Question

Compressed APV with Nonconstant Growth

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 5% rate. Sheldon’s unlevered cost of equity is 14% 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.

   $ million

Answer 1

Growth rate after 3 years			5% or	0.05
Unlevered cost of equity			14% or	0.14
Tax rate				45%
		1	2	3
Free cash flows ($ millions)		20	30	40
Interest exp.($ millions)		8	9	10
(a)
Unlevered horizon value of operations at year 3 = FCF for year 3 * (1+g) / (ke -g)
	40 * (1 + 0.05) / (0.14 - 0.05)
	466.6667
So, Unlevered horizon value of operations at year 3 is $466.67 millions.
(b)
Current unlevered value of operations is present value of FCF for 3 years and present value of horizon value at year 3
Year	Cash flows	P.V. F. @ 14%	Present value
1	20	0.87719298	$17.54
2	30	0.76946753	$23.08
3	40	0.67497152	$27.00
3	466.6667	0.67497152	$314.99
			$382.61
So, Current value of operations is $382.61 millions.
(c )
Horizon value of tax shield at 3 Year = Interest expense * (1 + g)* Tax rate / (Ke -g)
	10 * (1+0.05) * 0.45 / (0.14 - 0.05)
	52.5
So, Horizon value of tax shild is $52.5 millions.
(d )
Current value of tax shield is present value of tax shield for 3 years and present value of horizon value at year 3
Year	Interest exp.	Tax shield@ 45%	P.V. F. @ 14%	Present value
1	8	3.6	0.877193	$3.16
2	9	4.05	0.7694675	$3.12
3	10	4.5	0.6749715	$3.04
3 (horizon value of tax shield)		52.5	0.6749715	$35.44
				$44.75
So, Current value of the tax shield is $44.75millions.
(e )
Current total value of company = Current value of operations + Current value of tax shield
	$382.61 +$44.75
	$427.36
So, the current total value of company is $427.36