Your friend is talking to you about one of their investments. Yesterday, your friend received a...

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?

Solutions

Expert Solution

(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

jeff jeffy answered 1 year ago

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