income is highest in the first year and then gradually declines. Therefore, the interest
earned through the purchase of bonds is higher if the firm adopts the sum-of-the-digits
method.
If the interest rate associated with the second element of this composite investment
had been higher, say 4 or 5 percent, the disparity between the two average returns would
have been correspondingly higher.
DEPLETION ACCOUNTING BY
THE SINKING-FUND METHOD
An oil field is anticipated to yield an annual income, before depletion allowances, of
$120,000. The field will be dry after 5 years, at which time the land will have a residual
value of $60,000. If a firm desires a return of 10 percent on its investment, what is the
maximum amount it should invest in this oil field? Use a 4 percent interest rate for the
sinking fund.
Calculation Procedure:
- Determine the replacement cost of the asset
In this method of depletion accounting, it is assumed that the firm deposits a portion of
the annual income in a reserve fund to accumulate the capital needed to replace the asset.
Let C denote the investment required. Then the replacement cost r=C- $60,000 for this
venture. - Compute the annual deposit required
Let d = annual deposit required. Then d = r(SFP) for this venture, or any similar situation.
With i = 4 percent, n = 5, d= (C- $60,000)(0.18463) = 0.18463C- 11,077.80. - Compute the investment required
Set the residual income equal to 10 percent of the investment and solve for C. Or,
$120,000-(0.18463C- 11,077.80) = 0.1OC; C= $460,520.
Related Calculations: Note that this method can be applied to any situation
where there is a gradual depletion of a valuable, profit-generating asset. Further, 'the
method given here is homologous to the sinking-fund method of depreciation accounting.
INCOME FROM A DEPLETING ASSET
An oil field purchased for $800,000 is expected to be dry at the end of 4 years. If the re-
sale value of the land is $20,000, what annual income is required to yield an investment
rate of 8 percent? Use a sinking-fund rate of 3 percent.
Calculation Procedure:
- Compute the annual deposit required to accumulate
the replacement capital
The replacement cost = $800,000 - $20,000 = $780,000 = r. Use the relation annual de-
posit d = r(SFP). With i = 3 percent, n = 4,d= $780,000(0.23903) = $186,440.