Question

Investment X offers to pay you $4,700 per year for eight years, whereas Investment Y offers to pay you $6,700 per year for five years. Which of these cash flow streams has the higher present value if the discount rate is 5 percent? If the discount rate is 15 percent?

Answer 1

The present value (PV) of an annuity is calculated by using the formula :

PV = P*(1-(1+r)^-n)/r

CASE 1: discount rate (r) = 5%

Present value of 4,700 for 8 years at 5% means P =4,700, n =8 and r = 0.05

PV = 4,700*(1-1.05^-8)/0.05

PV = 30,377.10

Present value of 6,700 for 5 years at 5% means P=6,700, n=5 and r = 0.05

PV = 6,700*(1-1.05^-5)/0.05

PV = 29,007.49

Answer: The cash flow stream of $4,700 per year for eight years has a higher present value at 5%

CASE 2: discount rate (r) = 15%

Present value of 4,700 for 8 years at 15% means P =4,700, n =8 and r = 0.15

PV = 4,700*(1-1.15^-8)/0.15

PV = 21,090.41

Present value of 6,700 for 5 years at 15% means P=6,700, n=5 and r = 0.15

PV = 6,700*(1-1.15^-5)/0.15

PV = 22,459.44

Answer: The cash flow stream of $6,700 per year for five years has a higher present value at 15%