Related Calculations: As a general guide for selecting trial rate-of-return val-
ues, choose a higher value and a lower value around the estimated true rate of return.
Check the result by computing the dollar return. Interpolate linearly when higher and low-
er dollar returns are obtained.
INVESTMENTATAN INTERMEDIATE DATE
(AMBIGUOUS CASE)
A firm purchased an oil-producing property under terms which did not require an imme-
diate payment to the seller but which did require payment of royalties on income from
sale of the oil.
By the end of the third year, the primary reserves were nearly exhausted, and the firm
spent $2,830,000 on a water-injection program to extend the oil yield. Operations were
continued until the end of the sixth year. The income from the venture is listed in Table
- Compute the rate of return on this investment. Is more than one solution obtained?
How may the ambiguity inherent in this type of investment be resolved?
Calculation Procedure:
- Set up an equation for the rate of return
Selecting the end of the third year as the reference date, express the value of every sum of
money. Consider receipts to be positive and expenditures to be negative. Then
$600,000(SPCA for n = 2, i = ?) + $300,000(SPCA for n = 1, i = ?) + $100,000 +
$1,220,000(SPPW for TI = 1, i = ?) + $500,000(SPPW for /i = 2, i = ?) + $200,000(SPPW
for n = 3, j = ?) - $2,830,000 = O. - Solve the rate-of-return equation, using trial values
Assign a series of trial values for / in the equation in step 1. Record the results in Table - Then, by linear interpolation, i = 9.8 percent, or / = 30.1 percent.
- Evaluate the rates of return obtained
The polynomial in step 1 resembles a quadratic polynomial since it contains either two
real roots or none. That there are two values of i which satisfy this equation is explained
as follows.
TABLE 14. Trial Calculations for
Rate-of-Return Equation
TABLE 13. Income from an Asset! " ~~ ~; TTT
Interest rate, % Value of polynomial, $
^ Net income, $ - J^
1 600,000 10 -1,400
2 300,000 15 -21,300
3 100,000 20 -26,400
4 1,220,000 25 -19,400
5 500,000 30 -700
6 200,000 40 65,400