for a few years and that has had zero growth. Jaxair's market-determined beta is 1.8, and it has a current market value debt ratio (total debt to total assets) of 45% and a federal-plus-state tax rate of 25%. Air Tampa expects to have investment tax credits when it begins business, which reduces its federal-plus-state tax rate to 15%. Air Tampa's owners expect that the total book and market value of the firm's stock, if it uses zero debt, would be $14 million. Air Tampa's CFO believes that the MM and Hamada formulas for the value of a levered firm and the levered firm's cost of capital should be used because zero growth is expected.
Required:
a. Estimate the beta of an unlevered firm in the commuter airline business based on Jaxair's market-determined beta.
b. Now assume that rd= rRF= 10% and that the market risk premium RPM for an unlevered commuter airline. 5%. Find the required rate of return on equity
c. Air Tampa is considering three capital structures: (1) $2 million debt, (2) $4 million debt, and (3) $6 million debt. Estimate Air Tampa's rs for these debt levels.

Answer 1

Answer:

a. Unlevered beta = 1.12

b. Required rate of return on equity = 15.60%

c-1. rs = 16.37%

c-2. rs = 17.40%

c-2. rs = 18.81%

Explanation:

a. Estimate the beta of an unlevered firm in the commuter airline business based on Jaxair's market-determined beta.

Levered beta = Unlevered beta * (1 + (D/S)(1 - T))

Therefore, we have:

Unlevered beta = Levered beta / (1 + (D/S)(1 - T)) .............. (1)

Where:

Levered beta = Jaxair's market-determined beta = 1.8

D = Debt ratio = 45%, or 0.45

S = Equity ratio = 1 - D = 1 - 0.45 = 0.55

T = Federal-plus-state tax rate = 25%, or 0.25

Substituting the values into equation (1), we have:

Unlevered beta = 1.8 / (1 + (0.45/0.55)(1 - 0.25)) = 1.12

b. Now assume that rd= rRF= 10% and that the market risk premium RPM for an unlevered commuter airline. 5%. Find the required rate of return on equity

Required rate of return on equity = ro = Rf + beta(Rm - Rf) .............. (2)

Where;

rd = Rf = 10%, or 0.10

beta = Unlevered beta = 1.12

(Rm - Rf) = market risk premium = RPM for an unlevered commuter airline = 5%, or 0.05

Substituting the values into equation (2), we have:

Required rate of return on equity = ro = 10% + 1.12(5%) = 10% + (1.12 * 5%) = 15.60%

c. Air Tampa is considering three capital structures: (1) $2 million debt, (2) $4 million debt, and (3) $6 million debt. Estimate Air Tampa's rs for these debt levels.

c-1. $2 million debt

D = Debt = $2 million

Value of unlevered firm = $14 million

T = Tax rate at start-up = 15%, or 0.15

Value of lerevered firm = Value of unlevered firm + (Debt * T) = $14 + ($2 * 15%) = $14.30 million

S = Value of equity = Value of lerevered firm - Debt = $14.30 - $2 = $12.30 million

rs = ro + ((ro - rd) * (D / S) * (1 - T)) ................... (3)

Where;

ro = 15.60%

rd = Rf = 10%, or 0.10

D = Debt = $2 million

S = Value of equity = $12.30 million

T = Tax rate at start-up = 15%, or 0.15

Substituting the values into equation (3), we have:

rs = 15.60% + ((15.60% - 10%) * (2 / 12.30) * (1 - 0.15)) = 16.37%

c-2. $4 million debt

D = Debt = $4 million

Value of unlevered firm = $14 million

T = Tax rate at start-up = 15%, or 0.15

Value of lerevered firm = Value of unlevered firm + (Debt * T) = $14 + ($4 * 15%) = $14.60 million

S = Value of equity = Value of lerevered firm - Debt = $14.60 - $4 = $10.60 million

Substituting all the relevant values into equation (3), we have:

rs = 15.60% + ((15.60% - 10%) * (4 / 10.60) * (1 - 0.15)) = 17.40%

c-3. $6 million debt

D = Debt = $6 million

Value of unlevered firm = $14 million

T = Tax rate at start-up = 15%, or 0.15

Value of lerevered firm = Value of unlevered firm + (Debt * T) = $14 + ($6 * 15%) = $14.90 million

S = Value of equity = Value of lerevered firm - Debt = $14.90 - $6 = $8.90 million

Substituting all the relevant values into equation (3), we have:

rs = 15.60% + ((15.60% - 10%) * (6 / 8.90) * (1 - 0.15)) = 18.81%