Question

Two projects have equal net present values when calculated using a 5% annual effective rate. Project 1 requires an investment of $2,000 immediately and will return $800 at the end of one year and $1,500 at the end of two years. Project 2 requires investments of $1,000 immediately and $X in two years. It will return $300 at the end of one year and $1,400 at the end of three years. Find the difference in the net present values of the two projects if they are calculated using a 4% annual effective rate.

The final answer is $2.84 as we are given the final answer. Thanks in advanced!!!

Answer 1

NPV= C0+ CF1/(1+r)^1 + CF2/(1+r)^2 …………CFn/(1+r)^n

At 5%

Project 1

NPV = -2000+ 800/1.05^1 + 1500/1.05^2 = 122.45

Project 2

NPV = -1000+ 300/1.05+ X/1.05^2 + 1400/1.05^3 =

495.09+ X/1.05^2

Equating the two NPVs we get

495.09+ X/1.05^2= 122.45

X= -410.84

Now using 4% rate

Project 1

NPV = -2000+ 800/1.04^1 + 1500/1.04^2 = 156.07

Project 2

NPV = -1000+ 300/1.04- 410.84 /1.04^2 + 1400/1.04^3 = 153.22

Difference = NPV1- NPV 2

= $ 2.84