(g/0(l - «SFP). With D 1 = $13,636, g = -$1363.64, i = 8 percent, and n = 10, D =
$13,636 + (-$1363.64/0.08)[1 - 10(0.06903)] = $8357.- Compute the annual cost under sum-of-digits depreciation
Referring to step 2 and taking the difference between the equivalent depreciation charge
in the present case and the depreciation charge under the straight-line method, we deter-
mine the annual cost A = $9960 - ($8357 - $7500)(0.47) = $9557.
Related Calculations: A comparison of the two values of annual cost—$9960
when straight-line depreciation is used and $9557 when sum-of-digits depreciation is
used—confirms the statement made in an earlier calculation procedure. Since tax savings
accrue more quickly under sum-of-digits depreciation than under straight-line deprecia-
tion, the former method is more advantageous to the firm. In general, a firm seeks to write
off an asset rapidly in order to secure tax savings as quickly as possible, thus allowing it
to retain more capital for investment. For this reason depreciation accounting is subject to
stringent regulation by the IRS.
COST COMPARISON WITH ANTICIPATED
DECREASING COSTS
Two alternative machines, A and B, are available for a manufacturing operation. The life
span is 4 years for machine A and 6 years for machine B. The equivalent uniform annual
cost is estimated to be $16,000 for machine A and $15,000 for machine B. However, as a
result of advances in technology, the annual cost is expected to decline at a constant rate
from one life to the next, the rate of decline being 10 percent for machine A and 6 percent
for machine B. Applying an investment rate of 12 percent, determine which machine is
preferable.
Calculation Procedure:- Select the analysis period, and compute annual costs
for this period
The cost comparison will be made by the present-worth method. The analysis period is 12
years, since this is the lowest common multiple of 4 and 6. The annual costs are as fol-
lows: Machine A: first life, $16,000; second life, $16,000(0.90) = $14,400; third life,
$14,400(0.90) = $12,960. Machine B: first life, $15,000; second life, $15,000(0.94) =
$14,100. - Construct a money-time diagram
The equivalent uniform annual payments are shown in Fig. 6. - Compute the present worth of costs for the first analysis
period, and identify the more economical machine
For machine A, PW = $16,000(USPW, n = 4) + $14,400(USPW, n = 4)(SPPW, n = 4) +
$12,960(USPW, n = 4)(SPPW, n = 8). With / = 12 percent, PW = $16,000(3.037) +
$14,400(3.037)(0.6355) + $12,960(3.037)(0.4039) = $92,280. For machine B, PW =
$15,000(USPW, /1 = 6) + $14,100(USPW, n = 6)(SPPW, n = 6), or PW = $15,000(4.111)
- $14,100(4.111)(0.5066) = $91,030. Machine B should be used for the first 12 years be-
cause it costs less.