PE 26-5B Net present value—unequal lives

Project 1 requires an original investment of $55,000. The project will yield cash flows of $15,000 per year for seven years. Project 2 has a calculated net present value of $5,000 over a four-year life. Project 1 could be sold at the end of four years for a price of $38,000. (a) Determine the net present value of Project 1 over a four-year life, with residual value, assuming a minimum rate of return of 20%. (b) Which project provides the greatest net present value?

Answer:

a. Present value of $15,000 per year at 20% for 4 years*…………………………  $38,835 

Present value of $38,000 at 20% at the end of 4 years**………………………    18,316 

Total present value of Project 1…………………………………………………… $57,151 

Less total cost of Project 1……………………………………………………………   55,000 

Net present value of Project 1……………………………………………………… $  2,151 

* [$15,000 × 2.589 (Exhibit 2, 20%, 4 years)] 

** [$38,000 × 0.482 (Exhibit 1, 20%, 4 years)] 

b. Project 2. Project 1’s net present value of $2,151 is less than the net present 

value of Project 2, $5,000.