Valuation using Free Cash Flows

Problem

Do the Valuation using Free Cash Flows (FCF . The following free cash flows (in Million ) are projected for the next five years . The free cash flows are expected to grow at a stable rate of 7 for every year after year 5 . The opportunity cost of capital is 10 . Calculate the current value of the firm using the constant growth model after year 5 As a first step calculate the terminal value of the firm at the end of year 5

Year Year 1 Year 2 Year 3 Year 4 Year

5

FCF 5 12 24 44 69

Answer

Valuation of the firm will be appropriately computed by computing for the present value of the free cash flows of the firm . In the given problem , the free cash flows exhibits variable behavior during the first five years , and shows stable 7 growth thereafter

Year FCF

---- ------

1 5 million

2 12

3 24

4 44

5 69

n 1 FCFn (1 7

It is given that r opportunity cost of capital 10

The present value of the firm can be computed by adding the present values of the discounted free cash flows of the firm . In the present case , the actual present value of the firm will therefore be the present value of the cash flows during the 5-year period plus the present value of the cash flows thereafter . In other words , the firm 's value can be approximated by the sum of the variable growth period plus the stable growth period

-- Variable Growth

Year 1 to year 5 exhibits a variable growth model . Hence , the present value represents the sum of the discounted value of the cash flows over the 5-year period

PV CF1 (1 r )1 CF2 (1 r )2 CF3 (1 r )3 CF4 (1 r )4 CF5 (1 r )5

The summation gives the present value of the first 5 years ' FCF

Adding the cash flows would result to a sum of 154 ,000 ,000 . However discounting those cash flows using the formula stated above would yield free cash flows during the five-year period would be 105 ,390 ,000

-- Constant Growth

After year 5 , the firm is expected to exhibit stable growth specifically at 7 . The firm is thus assumed to have stable growth rate at 7 to perpetuity . We will assume that cost of capital will continue to be 10

For FCF exhibiting stable growth , we can compute for the terminal value

TV is given as FCF (r - g

Given that FCF is expected to grow 7 after year 5 , FCF starting year six should be equal to FCF in year 5 multiplied by the growth

FCF 69 million (1 7 73 .83 million

Hence , TV can be computed as

TV 73 .83 mill (r - g 73 .83 mill (10 - 7 2 ,461 million

Discounting the TV on account of the five year period we have

PV TV (1 r )^5 2 ,461 mill (1 10 )^5 1 ,528 million

The...