Question

ABC Inc. is an unlevered firm that has EBIT of $2,000,000 and a required return on equity of 10%.    The firm has a corporate tax rate of 40% and has estimated that the tax rates for its investors are 25% on stock income and 50% on bond income. Assume the M&M personal tax case holds.

A) Assume that ABC Inc. can issue any level of debt for a fixed before-tax rate of 6%. What will the total value of the firm be if it issues the following levels of debt and uses the proceeds to repurchase shares:

$1,000,000

$5,000,000

$10,000,000

B) Using the same assumptions as in (a), assume the firm estimates that the present value of any financial distress costs would be $4,000,000. The probability of financial distress for each level of debt is :

Amount of Debt                 Probability of Distress

$0                              0%

$1,000,000               7.5%

$5,000,000               25%

$10,000,000             50%

Redo the value calculations from part (a) including the impact of financial distress.

C) What do the results from (a) and (b) indicate about the optimal level of debt in a world with both corporate and personal taxes when financial distress is included in the analysis?

Answer 1

Answer :

Value Of Unlevered Firm = V_U = ( EBIT * (1-T_C )) / R_e

Where, T_{C =} Corporate Tax Rate

R_{e =} Return on Equity

Value Of Unlevered Firm =( $20,000,000 * (1 - 0.4)) / 0.10

                                             = $ 12,000,000 / 0.10

                                            = $ 120,000,000

A)     

Value Of Unlevered Firm = V_L = V_U + (1 – {(1- T_C ) (1- T_S )/ (1- T_B )}) * B

Where , T_{C =} Corporate Tax Rate

                           T_{S =} Personal Tax Rate on Equity Income

                           T_{B =} Personal Tax Rate on Interest Income

Case I ) When Amount of Debt is $1,000,000

Value Of Unlevered Firm = V_L = V_U + (1 – {(1- T_C ) (1- T_S )/ (1- T_B )}) * B

                                             =$120,000,000 + (1-{(1-0.4)*(1-0.25)/(1-0.5)})*$1,000,000

                                             = $120,000,000+ (1-{(0.6*0.75/0.5)}*$ 1,000,000

                                             = $120,000,000+ (1-0.9)*$ 1,000,000

                                             = $120,000,000+ (0.1)*$ 1,000,000

                                             = $120,000,000+ $ 100,000

                                             = $120,100,000

Case II ) When Amount of Debt is $5,000,000

Value Of Unlevered Firm = V_L = V_U + (1 – {(1- T_C ) (1- T_S )/ (1- T_B )}) * B

                                             =$120,000,000 + (1-{(1-0.4)*(1-0.25)/(1-0.5)})*$5,000,000

                                             = $120,000,000+ (1-{(0.6*0.75/0.5)}*$ 5,000,000

                                             = $120,000,000+ (1-0.9)*$ 5,000,000

                                             = $120,000,000+ (0.1)*$ 5,000,000

                                             = $120,000,000+ $ 500,000

                                             = $120,500,000

CaseIII ) When Amount of Debt is $10,000,000

Value Of Unlevered Firm = V_L = V_U + (1 – {(1- T_C ) (1- T_S )/ (1- T_B )}) * B

                                             =$120,000,000 + (1-{(1-0.4)*(1-0.25)/(1-0.5)})*$10,000,000

                                             = $120,000,000+ (1-{(0.6*0.75/0.5)}*$ 10,000,000

                                             = $120,000,000+ (1-0.9)*$ 10,000,000

                                             = $120,000,000+ (0.1)*$ 10,000,000

                                             = $120,000,000+ $ 1,000,000

                                             = $121,000,000

B)     

Value Of Unlevered Firm = V_L = V_U + (1 – {(1- T_C ) (1- T_S )/ (1- T_B )}) * B – (C_D* P_D)

Where , T_{C =} Corporate Tax Rate

                           T_{S =} Personal Tax Rate on Equity Income

                           T_{B =} Personal Tax Rate on Interest Income

C_{D =} Cost of Distress

P_{D =} Probability of Distress

Case I ) When Amount of Debt is $1,000,000

Value Of Unlevered Firm = V_L = V_U + (1 – {(1- T_C ) (1- T_S )/ (1- T_B )}) * B – (C_D* P_D)

                                             =$120,000,000 + (1-{(1-0.4)*(1-0.25)/(1-0.5)})*$1,000,000 – (7.5% * 4,000,000)

                                             = $120,000,000+ (1-{(0.6*0.75/0.5)}*$ 1,000,000 - $300,000

                                             = $120,000,000+ (1-0.9)*$ 1,000,000 - $300,000

                                             = $120,000,000+ (0.1)*$ 1,000,000 -$300,000

                                             = $120,000,000+ $ 100,000 -$300,000

                                             = $119,800,000

Case II ) When Amount of Debt is $5,000,000

Value Of Unlevered Firm = V_L = V_U + (1 – {(1- T_C ) (1- T_S )/ (1- T_B )}) * B – (C_D* P_D)

                                             =$120,000,000 + (1-{(1-0.4)*(1-0.25)/(1-0.5)})*$5,000,000 – (25% * 4,000,000)

                                             = $120,000,000+ (1-{(0.6*0.75/0.5)}*$ 5,000,000 - $1,000,000

                                             = $120,000,000+ (1-0.9)*$ 5,000,000 - $1,000,000

                                             = $120,000,000+ (0.1)*$ 5,000,000 -$ 1,000,000,

                                             = $120,000,000+ $ 500,000 - $ 1,000,000

                                             = $110,500,000

CaseIII ) When Amount of Debt is $10,000,000

Value Of Unlevered Firm = V_L = V_U + (1 – {(1- T_C ) (1- T_S )/ (1- T_B )}) * B – (C_D* P_D)

                                             =$120,000,000 + (1-{(1-0.4)*(1-0.25)/(1-0.5)})*$10,000,000 – (50%* $4,000,000)

                                             = $120,000,000+ (1-{(0.6*0.75/0.5)}*$ 10,000,000 - $2,000,000

                                             = $120,000,000+ (1-0.9)*$ 10,000,000 -$2,000,000

                                             = $120,000,000+ (0.1)*$ 10,000,000 - $ 2,000,000

                                             = $120,000,000+ $ 1,000,000 -$ 2,000,000

                                             = $119,000,000

C )

Debt Level	Value of Firm
$0	$ 120,000,000
$1,000,000	$119,800,000
$5,000,000	$119,500,000
$10,000,000	$119,000,000

Optimal level of debt in a above senario with both corporate and personal taxes when financial distress is included in the analysis is when ABC inc debt free state as value of Firm is maximum when Debt level is $0.