Question

​(MIRR)  Star Industries owns and operates landfills for several municipalities throughout the Midwestern part of the U.S. Star typically contracts with the municipality to provide landfill services for a period of 20 years. The firm then constructs a lined landfill​ (required by federal​ law) that has capacity for five years. The ​$9.8 million expenditure required to construct the new landfill results in negative cash flows at the end of years​ 5, 10, and 15. This change in sign on the stream of cash flows over the​ 20-year contract period introduces the potential for multiple​ IRRs, so​ Star's management has decided to use the MIRR to evaluate new landfill investment contracts. The annual cash inflows to Star begin in year 1 and extend through year 20 are estimated to equal $3.9 million​ (this does not reflect the cost of constructing the landfills every five​ years). Star uses a 9.6% discount rate to evaluate its new​ projects, so it plans to discount all the construction costs every five years back to year 0 using this rate before calculating the MIRR.

a.  What are the​ project's NPV,​ IRR, and​ MIRR?

b.  Is this a good investment opportunity for Star​ Industries? Why or why​ not?

Answer 1

					$ in millions
		Cash inflows	Cash outflows	Discounting rate	Discounted Cash inflows	Discounted cash outflows
			9.8	1		9.8
		3.9		0.91	3.56
		3.9		0.83	3.25
		3.9		0.76	2.96
		3.9		0.69	2.70
		3.9	9.8	0.63	2.47	6.20
		3.9		0.58	2.25
		3.9		0.53	2.05
1.096		3.9		0.48	1.87
		3.9		0.44	1.71
		3.9	9.8	0.40	1.56	3.92
		3.9		0.36	1.42
		3.9		0.33	1.30
		3.9		0.30	1.18
		3.9		0.28	1.08
		3.9	9.8	0.25	0.99	2.48
		3.9		0.23	0.90
		3.9		0.21	0.82
		3.9		0.19	0.75
		3.9		0.18	0.68
		3.9		0.16	0.62
					34.13	22.39
				NPV	11.74
				(Sum of Discounted Cash inflows - Sum of Discounted Cash outflows)
					$ in millions
		Cash inflows	Cash outflows	Discounting rate	Discounted Cash inflows	Discounted cash outflows
			9.8	1		9.8
		3.9		0.78	3.04
		3.9		0.61	2.37
		3.9		0.47	1.84
		3.9		0.37	1.43
		3.9	9.8	0.29	1.12	2.81
		3.9		0.22	0.87
		3.9		0.17	0.68
1.284		3.9		0.14	0.53
		3.9		0.11	0.41
		3.9	9.8	0.08	0.32	0.80
		3.9		0.06	0.25
		3.9		0.05	0.19
		3.9		0.04	0.15
		3.9		0.03	0.12
		3.9	9.8	0.02	0.09	0.23
		3.9		0.02	0.07
		3.9		0.01	0.06
		3.9		0.01	0.04
		3.9		0.01	0.03
		3.9		0.01	0.03
					13.64	13.64
				NPV	-0.00
				(Sum of Discounted Cash inflows - Sum of Discounted Cash outflows)
			IRR is the discounting rate at which NPV is Zero . Here 28.4% is the IRR.

It is a very good investment opportunity, because the NPV is +Ve and also high IRR than cost of capital.