Question

Investment X offers to pay you $3,400 per year for nine years,whereas Investment X offers to pay you $5,400 per year five years. Which of these cash flow streams has the higher present value if the discount rate is 6 percent? If the discount rate is 22 percent?

Answer 1

Answer:

At 6% ; $3400 has higher present value.

At 22% ; $5400 has higher present value

Explanation:

Using the PVA formula:

PVA = C({1 - [1 / (1 + r)^t]} / r )

Where ;

C = cashflow ; r = rate ; t = time

PVA of 3400 for 9 years at 6% = 0.06

PVA = 3400({1 - [1 / (1+ 0.06)^9]} / 0.06)

PVA = 3400([1 -[ 1 / 1.06^9]) / 0.06

PVA = 3400(0.4081015 / 0.06)

PVA = 3400(6.8016922)

PVA = 23125.753

PVA of 5400 for 5 years at 6%

PVA = 5400({1 - [1 / (1+ 0.06)^5]} / 0.06)

PVA = 5400([1 - [ 1 / 1.06^5]) / 0.06

PVA = 5400(0.2527418 / 0.06)

PVA = 5400(4.2123637)

PVA = 22746.764

B.)

PVA of 3400 for 9 years at 22% = 0.22

PVA = 3400({1 - [1 / (1+ 0.22)^9]} / 0.22)

PVA = 3400[1 -[ 1 / 1.22^9]) / 0.22)

PVA = 3400 (0.8329826 / 0.22)

PVA = 3400(3.7862848)

PVA = 12873.368

PVA of 5400 for 5 years at 22% = 0.22

PVA = 5400({1 - [1 / (1+ 0.22)^5]} / 0.22)

PVA = 5400([1 - [ 1 / 1.22^5]) / 0.22

PVA = 5400 (0.6300007 / 0.22)

PVA = 5400 (2.8636397)

PVA = 15463.654