Question

1. Net present value. You are considering investing in solar panels for your home. The upfront cost today of purchasing the panels is $12,000. The benefit you receive from the panels is equal to $1,000 per year starting next year and continuing in perpetuity. Calculate the year that these solar panels pay for themselves (i.e., have a positive NPV). Consider three different discount rates: 3%, 5%, and 10%. (a) Write an equation for the net present value of the investment after T years. (b) For each of the following three discount rates, find the year in which the NPV becomes positive: 3%, 5%, and 10%.

Answer 1

Answer:-

(A) The NPV for the investment in solar panels is given by:

NPV= - C + C1/(1+r) + C2/(1+r)^2 + .......+ CT/(1+r)^T

Where C is the initial cost, C(i) is the cash flow, r is the interest rate and T is the time period.

Thus, for the above question, NPV = - 12000 + 1000/(1+ r) + 1000/(1+r)^2 + .......+ 1000/(1+r)^T

= NPV = -12000 + 1000/r( 1 - 1/(1+r)^T)

(B) At r = 3%, NPV = -12000 + 1000/r( 1 - 1/(1+r)^T)

= -12000 + 1000/(0.03) ( 1 - 1/(1.03)^T)

which gives T = 16 years for NPV to be positive.

At r = 5%, NPV is positive at T + 19 years

At r=10%, NPV is positive at T = 17 years.