A consulting engineering firm is considering two models of suvs for the company principals. a gm model will have a first cost of $36,000, an operating cost of $4000, and a salvage value of $15,000 after 3 years. a ford model will have a first cost of $32,000, an operating cost of $4100, and also have a $15,000 resale value, but after 4 years. (a) at an interest rate of 12% per year, which model should the consulting firm buy? conduct an annual worth analysis. (b) what are the pw values for each vehicle?

Part (a) : Annual worthy analysis

Annual worthy = - Annuities of PV (cost) - Annual expenses + Annuities of FV (salvage cost)

Then,

For GM model:

Annual worthy = - 36,000 (A|P, 12%,3) - 4000 + 15,000 (A|F, 12%,3)

Where,

(A|P, 12%,3) = {[1 - (1+0.12) ^-3]/0.12}^-1 = 0.41635;

(A|F, 12%,3) = {[ (1+0.12) ^3-1]/0.12}^-1 = 0.29635

Therefore,

Annual worthy for GM model = - 36,000 (0.41635) - 4,000 + 15,000 (0.29635) = - $50,543.35

For Ford model:

Annual worthy = - 32,000 (A|P, 12%,4) - 4,100 + 15,000 (A|F, 12%,4)

Where,

(A|P, 12%,4) = {[1 - (1+0.12) ^-4]/0.12}^-1 = 0.32923

(A|F, 12%,2) = {[ (1+0.12) ^4-1]/0.12}^-1 = 0.20923

Therefore,

Annual worthy of Ford model = - 32,000 (0.32923) - 4,100 + 15,000 (0.20923) = - $11,496.91

It can be noted that Annual worth of Ford > Annual worthy of GM model and thus the best option is the Ford model

Part (b) : Present Worth (PW)

PW of GM model = - 36,000 - 4,000 (P/A, 12%,3) + 15,000 (P/F, 12%,3)

Where

(P/A, 12%,3) = [1 - (1+0.12) ^-3]/0.12 = 2.40183

(P/F, 12%,3) = 1 / (1+0.12) ^3 = 0.71178

Therefore,

PW of GM model = - 36,000 - 4,000 (2.40183) + 15,000 (0.71178) = - $34,930.62

PW of Ford model = - 32,000 - 4,100 (P/A, 12%,4) + 15,000 (P/F, 12%,4)

Where,

(P/A, 12%,4) = [1 - (1+0.12) ^-4]/0.12 = 3.03735

(P/F, 12%,4) = 1 / (1+0.12) ^4 = 0.63552

Therefore,

PW of Ford model = - 32,000 - 4,100 (3.03735) + 15,000 (0.63552) = - $10,014.065

Based on PW, PW of Ford model > PW for GM model and thus Ford model is the better option.