Question

Herculio Mining has net operating income of $5 million. It has $50 million of debt outstanding with a required rate of return of 6%. The required rate of return on assets in this industry is 12%, and the corporate tax rate is 40%. Assume there are corporate taxes but no personal taxes.

a. Determine the present value of the interest tax shield of Herculio Mining as well as the total value of the firm.

b. Determine the gain from leverage if there are no personal taxes of 20% on stock income and 30% on debt income.

Answer 1

Solution:
a.	Present value of the interest tax shield	$20,000,000
	Value of unlevered firm	$25,000,000
	Value of levered firm	$45,000,000
Working Notes:
		Levered	Unlevered
	EBIT	5,000,000	5,000,000	a
	Less: Interest paid [ 0.06 x 50,000,000]	3,000,000	0	b
	Taxable income	2,000,000	5,000,000	c=a-b
	Less: Taxes @ 40%	800,000	2,000,000	d=c x 40%
	Net Income	1,200,000	3,000,000	e=c-d
	Add: Interest paid	3,000,000	0	f=b
	Total income available to investors	4,200,000	3,000,000	g=e+f
	Present value of tax shield = Debt x tax rate	=50,000,000 x 40%
		=$20,000,000
	Value of unlevered firm = Net income / Capitalization rate
		=$3,000,000/12%
		=$25,000,000
	Capitalization rate = return on assets = 12%
	Value of levered firm = Value unlevered firm + PV tax shields
		=$25,000,000 + $20,000,000
		=$45,000,000
b.	Gain from leverage	$15,714,285.71
Working Notes:
Gain from leverage =[ 1 - {(1-corp. tax rate) (1-personal tax rate)}/(1-tax rate on debt income) ] x Debt amount
	Gain from leverage =[ 1 - {(1-0.40) (1-0.20)}/(1-0.30) ] x $50,000,000
	Gain from leverage =[ 1 - {0.60 x 0.80 }/(0.70) ] x $50,000,000
	Gain from leverage =[ 1 - 0.48/0.70 ] x $50,000,000
	Gain from leverage =[1-0.68571428571] x $50,000,000
	Gain from leverage =0.31428571429 x $50,000,000
	Gain from leverage =$15,714,285.7145
	Gain from leverage =$15,714,285.71
Please feel free to ask if anything about above solution in comment section of the question.