Question

Calculate the NPV and Payback for this project using the initial overall budget as the initial investment with 4% required return and 3% inflation. Cash inflows are expected to be $50K in year 1, $100K each of the next 5 years, and $50K for the final 2 years.

Answer 1

Computation of Net Present Value (NPV) :

NPV = Cash Flow/(1+r)^i

NPV = Net Present Value

Cash Flow = Cash Flow in the time period

r = Discount rate

i = time period

Using the same formula and assuming the cash flow to happen at the close of every year, we can compute the NPV as follows:

Year	Cash Flow ($)	Present Value($)	Computation
1	50000	48544	50000/(1.03)
2	100000	94260	100000/(1.03)^2
3	100000	91514	100000/(1.03)^3
4	100000	88849	100000/(1.03)^4
5	100000	86261	100000/(1.03)^5
6	100000	83748	100000/(1.03)^6
7	50000	40655	50000/(1.03)^7
8	50000	39470	50000/(1.03)^8
Total	650000	573300

Payback :

Overall budget with 4% required return is the Initial Investment. Hence the initial investment is calculated as follows:

Total Cash Flow in 8 years is $650000 and the required rate of return is 4%.

Initial Investment = $650000/(1+.04)^8 = $474949

Payback period of the Initial Investment is within 6th year of the project as calculated below:

					In $
Year	Opening Balance of Initial Investment	4% Return on Investment	Total	Cash Flow	Closing Balance of Initial Investment
1	474949	18998	493947	50000	443947
2	443947	17758	461704	100000	361704
3	361704	14468	376173	100000	276173
4	276173	11047	287220	100000	187220
5	187220	7489	194708	100000	94708
6	94708	3788	98497	100000	-1503