Question

Your company has the opportunity to enter a business that will generate cash-flows of 12,000€ per year, starting next year, and during 10 years. Calculate how much your company should invest today in order to obtain a yearly profitability of 5%. c) Your company has the opportunity to enter a business that will generate cash-flows of 12,000€ per year, starting in 5 years, and during 10 years. Calculate the future value of such delayed annuity under yearly profitability of 5%.. (Same as the previous exercise, but it will start generating cash-flows in 5 years instead of next year) Please show the workout and all the steps you follow to reach the final results. d) Your company has the opportunity to enter a business that will generate cash-flows of 12,000€ per year, starting in 5 years, and during 10 years. Calculate how much your company should invest today in order to obtain a profitability of 5%. Please show the workout and all the steps you follow to reach the final results

Answer 1

1). Amount required today if cash flow of 12,000 starts from next year and for 10 years

PV (if cash flow occurs at the end of next year): PMT = 12,000; N = 10; rate = 5%, solve for PV. PV1 (present value at the end of this year) = 92,660.82

PV0 (present value now) = 92,660.82/(1+5%) = 88,248.40 (amount to be invested now)

PV (if cash flow occurs at the beginning of next year) = 92,660.82 (as calculated above)

2). FV of delayed annuity (assuming end of the year cash flows): PMT = 12,000; N = 10; rate = 5%, solve for FV. FV = 150,934.71

3). PV of investment required to get delayed annuity payments shown in part (2):

Investment required now = FV at the end of 15 years/(1+5%)^15 = 150,934.71/(1+5%)^15 = 72,602.18