Question

You are considering a project that will require an initial outlay of $54,200. This project has an expected life of 5 years and will generate after-tax flows to the company as a whole of $20,608 at the end of each year over its 5-year life. In addition to the $20, 608 cash flow from operations during the fifth and final year, there will be an additional cash outflow of $23,608 at the end of the fifth and final year associated with the removal of environmental waste, making the cash flow in year 5 equal to $-3,000. Given a required rate of return of 15 %

a. Calculate the IRR.

b. Calculate the net present value (NPV).

c. Calculate the MIRR.

d. Based on the answers above, should the project be accepted? Explain.

Answer 1

a
Project
IRR is the rate at which NPV =0
IRR	0.179271889
Year	0	1	2	3	4	5
Cash flow stream	-54200	20608	20608	20608	20608	-3000
Discounting factor	1	1.179272	1.390682	1.639992	1.9339969	2.280708
Discounted cash flows project	-54200	17475.19	14818.63	12565.91	10655.653	-1315.38
NPV = Sum of discounted cash flows
NPV Project =	1.30587E-06
Where
Discounting factor =	(1 + IRR)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
IRR=	17.93%
b
Project
Discount rate	0.15
Year	0	1	2	3	4	5
Cash flow stream	-54200	20608	20608	20608	20608	-3000
Discounting factor	1	1.15	1.3225	1.520875	1.7490063	2.011357
Discounted cash flows project	-54200	17920	15582.61	13550.09	11782.691	-1491.53
NPV = Sum of discounted cash flows
NPV Project =	3143.86
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
c
Project
Combination approach
All negative cash flows are discounted back to the present and all positive cash flows are compounded out to the end of the project’s life
Thus year 5 modified cash flow=(36043.52)+(31342.19)+(27254.08)+(23699.2)
=118338.99
Thus year 0 modified cash flow=-54200-1491.53
=-55691.53
Discount rate	0.15
Year	0	1	2	3	4	5
Cash flow stream	-54200	20608	20608	20608	20608	-3000
Discount factor	1	1.15	1.3225	1.520875	1.7490063	2.011357
Compound factor	1	1.749006	1.520875	1.3225	1.15	1
Discounted cash flows	-54200	0	0	0	0	-1491.53
Compounded cash flows	-1.84502E-05	36043.52	31342.19	27254.08	23699.2	0
Modified cash flow	-55691.53	0	0	0	0	118339
Discounting factor (using MIRR)	1	1.1627	1.351872	1.571822	1.8275572	2.124901
Discounted cash flows	-55691.53	0	0	0	0	55691.53
NPV = Sum of discounted cash flows
NPV=	5.52827E-05
MIRR is the rate at which NPV = 0
MIRR=	16.27%
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
Compounding factor =	(1 + reinvestment rate)^(time of last CF-Corresponding period in years)

d

Accept project as NPV is positive and MIRR & IRR is greater than 15%