Question

A consulting engineering firm's CFO wants to purchase either Ford Explores or Toyota 4Runners for company principles. The two models under consideration cost $30,900 for the Ford and $36,400 for the Toyota. When considering life cycle costs the AOC of the explorer is expected to be $600 per year more than that of the 4Runner. The trade-in value after 3 years are estimated to be 50% of the first cost or the Explorer and 60% for the 4Runner . (a) what is the incremental ROR between the two vehicles? (b) Provided the firm's MARR is 18% per year, which vehicle should it buy?

Answer 1

Salvage value of Ford = 0.5 * 30900 = 15450

Salvage value of Toyota = 0.6 * 36400 = 21840

Incremental initial cost (Toyota - Ford) = 36400 - 30900 = 5500

Incremental annual cost (Toyota - Ford) = -600 (Annual savings)

Incremental salvage (Toyota - Ford) = 21840 - 15450 = 6390

Let i% be the incremental IRR, then

600*(P/A,i%,3) + 6390* (P/F,i%,3) = 5500

Dividing by 5

120*(P/A,i%,3) + 1278* (P/F,i%,3) = 1100

using trail and error method

When i = 15%, value of 120*(P/A,i%,3) + 1278* (P/F,i%,3) = 120*2.283225 + 1278*0.657516 = 1114.292

When i = 16%, value of 120*(P/A,i%,3) + 1278* (P/F,i%,3) = 120*2.245890 + 1278*0.640658 = 1088.267

using interpolation

i = 15% + (1114.292-1100) /(1114.292-1088.267)*(16%-15%)

i = 15% + 0.55%

i = 15.55% (Approx)

Firm should buy Ford as the incremental IRR is less than the MARR