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 ​$9.6 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 ​$3.5 million​ (this does not reflect the cost of constructing the landfills every five​ years). Star uses a 10.4​% 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

NPV	$ 7.802402 million	or	7,802,402.09	$
IRR	24.04%
MIRR	12.14%

(a): NPV:

	A	B	C = A - B
Year (n)	Costs (in $ millions)	Cash inflow (in $ millions)	Net cash flow (in $ millions)	1+r	PVIF = 1/1+R^n	PV = net cash flow * PVIF
0	-                                          9.60		-                                                   9.60	1.104	1.0000	-                                             9.60
1		3.50	3.50		0.9058	3.17
2		3.50	3.50		0.8205	2.87
3		3.50	3.50		0.7432	2.60
4		3.50	3.50		0.6732	2.36
5	-                                          9.60	3.50	-                                                   6.10		0.6098	-                                             3.72
6		3.50	3.50		0.5523	1.93
7		3.50	3.50		0.5003	1.75
8		3.50	3.50		0.4532	1.59
9		3.50	3.50		0.4105	1.44
10	-                                          9.60	3.50	-                                                   6.10		0.3718	-                                             2.27
11		3.50	3.50		0.3368	1.18
12		3.50	3.50		0.3051	1.07
13		3.50	3.50		0.2763	0.97
14		3.50	3.50		0.2503	0.88
15	-                                          9.60	3.50	-                                                   6.10		0.2267	-                                             1.38
16		3.50	3.50		0.2054	0.72
17		3.50	3.50		0.1860	0.65
18		3.50	3.50		0.1685	0.59
19		3.50	3.50		0.1526	0.53
20		3.50	3.50		0.1382	0.48
					NPV	7.802402

Thus NPV = $7.802402 million or $7,802,402.09

IRR: This has been computed using trial and error approach as shown below:

Year (n)	Costs (in $ millions)	Cash inflow (in $ millions)	Net cash flow (in $ millions)	1+r	PVIF = 1/1+R^n	PV = net cash flow * PVIF
-	-                                            9.6		-                                                      9.6	1.1	1.0	-                                               9.6
1		3.5	3.5		0.9	3.2
2		3.5	3.5		0.8	2.9
3		3.5	3.5		0.7	2.6
4		3.5	3.5		0.7	2.4
5	-                                            9.6	3.5	-                                                      6.1		0.6	-                                               3.7
20		3.5	3.5		0.1	0.5
					NPV	7.802402

Thus IRR = 24.04%

MIRR:

MIRR formula is: Present value of costs = Terminal value/(1+MIRR)^n

Present value of costs = 9.6 + 9.6/1.104^5 + 9.6/1.104^10 + 9.6/1.104^15 = 21.20 million

Terminal value = 3.50*(1.104^19)+3.50*(1.104^18)+…..3.50*(1.104^1) + 3.5 = 209.80 million

Thus 21.20 million = 209.80 million/(1+MIRR)^20

Or (1+MIRR)^20 = 9.90

OR 1+Mmirr = 1.1214

Or MIRR = 12.14%

(b): Yes, this is a good investment opportunity because NPV is positive, IRR > hurdle rate of 10.4% and MIRR > hurdle rate of 10.4%