Question

MIRR unequal lives. Singing Fish Fine Foods has $1,860,000 for capital investments this year and is considering two potential projects for the funds. Project 1 is updating the​ store's deli section for additional food service. The estimated​ after-tax cash flow of this project is ​$620,000 per year for the next five years. Project 2 is updating the​ store's wine section. The estimated annual​ after-tax cash flow for this project is $530,000 for the next six years. The appropriate discount rate for the deli expansion is 9.7​% and the appropriate discount rate for the wine section is 9.2​%. What are the MIRRs for the Singing Fish Fine Foods​ projects? What are the MIRRs when you adjust for unequal​ lives? Do the MIRR adjusted for unequal lives change the decision based on​ MIRRs? ​Hint: Take all cash flows to the same ending period as the longest project.

Answer 1

MIRR = [FV(Positive cash flows x Cost of Capital) / PV (Initial Outlays x Financing costs) ]^1/n -1

For Project 1,

n = 5 years,

discount rate = 9.7%

PV of Initial Outlay = 1,860,000

FV of cash flows = 620,000 x (1 + 0.097)⁴ + 620,000 x (1 + 0.097)³​​​​​​​ + 620,000 x (1 + 0.097)²​​​​​​​ + 620,000 x (1 + 0.097)​​​​​​​ + 620,000 x (1 + 0.097)⁰

FV of cash flows = $3,762,619.974

MIRR = (3,762,619.974 / 1,860,000)^1/n - 1 = 0.15132 or 15.132%

For Project 2,

n = 6 years,

discount rate = 9.2%

PV of Initial Outlay = 1,860,000

FV of cash flows = 530,000 x (1 + 0.092)⁵​​​​​​​ + 530,000 x (1 + 0.092)⁴​​​​​​​ + 530,000 x (1 + 0.092)³​​​​​​​ + 530,000 x (1 + 0.092)²​​​​​​​ + 530,000 x (1 + 0.092)​​​​​​​ + 530,000

FV of cash flows = 4,007,540.276

MIRR = (4,007,540.276 / 1,860,000)^1/6 - 1 = 0.13648 or 13.648%

Since Project 1 is the shortest project, we will adjust it

FV of cash flows = 620,000 x (1 + 0.097)⁵​​ +​​​​​ 620,000 x (1 + 0.097)⁴​​​​​​​ + 620,000 x (1 + 0.097)³​​​​​​​ + 620,000 x (1 + 0.097)²​​​​​​​ + 620,000 x (1 + 0.097)​​​​​​​

FV of cash flows = 4,127,594.112

MIRR = (4,127,594.112 / 1,860,000)^1/6 = 0.14208 or 14.208%

Both the adjusted and unadjusted MIRR for Project 1 are higher than that of Project 2, so Project 1 will be selected.