Question

	year 0	year 1	year 2	year 3	year 4
cashflow for S	-100	40	50	30	30
cashflow for L	-100	10	10	50	90

If the company's cost of capital is 5% and the decision is made by choosing the project with the higher IRR, how much value will be forgone?

a. $4.01

b. $20.80

c. $29.89

d. $1.79

e. $12.45

Answer 1

Project S
IRR is the rate at which NPV =0
IRR	0.199347165
Year	0	1	2	3	4
Cash flow stream	-100	40	50	30	30
Discounting factor	1	1.199347	1.438434	1.725181	2.0690913
Discounted cash flows project	-100	33.35148	34.76003	17.38948	14.499119
NPV = Sum of discounted cash flows
NPV Project S =	0.000105764
Where
Discounting factor =	(1 + IRR)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
IRR=	19.93%
Project L
IRR is the rate at which NPV =0
IRR	0.152058482
Year	0	1	2	3	4
Cash flow stream	-100	10	10	50	90
Discounting factor	1	1.152058	1.327239	1.529057	1.7615627
Discounted cash flows project	-100	8.680115	7.534439	32.6999	51.091
NPV = Sum of discounted cash flows
NPV Project L =	0.005455073
Where
Discounting factor =	(1 + IRR)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
IRR=	15.21%
Project S
Discount rate	0.05
Year	0	1	2	3	4
Cash flow stream	-100	40	50	30	30
Discounting factor	1	1.05	1.1025	1.157625	1.2155063
Discounted cash flows project	-100	38.09524	45.35147	25.91513	24.681074
NPV = Sum of discounted cash flows
NPV Project S =	34.04
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
Project L
Discount rate	0.05
Year	0	1	2	3	4
Cash flow stream	-100	10	10	50	90
Discounting factor	1	1.05	1.1025	1.157625	1.2155063
Discounted cash flows project	-100	9.52381	9.070295	43.19188	74.043223
NPV = Sum of discounted cash flows
NPV Project L =	35.83
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor

Project S has higher IRR thus it will be chosen but its NPV is 35.83-34.04 = 1.79 lesser than project L