Question

0.7. A large automobile manufacturer is considering the installation of a high-tech material handling system for $25,000,000. This system will save $7,500,000 per year in manual labor, and it will incur $2,750,000 in annual operating and maintenance expenditures. The salvage value at the end of the system's 10-year life is $1,500,000. If the company's hurdle rate (MARR) is 10% per year, should the system be recommended for implementation? Use IRR method to make your recommendation

Answer 1

Let IRR be i%

PW at IRR is 0

PW = -25000000 + (7500000 - 2750000) *(P/A, i%,10) + 1500000 * (P/F, i%,10) = 0

-25000000 + 4750000 *(P/A, i%,10) + 1500000 * (P/F, i%,10) = 0

4750000 *(P/A, i%,10) + 1500000 * (P/F, i%,10) = 25000000

dividing by 50000

95 *(P/A, i%,10) + 30 * (P/F, i%,10) = 500

using trail and error method

when i = 14%, value of 95 *(P/A, i%,10) + 30 * (P/F, i%,10) = 95 * 5.216116 + 30 * 0.269744 = 503.623301

when i = 15%, value of 95 *(P/A, i%,10) + 30 * (P/F, i%,10) = 95 * 5.018769 + 30 * 0.247185 = 484.198561

using interpolation

i = 14% + (503.623301 - 500) / (503.623301 - 484.198561) *(15%-14%)

i = 14% + 0.18653%

i = 14.186% = 14.19% (Approx)

As IRR is greater than 10%, this project is acceptable