Question

Your division is considering two investment projects, each of which requires an up-front expenditure of $20 million. You estimate that the investments will produce the following net cash flows:

Year Project A Project B

1 $4,500,000 $20,000,000

2 10,000,000 10,000,000

3 20.000.000 6,500,000

1. What are the two project’s NPVs assuming the cost of capital is 3%, 12%, 17%?
2. What are the two projects’ IRRs at those same costs of capital?

Answer 1

a

Project A
Discount rate	0.03
Year	0	1	2	3
Cash flow stream	-20000000	4500000	10000000	20000000
Discounting factor	1	1.03	1.0609	1.092727
Discounted cash flows project	-20000000	4368932	9425959	18302833
NPV = Sum of discounted cash flows
NPV Project A =	12097724.32
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
Project B
Discount rate	0.03
Year	0	1	2	3
Cash flow stream	-20000000	20000000	10000000	6500000
Discounting factor	1	1.03	1.0609	1.092727
Discounted cash flows project	-20000000	19417476	9425959	5948421
NPV = Sum of discounted cash flows
NPV Project B =	14791855.61
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor

Project A
Discount rate	0.12
Year	0	1	2	3
Cash flow stream	-20000000	4500000	10000000	20000000
Discounting factor	1	1.12	1.2544	1.404928
Discounted cash flows project	-20000000	4017857	7971939	14235605
NPV = Sum of discounted cash flows
NPV Project A =	6225400.87
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
Project B
Discount rate	0.12
Year	0	1	2	3
Cash flow stream	-20000000	20000000	10000000	6500000
Discounting factor	1	1.12	1.2544	1.404928
Discounted cash flows project	-20000000	17857143	7971939	4626572
NPV = Sum of discounted cash flows
NPV Project B =	10455653.24
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor

Project A
Discount rate	0.17
Year	0	1	2	3
Cash flow stream	-20000000	4500000	10000000	20000000
Discounting factor	1	1.17	1.3689	1.601613
Discounted cash flows project	-20000000	3846154	7305136	12487411
NPV = Sum of discounted cash flows
NPV Project A =	3638700.49
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
Project B
Discount rate	0.17
Year	0	1	2	3
Cash flow stream	-20000000	20000000	10000000	6500000
Discounting factor	1	1.17	1.3689	1.601613
Discounted cash flows project	-20000000	17094017	7305136	4058409
NPV = Sum of discounted cash flows
NPV Project B =	8457561.22
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor

b

Project A
IRR is the rate at which NPV =0
IRR	0.256425298
Year	0	1	2	3
Cash flow stream	-20000000	4500000	10000000	20000000
Discounting factor	1	1.256425	1.578605	1.983399
Discounted cash flows project	-20000000	3581590	6334709	10083701
NPV = Sum of discounted cash flows
NPV Project A =	3.63216E-06
Where
Discounting factor =	(1 + IRR)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
IRR=	25.64%
Project B
IRR is the rate at which NPV =0
IRR	0.484352898
Year	0	1	2	3
Cash flow stream	-20000000	20000000	10000000	6500000
Discounting factor	1	1.484353	2.203304	3.27048
Discounted cash flows project	-20000000	13473885	4538639	1987476
NPV = Sum of discounted cash flows
NPV Project B =	1.59722E-07
Where
Discounting factor =	(1 + IRR)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
IRR=	48.44%