Question

Sheldon Corporation projects the following free cash flows (FCFs) and interest expenses for the next 3 years, after which FCF and interest expenses are expected to grow at a constant 8% rate. Sheldon’s unlevered cost of equity is 13% its tax rate is 45%.

	Year
	1	2	3
Free cash flow ($ millions)	$20	$30	$40
Interest expense ($ millions)	$8	$9	$10

1. What is Sheldon’s unlevered horizon value of operations at Year 3? Enter your answer in millions. For example, an answer of $1.2 million should be entered as 1.2, not 1,200,000. Do not round intermediate calculations. Round your answer to two decimal places.

   $  million

2. What is the current unlevered value of operations? Enter your answer in millions. For example, an answer of $1.2 million should be entered as 1.2, not 1,200,000. Do not round intermediate calculations. Round your answer to two decimal places.

   $  million

3. What is horizon value of the tax shield at Year 3? Enter your answer in millions. For example, an answer of $1.2 million should be entered as 1.2, not 1,200,000. Do not round intermediate calculations. Round your answer to two decimal places.

   $  million

4. What is the current value of the tax shield? Enter your answer in millions. For example, an answer of $1.2 million should be entered as 1.2, not 1,200,000. Do not round intermediate calculations. Round your answer to two decimal places.

   $  million

5. What is the current total value of the company? Enter your answer in millions. For example, an answer of $1.2 million should be entered as 1.2, not 1,200,000. Do not round intermediate calculations. Round your answer to two decimal places.

Answer 1

a).

r_sU (unlevered cost of equity) = 13%

g (constant growth rate) = 8%

FCF_N+1 = FCF₃*(1+g) = 40*(1+8%) = 43.2 million

Horizon value = 43.2/(13%-8%) = $864.00 million

b).

Formula	Year (n)	1	2	3	Perpetuity
	FCF	20	30	40	864
1/(1+d)^n	Discount factor @ 13%	0.8850	0.7831	0.6931	0.6931
(FCF*Discount Factor)	Discounted FCF	17.70	23.49	27.72	598.80
Sum of Discounted FCF	Unlevered value of operations	667.71

c).

Tax Saving at year 3 = (interest expense)(tax rate) = 10*45% = 4.5 million

TS_N+1 = TS_N(1+g) = 4.5*(1+8%) = 4.86 million

Horizon value of tax shield = 4.86/(13%-8%) = $97.20 million

d).

Formula	Year (n)	1	2	3	Perpetuity
	Interest expense	8	9	10	10.8
(Interest exp.)(Tax rate)	Tax shield @45%	3.6	4.05	4.5	4.86
1/(1+d)^n	Discount factor @ 13%	0.8850	0.7831	0.6931	0.6931
(FCF*Discount Factor)	Discounted FCF	3.19	3.17	3.12	3.37
Sum of Discounted FCF	Current value of tax shield	12.84

e). Value of operations for the unlevered firm = value of unlevered operations + value of tax shield = 667.71 + 12.84 = $680.56 million