Question

MIRR unequal lives. Grady Enterprises is looking at two project opportunities for a parcel of land the company currently owns. The first project is a? restaurant, and the second project is a sports facility. The projected cash flow of the restaurant is an initial cost of $1,430,000 with cash flows over the next six years of $240,000 ?(year one), $210,000 ?(year two), $250,000 ?(years three through? five), and ?$1,730,000 ?(year six), at which point Grady plans to sell the restaurant. The sports facility has the following cash? flows: initial cost of $2,300,000 with cash flows over the next four years of ?$440,000 ?(years one through? three) and $3,070,000 ?(year four), at which point Grady plans to sell the facility. The appropriate discount rate for the restaurant is 10.0?% and the appropriate discount rate for the sports facility is 12.5?%.

What are the MIRRs for the Grady Enterprises? projects? What are the MIRRs when you adjust for the unequal? lives? Do the MIRR adjusted for unequal lives change the decision based on the? MIRRs????Hint: Take all cash flows to the same ending period as the longest project.

Answer 1

MIRR assumes that the positive cashflows of a project are reinvested at the firm’s cost of capital while the initial outlay is financed at the firm’s financing rate. IRR assumes that they are reinvested at the IRR. Here, as the appropriate rates for both projects that we need to consider have already been given, we can use spreadsheet MIRR formula by using the given rate for the project both as the financing rate and the reinvestment rate

Project 1: The Restaurant.

We have the following cash flows:

year	Cash flow
0	-1430000
1	240000
2	210000
3	250000
4	250000
5	250000
6	1730000

Rate ( both reinvestment and financing ) = 10%

MIRR = 15.1534%

Project 2: Sports facility

Cash flows:

Year	Cash Flow
0	-2300000
1	440000
2	440000
3	440000
4	3070000

Rate ( both reinvestment and financing ) = 12.5%

MIRR = 19.868%

As you can observe, Sports facility looks a better investment from an MIRR perspective.

To adjust for unequal lives, we’ll follow the Least common multiple approach. Here, we’ll take the LCM of the time periods of the projects and replicate the cash flows until then. Then with equal lives, we can compare the MIRRs of the two projects.

Here, LCM of 4 and 6 is 12. So we’ll replace the cash flows for the restaurant twice ( 6 + 6 ) and for the sports facility thrice ( 4 + 4 + 4 ) and then calculate their MIRRs using the same rates.

We have the following cash flows: Note that for the restaurant year 7 cash flow will include the outflow. So the cash flow will be -1430000 + 240000 = -1190000

Similarly, for sports facility in year 5 and year 9, cash flow will be -2300000 + 440000 = =1860000

Year	CF- restaurant	CF- Sports Facility
0	-1430000	-2300000
1	240000	440000
2	210000	440000
3	250000	440000
4	250000	3070000
5	250000	-1860000
6	1730000	440000
7	-1190000	440000
8	210000	3070000
9	250000	-1860000
10	250000	440000
11	250000	440000
12	1730000	3070000

Now, MIRR_restaurant = 13.01%

And MIRR_Sports = 15.711%

Thus we can see that investment decision remains unchanged even after considering the unequal lives.