Question

1. A company is considering a project that is expected to generate its first cash flow in the amount of $1 million in 6 years. The cash flows thereafter are expected to grow 15% a year until the last cash flow in year 24. Appropriate discount rate of the project is 13%.

1. What is the maximum investment the company should dedicate for this project today?
2. A reevaluation of the project shows that starting from year 25 the project is going to generate the same cash flow it is expected to generate in year 24 every year forever. By how much does your answer to part a change?

Answer 1

a. Year 6 Cash Flow = 1
Year 7 Cash Flow = 1 *(1+15%) = 1*1.15
Year 8 Cash Flow = 1 *(1+15%)² = 1*1.15²
and so on till
Year 24 Cash Flow = 1 *(1+15%)²⁴ = 1.15¹⁸

Value of Cash flows at year 6 = 1 + 1*1.15/(1+13%) + 1*1.15²/(1+13%)².......+1*1.15¹⁸/(1+13%)¹⁸
= 1*((1.15/1.13)¹⁸-1)/(1.15/1.13-1)
Applying sum of GP formula = 1*((1.15/1.13)^(18+1)-1)/(1.15/1.13-1) = 22.3528

PV of year 6 value = 22.3528/(1+13%)⁶ = 10.74

b. Year 25 cash flow = 1*1.15^(24-6) = 1.15^18
Value of Cash flow forever till year 24 = (1.15^18)/(15%-13%) = 618.77
PV of Cash flows = 618.77/(1+13%)²⁴ = 32.93

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