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.
<u>c-1. $2 million debt</u>
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%
<u>c-2. $4 million debt</u>
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%
<u>c-3. $6 million debt</u>
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%
