Question

It is January 1, 2020. Free cash flow for 2020, 2021, 2022, and 2023 are expected to be -$5,000; -$1,000; $5,000; and $15,000. Cash flow growth beyond 2023 is expected to stabilize at 10% for 2 years, beyond which point free cash flows are expected to grow at 4% in perpetuity. If the discount rate is 20%, what should be the value of the firm today if there is $1,000 excess cash? What should the enterprise value be (assuming the firm has no majority interest in a subsidiary)? Assume cash flows occur continuously throughout the year.

Answer 1

Value of Firm= C₁ / (1+r)¹ + C₂/ (1+r)² + C₃/ (1+r)³ + ---------+  C_n/ (1+r)ⁿ + C_n (1+g)/ (r-g)

^{where, C= Free Cash Flows, n= Number of years, r= rate of interest, g= growth rate}

^{Some important points}

^{Rate of interest should be constant, so while calculating free cash flow for 2024, we should discount the cash flows by 10% to arrive at 2024 projected cash flows}

While Calculating Free cash flows we do not include cash, so it will be adjusted at the end

^{If question is having growth rate then it will be deducted from discounted rate}

=-5000 / (1+ 0.2)¹ + -1000/ (1+0.2)² + 5000/ (1+0.2)³ + 15000/ (1+ 0.2)⁴ + 10245^*/ (1+ 0.1)⁵ + 10245/ (1+0.1)⁶ +

10245 (1+ 0.4)/ (10%-4%)

=(-5000* 0.833) + (-1000* 0.694) + (5000 * 0.578) + (15000 * 0.482) + (10245* 0.621) + (10245 * 0.564) +177580

= -4165 -694 + 2890 + 7230 + 6362 + 5778 + 177580

= 194981

Total value of firm = 194981+1000= 195981

Note---* 15000 / (1+0.10)⁴ = 10245