First, consider that i = 9.8 percent, causing the polynomial to assume the value of zero.
Then replace 9.8 percent with the higher rate of 30.1 percent. Second, when this substitu-
tion is made, the value of the income received prior to the end of the third year is in-
creased by a certain amount. The value of the income received after that date is decreased
by the same amount. Hence, the value of the polynomial remains zero.
- Make a realistic appraisal of the investment
A realistic appraisal of an investment of this type requires consideration of the reinvest-
ment rate earned by either the entire income or that part of the income received prior to
the expenditure. In the present instance, assume that the income received up to the end of
the third year was reinvested at 8 percent. Its value at the date of the expenditure for water
injection is, by the equation from step 1, $600,000(1.166) + $300,000(1.080) + $100,000
-$1,123,600.
Then the effective investment = $2,830,000 - $1,123,600 = $1,706,400. To determine
the rate of return, set the effective investment $1,706,400 = $1,220,000(SPPW for n = 1)
- $500,000(SPPW for /i = 2) + $200,000(SPPW for n = 3) and solve for i. The result of
this solution is / = 8.5 percent.
Related Calculations: This procedure illustrates the fact that in financial analy-
ses it is not possible to place exclusive reliance on mathematical results. However rigor-
ous the mathematical solution may appear to be, the results must be interpreted in a prac-
tical manner. Note that this procedure may be used for any type of asset.
PAYBACK PERIOD OF AN INVESTMENT
A firm has a choice of two alternative investment plans, A and B. Each plan requires an
immediate expenditure of $2,000,000, lasts 10 years, and yields an income at the end of
each year. Under plan A, the annual income is expected to be $450,000 for the first 5
years and $33,000 for the remaining 5 years. Under plan B, the annual income is expected
to be $150,000 for the first 3 years, $250,000 for the next 3 years, and $650,000 for the
last 4 years. If the decision is to be based on a short payback period, which investment
plan should the firm adopt?
Calculation Procedure:- Compute the payback period under plan A
For various reasons, a firm often prefers an investment that allows it to recover its capital
quickly. The speed with which capital is recovered is measured by the payback period,
defined thus: Assume that all income accruing from the investment initially represents re-
covered capital, and all income accruing after capital has been fully recovered represents
interest. The time required for completion of capital recovery is called the payback peri-
od.
Under plan A, the first four payments total $1,800,000, and the first five payments to-
tal $2,250,000. Thus, the fifth payment completes capital recovery, and the payback peri-
od is 5 years. - Compute the payback period under plan B
The first seven payments total $1,850,000, and the first eight payments total $2,500,000.
Thus, the payback period is 8 years.