A certain company;s cash flows are expected to grow at a rate of 20% for the...

A certain company;s cash flows are expected to grow at a rate of 20% for the next seven years before tapering off to a constant growth rate of 5% forever. The current year's cash flow is $35,000. If the firm's cost of capital is 25%, what should its fair market value be? Please show work

Expert Solution

The fair market value is computed as shown below:

Cash flow at end of year 1 = $ 35,000 ( 1.20 ) = $ 42,000

Cash flow at end of year 2 = $ 35,000 ( 1.20 )² = $ 50,400

Cash flow at end of year 3 = $ 35,000 ( 1.20 )³ = $ 60,480

Cash flow at end of year 4 = $ 35,000 ( 1.20 )⁴ = $ 72,576

Cash flow at end of year 5 = $ 35,000 ( 1.20 )⁵ = $ 87,091.2

Cash flow at end of year 6 = $ 35,000 ( 1.20 )⁶ = $ 104,509.44

Cash flow at end of year 7 = $ 35,000 ( 1.20 )⁷ = $ 125,411.328

Cash flow at end of year 8 = $ 125,411.328 ( 1.05 ) = $ 131,681.8944

Fair market value would be computed as follows:

= Cash flow at end of year 1 / ( 1 + cost of capital )¹ + Cash flow at end of year 2 / ( 1 + cost of capital )² + Cash flow at end of year 3 / ( 1 + cost of capital )³ + Cash flow at end of year 4 / ( 1 + cost of capital )⁴ + Cash flow at end of year 5 / ( 1 + cost of capital )⁵ + Cash flow at end of year 6 / ( 1 + cost of capital )⁶ + Cash flow at end of year 7 / ( 1 + cost of capital )⁷ + 1 / (cost of capital )⁷ [ ( Cash flow at end of year 8 / (Cost of capital - growth rate ) ]

By feeding the above calculated numbers in the above mentioned equation, we shall get

= $ 42,000 / 1.25¹ + $ 50,400 / 1.25² + $ 60,480 / 1.25³ + $ 72,576 / 1.25⁴ + $ 87,091.2 / 1.25⁵ + $ 104,509.44 / 1.25⁶ + $ 125,411.328 / 1.25⁷ + 1 / 1.25⁷ [ ($ 131,681.8944 / ( 0.25 - 0.05 ) ]

= $ 346,862.5925

Feel free to ask in case of any query relating to this question

jeff jeffy answered 2 days ago

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