Question

Consider the following project cash flow series along with project balances. Knowing the relationship between the project cash flow and their project balances calculate interst rate used net future worth at the project life, and its percent worth

Year	Cash flow	Project balance
0	$-1000	$-1000
1	$200	$ -900
2	$490	-$500
3	$550	$0
4	-$100	-$100
5	$310	$200

Answer 1

Year	Cash flow	Project balance	DF at 10%	DF at 15%	NPV at 10%	NPV at 15%
0	-1000	-1000	1.00	1.00	-1000.00	-1000.00
1	200	-900	0.91	0.87	181.82	173.91
2	490	-500	0.83	0.76	404.96	370.51
3	550	0	0.75	0.66	413.22	361.63
4	-100	-100	0.68	0.57	-68.30	-57.18
5	310	200	0.62	0.50	192.49	154.12
	? 0.14			NPV	124.18	3.01

So, we need to find interest rate (IRR) at which NPV is zero

IRR = R1+((NPV1*(R2-R1))/(NPV1-NPV2))
R1 = Lower discount rate
R2 = Higher discount rate
NPV1 = Higher Net Present Value at R1
NPV2 = Lower Net Present Value at R2

IRR = 0.1+ (124.18*(0.15-0.1))/(124.18-3) = 0.1+0.0512 = 0.1512 or 15.12 percent

NPW is zero at 15.12 percent

Year	Cash flow	Project balance	Compounding factor	Future worth
0	-1000	-1000	1.00	-1000.00
1	200	-900	1.15	230.24
2	490	-500	1.33	649.38
3	550	0	1.53	839.10
4	-100	-100	1.76	-175.63
5	310	200	2.02	626.78
			NFW	1169.87

So, NFW = $1169.87