Question

0 Firms U and L are in the same risk class and that both have EBIT = $1,000,000. Firm U uses no debt financing and its cost of equity is KsU-15%. Firm L has $2 million of debt outstanding at a cost of Kd = 5%. There are no taxes and MM assumptions hold. 1 , Using the data given above, but now assuming that firms L and U are both subject to a 40% corporate tax rate, repeat the analysis under the MM with tax model. Now suppose investors are subiect to the following tax rtes: TD 20% and Ts 10%. What is the gain from leverage according to the Miller's Model? How does this gain compare to the gain in the MM model with corporate taxes? Some Relevant and Useful Formulas: 4 Find V, S, Ks, and WACC for firms U and L. 9 10 Vu-EBIT/K 12 13 14 15 16 17 18 19 20 21 M&M Proposition I: Vi-Vu+ TD M&M Proposition II: KSL-Ku(K,U-K) (1 - T) (D/S). Vu = EBIT( 1-T)/KSU KK (K,u - Kd) (1-T)D/S) WACCL= (D/V) Kd (1-T) + (S/V)K, and VL-Vu + TCD

Answer 1

The calculation for part 1 has been done as follows :

a. Find V_u and V_L

V_U = EBIT/K_U

  =$1,000,000/0.15

=$6,666,667

V_U=V_L =$6,666,667

b. Find the market value of Firm L's debt and equity

V_L =D+S =$6,666,667

$6,666,667 = $2,000,000 + S

$4,666,667 =S

c. Find KsL

K_SL = K_SU+ (K_SU -K_D) (D/S)

K_SL =15+(15-5)2,000,000/4,666,667

=19.28%

d. WACC for firm U is equal to r_su

For Firm L is:

WACC =W_D K_D + W_CE K_S =(D/V)K_D +(S/V) K_S

=2,000,000/6,666,667)5+(4,666,667/6,666,667)19.28

= 15%

  

2.The calculation for part 2 has been done as follows :

a.Find V_u and V_L

V_U = EBIT(1-t)/K_U

  =$1,000,000(0.60)/0.15

=$4,000,000

    V_L = V_U + TD

=$4,000,000+0.60*2,000,000

= $5,200,000

b. Find the market value of Firm L's debt and equity

V_L =D+S =$5,200,000

$5,200,000 = $2,000,000 + S

$3,200,000 =S

c. Find K_SL

K_SL = K_SU + (K_SU -K_D)(1-T) D/S

K = 15+ (15-5)*.60*2,000,000/3,200,000

= 18.75%

d. Find Firm L's Wacc

WACCL= (D/V)K_D(1-T) +(S/V)KS

= 2,000,000/5,200,000*50.60+3,200,000/5,200,000*18.75

=12.65

When corporate taxes are considered Wacc is lower for firm L than Firm U.

3. The calculation for part 3 are as follows :

Now we need to compute gain from leverage

V_L = V_U +{1- [(1-t_C ) (1-t_S)]/(1-t_D)}*D

Where, t_C = Corporate tax

t_s = personal tax rate on Stock income

tD = personal tax rate on debt

V_L = V_U +{1-[(1-0.40)(1-.10)]/ (1-.20)}*D

= V_U +{1-0.675}*D

= V_U + 0.325D

Value rises by debt ;each $100 increase in debt raises L's value by $32.5

4.The calculation for part 4 are as follows :

If only corporate taxes then,

V_L = V_U +t_c D

= V_U +0.40D

Here $100 increase in debt, raises L's value by $40. Thus personal tax lowers the gain from leverage but the net effect depends on tax rates.