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 6% 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.

   $ million

Answer 1

Growth rate after 3 years			6% or	0.06
Unlevered cost of equity			13% or	0.13
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 + 0.06) / (0.13-0.06)
	605.7143
So, Unlevered horizon value of operations at year 3 is $605.71 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. @ 13%	Present value
1	20	0.884955752	$17.70
2	30	0.783146683	$23.49
3	40	0.693050162	$27.72
3	605.7143	0.693050162	$419.79
			$488.71
So, Current value of operations is $488.71 millions.
(c )
Horizon value of tax shield at 3 Year = Interest expense * (1 + g)* Tax rate / (Ke -g)
	10 * (1+0.06) * 0.45 / (0.13-0.06)
	68.14286
So, Horizon value of tax shild is $68.14 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. @ 13%	Present value
1	8	3.6	0.88495575	$3.19
2	9	4.05	0.78314668	$3.17
3	10	4.5	0.69305016	$3.12
3 (horizon value of tax shield)		68.14	0.69305016	$47.23
				$56.70
So, Current value of the tax shield is $56.70 millions.
(e )
Current total value of company = Current value of operations + Current value of tax shield
	$488.71 + $56.70
	$545.41
So, the current total value of company is $ 545.41