Question

Project S has a cost of $10,000 and is expected to produce benefits (cash flows) of $3,000 per year for 5 years. Project L costs $25,000 and is expected to produce cash flows of $7,400 per year for 5 years. Calculate the two projects' NPVs, assuming a cost of capital of 12%. Do not round intermediate calculations. Round your answers to the nearest cent.

Answer 1

Instructions are below.

Step-by-step explanation:

Giving the following information:

Project S:

Cash flows= $3,000

Number of periods= 5 years

Initial investment (Io)= $10,000

Project L:

Cash flows= $7,400

Number of periods= 5 years

Initial investment (Io)= $25,000

Cost of capital= 12%.

To calculate the net present value, we need to use the following formula:

NPV= -Io + ∑[Cf/(1+i)^n]

Project S:

To calculate the present value of the cash flows, first, we will determine the future value and then the present value.

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

A= annual cash flow

FV= {3,000*[(1.12^5) - 1]} / 0.12

FV= $19,058.54

Now, the present value:

PV= FV / (1+i)^n

PV= 19,058.54 / (1.12^5)= $10,814.33

Finally, the NPV:

NPV= -10,000 - 10,814.33

NPV= 814.33

Project L:

∑[Cf/(1+i)^n]:

FV= {7,400*[(1.12^5) - 1]} / 0.12

FV= $47,011.07

PV= 47,011.07/1.12^5= $26,675.34

NPV= -25,000 - 26,675.34

NPV= 1,675.34