ENDOWMENT WITH ALLOWANCE
FOR INFLATION
An endowment fund is to provide perpetual annual payments to a research institute. The
first payment, to be made 1 year hence, will be $10,000. Each subsequent payment will be
2 percent more than the preceding payment, to allow for inflation. If the interest rate of
the fund is 7 percent per annum, what amount must be deposited in the fund now? Verify
the result.
Calculation Procedure:
- Compute the amount to be deposited
The payments form a uniform-rate series, and the amount to be deposited = P = present
worth of series. Refer to Eq. 9 for the present-worth factor. When r < 1 + i and n is infi-
nite, URSPW = 1/(1 + i - r). With i = 7 percent and r = 1.02, URSPW = 1/(1.07 - 1.02) = - Then P = ^ 1 URSPW) = $10,000(20) - $200,000.
- Prove that this deposit will provide an endless
stream of payments
The proof consists in finding the rate at which the principal in the fund is growing. At the
end of the first year, principal = $200,000(1.07) - $10,000 •= $204,000. The rate of in-
crease in principal = ($204,000 - $200,000)/$200,000 = 2 percent per year. Similarly, at
the end of the second year, principal = $204,000(1.07) - $10,000(1.02) = $208,080. The
rate of increase in principal = ($208,080 - $204,000)/$204,000 = 2 percent per year.
Thus, the end-of-year principal expands at the same rate as the payments, and so the pay-
ments can continue indefinitely.
Related Calculations: If the interest period of the fund differs from the payment
period, it is necessary to use the interest rate corresponding to the payment period. For ex-
ample, assume that the interest rate is 7 percent per annum compounded quarterly. The cor-
responding annual (or effective) rate is i = (1.0175)^4 - 1 = 7.186 percent, and URSPW =
17(1.07186 - 1.02) = 19.283. The amount to be deposited = $192,830. Note that if r > 1 +1,
URSPW becomes infinite as n becomes infinite. Thus, if the interest rate of the fund is 7
percent per annum, it is impossible to allow the payments to increase by 7 percent or more.
Evaluation of InvestmentsPREMIUM-WORTH METHOD OF
INVESTMENT EVALUATION
A firm contemplates investing in a depleting asset and has a choice between two enter-
prises. Project A requires the investment of $57,500; project B requires the investment of
$63,000. The forecast end-of-year dividends are as follows:
Year Project A, $ Project B, $
1 10,00 0 15,00 0
2 15,00 0 25,00 0
3 25,00 0 30,00 0
4 20,00 0 20,00 0
5 10,00 0