Question

13-46) Sacramento Cab Company owns several taxis that were purchased for $25,000 each 4 years ago. The cabs’ current market value is $12,000 each, and if they are kept for another 6 years they can be sold for $2,000 per cab. The annual maintenance cost per cab is $1,000 per year. Sacramento Cab has been approached about a leasing plan that would replace the cabs. The leasing plan calls for payments of $6,000 per year. The annual maintenance cost for each leased cab is $750 per year. Should the cabs be replaced if the interest rate is 10%?

Answer 1

We will use present worth analysis to decide on whether to replace the cabs.

Alternative 1 (Using the existing cabs)

Annual Maintenance Cost = $1,000 each or 1,000 × 4 = $4,000

Salvage Value = $2,000 each or 2,000 × 4 = $8,000

Life (n) = 6 years

Interest Rate (i)= 10% per annum or 0.1

Present Worth (PW) = Annual Maintenance Cost(P/A, i, n) – Salvage Value(P/F, i, n)

PW = 4,000(P/A, 10%, 6) – 8,000(P/F, 10%, 6)

PW = 4,000[((1+0.1)⁶ – 1)/0.1 (1+0.1)⁶] – 8,000/(1 + 0.1)⁶

PW = 17,420 – 4,516

Present Worth of Alternative 1 = $12,904

Alternative 2 (Leasing cabs)

Annual Payment = $6,000

Annual Maintenance Cost = $750 each or 750 × 4 = $3,000

Life (n) = 6 years

Interest Rate (i)= 10% per annum or 0.1

Present Worth (PW) = Annual Payment(P/A, i, n) + Annual Maintenance Cost(P/A, i, n)

PW = 6,000(P/A, 10%, 6) + 3,000(P/A, 10%, 6)

PW = 6,000[((1+0.1)⁶ – 1)/0.1 (1+0.1)⁶] + 3,000[((1+0.1)⁶ – 1)/0.1 (1+0.1)⁶]

Present Worth of Alternative 2 = $39,195

Since, the present worth of the cost of Alternative 1 is less than that of Alternative 2, so we can say that the cabs should not be replaced.