Question

A certain companyʹs cash flows are expected to grow at a rate of 15% for the next eight years before tapering off to a constant growth rate of 6% forever. The current yearʹs cash flow is $50,000 (already paid). If the firmʹs cost of capital is 20%, what should its fair market value be? Round your answer to the nearest dollar.

Answer 1

$585,937

Step-by-step explanation:

The current Cash flow at year zero is $50,000

Cash flow Y1 = CFY0 * (1 + g) = $50,000 * (1 + 15%) = $57,500

Cash flow Y2 = CFY1 * (1 + g) = $57,500 * (1+15%) = $66,125

Cash flow Y3 = CFY2 * (1 + g) = $66,125 * (1+15%) = $76,044

Cash flow Y4 = CFY3 * (1 + g) = $76,043.75 * (1+15%) = $87,450

Cash flow Y5 = CFY4 * (1 + g) = $87,450.3125 * (1+15%) = $100,568

Cash flow Y6 = CFY5 * (1 + g) = $100,567.859 * (1+15%) = $115,653

Cash flow Y7 = CFY6 * (1 + g) = $115,653.038 * (1+15%) = $133,001

Cash flow Y8 = CFY7 * (1 + g) = $133,000.99 * (1+15%) = $152,951

Cash flow Y9 = CFY8 * (1 + g1) = $152,951.143 * (1+6%) = $162,128

Now we will calculate the Horizon value at the end of year 8 and considering cash flows of year 9

Horizon value = CF9 / (r - g1)

By putting values we have:

Horizon value = $162,128 / (20% - 6%)

Horizon value = $162,128 / 0.14

Horizon value = $1,092,508

Now we will discount back the above calculated amount to present value and will add these values to calculate the fair market value of the company which is calculated as under: