Question

Projects A and B have first costs of $5000 and $9000, respectively. Project A has net annual benefits of $2500 during each of its 5-year useful life, after which it can be replaced identically. Project B has net annual benefits of $3300 during each year of its 10-year life.  Use Present Worth analysis, an interest rate of 30% per year, and a 10-year analysis period to determine which project to select. Please provide the present worth of the best alternative.

(show all equations)

Answer 1

Project A
Discount rate	0.3
Year	0	1	2	3	4	5	6	7	8	9	10
Cash flow stream	-5000	2500	2500	2500	2500	-2500	2500	2500	2500	2500	2500
Discounting factor	1	1.3	1.69	2.197	2.8561	3.71293	4.826809	6.274852	8.157307	10.6045	13.78585
Discounted cash flows project	-5000	1923.077	1479.29	1137.915	875.31949	-673.323	517.9405	398.4158	306.4737	235.749	181.3454
NPV = Sum of discounted cash flows
NPV Project A =	1382.2
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
Project B
Discount rate	0.3
Year	0	1	2	3	4	5	6	7	8	9	10
Cash flow stream	-9000	3300	3300	3300	3300	3300	3300	3300	3300	3300	3300
Discounting factor	1	1.3	1.69	2.197	2.8561	3.71293	4.826809	6.274852	8.157307	10.6045	13.78585
Discounted cash flows project	-9000	2538.462	1952.663	1502.048	1155.4217	888.7859	683.6815	525.9088	404.5453	311.1887	239.3759
NPV = Sum of discounted cash flows
NPV Project B =	1202.08
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor

Project A is best as it has higher NPV (present worth)