Question

9. A vehicle has a first cost of $20,000. Its market value declines by 15% annually. The cost of the vehicle is $700 the first year, and increases by $700 each year thereafter (so $1400 the second year, 2100 the 3rd year, etc.) The firm’s MARR is 10%. What is the minimum EUAC for the vehicle and its economic life?

Answer 1

We need to find EUAC for the vehicle. The market value for the first year is 20000(1 - 15%) = 17000. Cost in the first is $700 and the gradient is $700. For the second year, MV is 20000(1 - 15%)^2 = 14450

Find EUAC for n = 1, 2, 3, 4... years as

EUAC (n = 1) = (20000 + 700(P/A, 10%, 1) + 700(P/G, 10%, 1) - 17000(P/F, 10%, 1))(A/P, 10%, 1) = 5700

EUAC (n = 2) = (20000 + 700(P/A, 10%, 2) + 700(P/G, 10%, 2) - 14450(P/F, 10%, 2))(A/P, 10%, 2) = 5676.20

EUAC (n = 3) = (20000 + 700(P/A, 10%, 3) + 700(P/G, 10%, 3) - 12282.50(P/F, 10%, 3))(A/P, 10%, 3) = 5687.20

Since EUAC is minimum in year 2, economic life is 2 years and its EUAC is 5676.20