Question

Problem 21-07
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 6% rate. Sheldon’s unlevered cost of equity is 12% 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

		0	1	2	3
	FCF ($ millions)		$              20	$              30	$             40
a)	Unlevered horizon value of operations at Year 3 = 40*1.06/(0.12-0.06) =				$           707
b)	Total FCF value		$              20	$              30	$           747
	PVIF at 12% [PVIF = 1/1.12^n]		0.89286	0.79719	0.71178
	PV of FCF		$        17.86	$        23.92	$     531.46
	Current unlevered value of operations = Sum of PV of FCF =	$      573.24
c)	Interest expense		$           8.00	$          9.00	$       10.00
	Tax shield at 45%		$           3.60	$          4.05	$          4.50
	Horizon value of tax shield at Year 3 = 4.5*1.06/(0.12-0.06) =				$       79.50
d)	Total tax shield		$           3.60	$          4.05	$       84.00
	PV of tax shield		$           3.21	$          3.23	$       59.79
	Current value of tax shield = Sum of PV of TS =	$        66.23
e)	Current total value of the company = 573.24+66.23 =	$      639.47