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. Jaxair has been around for a few years, and it has about the same basic business risk as Air Tampa would have. Jaxair's market-determined beta is 1.9, and it has a current market value debt ratio (total debt to total assets) of 45% and a federal-plus-state tax rate of 35%. Air Tampa expects to be only marginally profitable at start-up; hence its tax rate would only be 30%. Air Tampa's owners expect that the total book and market value of the firm's stock, if it uses zero debt, would be $10 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. (These are given in equations VL = VU + VTax shield = VU + TD, rsL = rsU + (rsU - rd)(1 - T)(D/S), and b = bU[1 + (1 - T)(D/S)].) Estimate the beta of an unlevered firm in the commuter airline business based on Jaxair's market-determined beta. (Hint: This is a levered beta; use Equation b = bU[1 + (1 - T)(D/S)] and solve for bU.) Do not round intermediate calculations. Round your answer to three decimal places. 1.240 Now assume that rd = rRF = 8% and that the market risk premium RPM = 7%. Find the required rate of return on equity for an unlevered commuter airline. Do not round intermediate calculations. Round your answer to three decimal places. 16.681 % Air Tampa is considering three capital structures: (1) $3 million debt, (2) $5 million debt, and (3) $8 million debt. Estimate Air Tampa's rs for these debt levels. Do not round intermediate calculations. Round your answers to two decimal places. Air Tampa's rs for $3 million debt is %. Air Tampa's rs for $5 million debt is %. Air Tampa's rs for $8 million debt is %. Calculate Air Tampa's rs at $8 million debt while assuming its federal-plus-state tax rate is now 40%. (Hint: The increase in the tax rate causes VU to drop to $8 million.) Do not round intermediate calculations. Round your answer to two decimal places. % Compare this with your corresponding answer to part c. Higher tax rate the financial risk premium at a given market value debt/equity ratio.

Answer 1

Estimate the beta of an unlevered firm in the commuter airline business based on Jaxair's market-determined beta. (Hint: This is a levered beta; use Equation b = bU[1 + (1 - T)(D/S)] and solve for bU.) Do not round intermediate calculations. Round your answer to three decimal places. 1.240

b = bU[1 + (1 - T)(D/S)]

b = 1.9, T = 35%, current market value debt ratio (total debt to total assets) = D / (D + S) = 45%; Hence, S / (D + S) = 1 - 45% = 55%. Hence, D / S = 45% / 55% =  0.8182

Unlevered beta = bU = b / [1 + (1 - T)(D/S)] = 1.9 / [1 + (1 - 35%) x 0.81821} = 1.240356083 = 1.240

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Find the required rate of return on equity for an unlevered commuter airline. Do not round intermediate calculations. Round your answer to three decimal places. 16.681 %

The required rate of return on equity for an unlevered commuter airline = rRF + bU x RPM = 8% + 1.240356083 x 7% = 16.682%

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Air Tampa is considering three capital structures: (1) $3 million debt, (2) $5 million debt, and (3) $8 million debt. Estimate Air Tampa's rs for these debt levels.

Please see the table below. Please read the table along with the following notes. This will help you understand the mathematics:

• Financial figures are in $ mn
• Please refer to row 2. It tells you hiw each column has been calculated.
• Column 1 is the value of unlevered firm given to be $ 10 mn when there is no debt. Column 2 is tax rate applicable to Air Tampa = 30%.
• Column 3 is three different debt levels: 3 mn, 5 mn and 8 mn
• Column 4 and 5 are driven by formula. Column 5 gives value of levered firm = VL = Market value of debt + market value of equity = D + S. Hence,S = VL - D. This is done in column no. 6. Column number 7 is debt to equity ratio.
• Column no. 8 is rsU = 16.682% calculated earlier in the second sub part.
• Column 9 is pre tax cost of debt = rRF = 8%
• Column 10 is your answer based on the formula for rsL given in the question.

1	2	3	4	5	6	7	8	9	10
VU	T	D	T x D	VL = VU + T x D	S = VL - D	D / S	rsU	rD	rsL = rsU + (rsU - rd)(1 - T)(D/S)
10	30%	3	0.9	10.9	7.9	0.3797468	16.682%	8%	18.99%
10	30%	5	1.5	11.5	6.5	0.7692308	16.682%	8%	21.36%
10	30%	8	2.4	12.4	4.4	1.8181818	16.682%	8%	27.73%

Based on column 10 in the table above,

Air Tampa's rs for $3 million debt is 18.99%.

Air Tampa's rs for $5 million debt is 21.36%.

Air Tampa's rs for $8 million debt is 27.73%

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Calculate Air Tampa's rs at $8 million debt while assuming its federal-plus-state tax rate is now 40%. (Hint: The increase in the tax rate causes VU to drop to $8 million.) Do not round intermediate calculations. Round your answer to two decimal places. %

VU = $ 8 mn

T = 40%

D = $ 8 mn

Hence, VL = VU + T x D = 8 + 40% x 8 = $ 11.2 mn

S = VL - D = 11.2 - 8 = $ 3.2 mn

rsL = rsU + (rsU - rD) x (1 - T) x D / S = 16.682% + (16.682% - 8%) x (1 - 40%) x 8 / 3.2 = 29.71%

Air Tampa's rs at $8 million debt while assuming its federal-plus-state tax rate is now 40% = 29.71%

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Compare this with your corresponding answer to part c.

The required return on stock is higher in case of higher tax rate.

Higher tax rate increases the financial risk premium at a given market value debt/equity ratio.