An investor deposits 8000 into a fund at t0 and additional 1

An investor deposits $8,000 into a fund at t=0 and additional $10,000 at t=1. He then receives cash inflows starting at t=2. The first payment is $3,000 and subsequent annual payments increase by 3% per annum into perpetuity. What is the smallest required rate in order that the net present value of the investment be positive?

Solution

This will be solved using hit and Trail method by using different rates .

Thus by using rate 21 %

NPV= -8000-10000/(1.21)+3000/(1.21^2)+(3000*(1.03)/(0.21-0.03))/(1.21^2)

=-8000-8264.46+2049.04+16441.59= $ 2226.17

It gives us positive NPV

Now lets try it by 24%

NPV= -8000-10000/(1.24)+3000/(1.24^2)+(3000*(1.03)/(0.24-0.03))/(1.24^2)

=-$ 200.52

Since at 24% we are getting -ve $200 npv

So the rate should be less than 24 , lets try with 23.71 %

NPV= -8000-10000/(1.2371)+3000/(1.2371^2)+(3000*(1.03)/(0.2371-0.03))/(1.2371^2)

= 3.03 which is closest to zero

Hence the Approx this 23.71 % will be the rate to make NPV positive