ANNUAL COSTBY THEAMORTIZATION
(SINKING-FUND-DEPRECIATIONUVIETHOD __^
A machine costs $30,000 and will be retired at the end of 8 years with a salvage value
of $5000. The annual operating cost is $3200. Determine the annual cost by the amorti-
zation method if the interest rate on the loan is 6 percent and that of the sinking fund is
3 percent.
Calculation Procedure:
Compute the annual cost of the asset
The amortization method is based on the following assumptions: The asset is purchased
with borrowed funds; interest on the loan is paid annually; the loan principal is paid as a
lump sum at the retirement of the asset; the funds required to retire the debt are accumu-
lated by uniform annual deposits in a reserve fund. This assumed method of financing is
unrealistic; the amortization method is therefore approximate.
Let I 1 = interest rate on loan; I 2 = interest rate on sinking fund. Then A = (P- L)(SFP)
- Pii + c. In this equation the SFP factor is based on I 2. Apply this equation, using P =
$30,000, L = $5000, TV= 8, c = $3200,1 1 = 6 percent, / 2 = 3 percent. Thus, A = $7812.
ANNUAL COST BY THE
STRAIGHT-LINE-DEPRECIATION METHOD
The director of a corporation recommends that a firm buy a computer instead of renting at
the rate of $50 per hour. A new computer costs $120,000; annual operating, maintenance,
and insurance costs total $8500. The computer will be traded at the end of 10 years for
$30,000. The director forecasts computer usage for 480 h/year. He bases his calculation
of annual cost on the straight-line-depreciation method with an interest rate of 6 percent.
Is his recommendation sound?
Calculation Procedure:- Compute the annual cost of owning the asset
The straight-line method is an approximate one which assumes that the asset is purchased
with borrowed funds. However, the method disregards the timing of payments and con-
siders only their arithmetic average. Thus, the annual cost A = (P- L)IN +(P- L)I 1 (N +
l)/2N + Li 1 + c. So A = $90,000/10 + $90,000(0.06)(11/20) + $30,000(0.06) + $8500 =
$22,270. - Compute the annual cost of renting the asset
The annual cost of renting the asset = (hourly rate, $)(annual use, hr) = ($50)(480) =
$24,000.
Since the annual cost of owning the asset is less than the annual cost of renting it,
the firm would save money by owning the asset. Note that this is an approximate
method.