Question

Consider the following two mutually exclusive projects:

Year	Cash Flow (X)				Cash Flow (Y)
0	–$	20,900			–$	20,900
1		9,075				10,550
2		9,550				8,025
3		9,025				8,925

A) Calculate the IRR for each project

B)

What is the crossover rate for these two projects?

C) What is the NPV of Projects X and Y at discount rates of 0 percent, 15 percent, and 25 percent?

Answer 1

A

CF X
IRR is the rate at which NPV =0
IRR	0.154224395
Year	0	1	2	3
Cash flow stream	-20900	9075	9550	9025
Discounting factor	1	1.154224	1.332234	1.537697
Discounted cash flows project	-20900	7862.423	7168.411	5869.167
NPV = Sum of discounted cash flows
NPV CF X =	0.000172921
Where
Discounting factor =	(1 + IRR)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
IRR=	15.42%
CF Y
IRR is the rate at which NPV =0
IRR	0.15626917
Year	0	1	2	3
Cash flow stream	-20900	10550	8025	8925
Discounting factor	100.00%	1.156269	1.336958	1.545884
Discounted cash flows project	-20900	9124.173	6002.431	5773.397
NPV = Sum of discounted cash flows
NPV CF Y =	0.000202099
Where
Discounting factor =	(1 + IRR)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
IRR=	15.63%
B
CF Y-CF X Cash flow values are as follows
Year	Cash flow stream
0	0
1	1475
2	-1525
3	-100
Incremental IRR is calculated based on difference of the cash flow of the two projects
Incremental CF
IRR is the rate at which NPV =0
IRR	0.095769303
Year	0.00%	1	2	3
Cash flow stream	0	1475	-1525	-100
Discounting factor	1	1.095769	1.20071	1.315702
Discounted cash flows project	0	1346.086	-1270.08	-76.0051
NPV = Sum of discounted cash flows
NPV Incremental CF =	-0.000303177
Where
Discounting factor =	(1 + IRR)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
IRR=	9.58%
C
CF X
Discount rate	0
Year	0	1	2	3
Cash flow stream	-20900	9075	9550	9025
Discounting factor	1	1	1	1
Discounted cash flows project	-20900	9075	9550	9025
NPV = Sum of discounted cash flows
NPV CF X =	6750
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
CF Y
Discount rate	0
Year	0	1	2	3
Cash flow stream	-20900	10550	8025	8925
Discounting factor	1	1	1	1
Discounted cash flows project	-20900	10550	8025	8925
NPV = Sum of discounted cash flows
NPV CF Y =	6600
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor

CF X
Discount rate	0.15
Year	0	1	2	3
Cash flow stream	-20900	9075	9550	9025
Discounting factor	1	1.15	1.3225	1.520875
Discounted cash flows project	-20900	7891.304	7221.172	5934.084
NPV = Sum of discounted cash flows
NPV CF X =	146.56
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
CF Y
Discount rate	0.15
Year	0	1	2	3
Cash flow stream	-20900	10550	8025	8925
Discounting factor	1	1.15	1.3225	1.520875
Discounted cash flows project	-20900	9173.913	6068.053	5868.332
NPV = Sum of discounted cash flows
NPV CF Y =	210.30
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor

CF X
Discount rate	0.25
Year	0	1	2	3
Cash flow stream	-20900	9075	9550	9025
Discounting factor	1	1.25	1.5625	1.953125
Discounted cash flows project	-20900	7260	6112	4620.8
NPV = Sum of discounted cash flows
NPV CF X =	-2907.2
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
CF Y
Discount rate	0.25
Year	0	1	2	3
Cash flow stream	-20900	10550	8025	8925
Discounting factor	1	1.25	1.5625	1.953125
Discounted cash flows project	-20900	8440	5136	4569.6
NPV = Sum of discounted cash flows
NPV CF Y =	-2754.40
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor