Question

Your friend is talking to you about one of their investments. Yesterday, your friend received a cheque from the investment for $6,000. According to the company’s annual report and forecast, the company expects the amount of the cash flow to increase or grow at 15 percent for the next 5 years and then to grow at 2 percent forever.

1. If you require a 15% return on your investment, what is the value of this investment today?

2. If interest rates are 15% per year and the first cash flow of $6,000 occurs three months from now, what is this investment worth today?

3. If the first cash flow of $6,000 occurs today, what is the value of the investment today?

Answer 1

(1) The Investment cash flows of $ 6000 (received yesterday at t=0) are expected to grow at 15% per annum for the next 5 years and then settle down at the perpetual growth rate of 2 % per annum.

CF(Cash Flow) at end of Year 1 = 6000 x 1.15 = $ 6900

CF(Cash Flow) at end of Year 2 = 6000 x (1.15)^(2) = $ 7935

CF(Cash Flow) at end of Year 3 = 6000 x (1.15)^(3) = $ 9125.25

CF(Cash Flow) at end of Year 4 = 6000 x (1.15)^(4) = $ 10494.0375

CF(Cash Flow) at end of Year 5 = 6000 x (1.15)^(5) = $ 12068.14313

Required Rate of Return = 15 %

CF at the end of Year 6 = 12068.14313 x 1.02 = $ 12309.50599 or $ 12309.506 approximately

Terminal Value of perpetual CFs at end of Year 5 = TV = 12309.506 / (0.15 - 0.02) = $ 94688.50769

PV of TV of Perpetual CFs = P1 = 94688.50769 / (1.15)^(5) = $ 47076.92312

PV of CFs during first five year = P2 = 6900 / 1.15 + 7935 / (1.15)^(2) + 9125.25 / (1.15)^(3) + 10494.0375 / (1.15)^(4) + 12068.14313 / (1.15)^(5) = $ 30000

Total Investment Value = P1 + P2 = $ 77076.9231

(2) We need to first calculate the PV of cash flows at t=3 months or 0.25 years and then discount the total value to t=0.

PV of All Cash Flows at 3 months from now = Total Investment Value = $ 77076.9231 (calculated in part (1))

PV of Cash Flows at t= 0 will be = P0 = 77076.9231 / (1.15)^(3/12) = $ 74430.324

NOTE: Another possible value would involve calculating the nominal interest rate for the 3 month period as given below :

Nominal Interest Rate for 3 months = 15 / 4 = 3.75 %

Hence, P0 = 77076.9231 / 1.0375 = $ 74291.01 which is close to the previous value.

(3) If first cash flow occurs today at $ 6000, the original condition of cash flows growing at 15 % per annum for the next 5 years remain unaltered. Hence, current investment value = 6000 + P0 = 77076.9231 + 6000 = $ 83076.9231