Question

In: Finance

Compressed APV with Nonconstant Growth Sheldon Corporation projects the following free cash flows (FCFs) and interest...

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

Solutions

Expert Solution

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

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