Question

Investment X offers to pay you $4,700 per year for 9 years, whereas Investment Y offers to pay you $6,400 per year for 5 years.

Requirement 1:
A. If the discount rate is 8 percent, what is the present value of these cash flows?
B. Which of these cash flow streams has the higher present value at 8 percent?
Requirement 2:
A) If the discount rate is 20 percent, what is the present value of these cash flows?
B) Which of these cash flow streams has the higher present value at 20 percent?

Answer 1

Instructions are below.

Step-by-step explanation:

Giving the following information:

Investment X offers to pay you $4,700 per year for 9 years

Investment Y offers to pay you $6,400 per year for 5 years.

Requirement 1:

First, we need to calculate the final value, using the following formula:

FV= {A*[(1+i)^n-1]}/i

A= annual cash flow

Investment X:

FV= {4,700*[(1.08^9)-1]} / 0.08

FV= $58,691.52

Investment Y:

FV= {6,400*[(1.08^5)-1]} / 0.08

FV= $37,546.25

Now, the present value:

PV= FV/(1+i)^n

Investment X:

PV= 58,691.52/(1.08^9)

PV= $29,360.37

Investment Y:

PV= 37,546.25/(1.08^5)

PV= $25,553.35

Investment X provides the higher present value, therefore, it should be the one to choose.

Requirement 2:

First, we need to calculate the final value, using the following formula:

FV= {A*[(1+i)^n-1]}/i

A= annual cash flow

Investment X:

FV= {4,700*[(1.20^9)-1]} / 0.20

FV= $97,754.84

Investment Y:

FV= {6,400*[(1.20^5)-1]} / 0.20

FV= $47,626.24

Now, the present value:

PV= FV/(1+i)^n

Investment X:

PV= 97,754.84/(1.20^9)

PV= $18,945.54

Investment Y:

PV= 47,626.24/(1.20^5)

PV= $19,139.92

Investment Y provides the higher present value, therefore, it should be the one to choose.