A recent graduate who wants to start an excava­tion/earth-moving business is trying to determine which size of used dump truck to buy. He knows that as the bed size increases, the net income in­creases, but he is uncertain whether the incremen­tal expenditure required for the larger trucks is justified. The cash flows associated with each size truck are estimated below. The contractor has es­tablished a MARR of 18% per year, and all trucks are expected to have a remaining economic life of 5 years. (a) Determine which size truck he should purchase. (b) If two trucks are to be purchased, what should be the size of the second truck?

Question

Answer 1

These are revenue alternatives; add DN

(a) 8 vs. DN: 0 = -30,000(A/P,i*,5) + (26,500 – 14,000) + 2000(A/F,i*,5)
Solve for i* by trial and error or spreadsheet
i* = 31.7% (spreadsheet)
Eliminate DN

10 vs. 8: 0 = -4000(A/P,?i*,5) + (14,500 – 12,500) + 500(A/F,?i*,5)
?i* = 42.4%
Eliminate 8

15 vs. 10: 0 = -4000(A/P,?i*,5) + (15,500 – 14,500) + 500(A/F,?i*,5)
?i* = 10.9%
Eliminate 15

20 vs. 10: 0 = -14,000(A/P,?i*,5) + (19,500 – 14,500) + 1000(A/F,?i*,5)
?i* = 24.2%
Eliminate 10

25 vs. 20: 0 = -9000(A/P,?i*,5) + (23,000 – 19,500) + 1100(A/F,?i*,5)
?i* = 29.0%
Eliminate 20

Purchase 25 m³ truck
(b) For second truck, purchase truck that was eliminated next to last: 20 m³