TABLE 15. Value of Expenditures and Income
Life of asset, Value of Value of
years expenditures, $ income, $
1 36,81 8 10,90 9
2 37,52 1 20,82 6
3 38,12 2 26,83 6
4 38,63 4 32,30 0
5 39,06 9 37,26 7
6 39,43 5 40,65 4costing $120,000 at the end of every 10-year period. The life of the dam may be assumed
to be infinite. The reduction in losses due to flood damage is estimated to be $300,000 per
year. However, there will be an immediate loss of $100,000 in the value of the property
surrounding the dam, and this loss will be borne by the public. Applying an interest rate
of 6 percent, determine whether the proposed dam is feasible.
Calculation Procedure:- Compute the present worth of costs
With reference to a federal project, any income or reduction in loss that accrues to the
public is called a benefit, any loss that accrues to the public is called a disbenefit, and the
difference between the benefits and disbenefits is called the net benefit. The ratio of net
benefit to costs is called the benefit-cost (BIC) ratio. If this ratio exceeds 1, the project is
considered desirable.
A uniform-payment series that continues indefinitely is called & perpetuity. The value
of a perpetuity at its origin date (i.e., one payment period before the first payment) is
R/[(\ +i)
m
-l], where R = periodic payment, i = interest rate, and m = number of interest
periods in one payment period.
The present worths are: First cost, PW = $5,000,000; annual maintenance, PW =
$24,000/0.06 = $400,000; repairs and reconstruction, PW = $120,000/[(1.06)
10- 1] =
$151,700. Then PW of costs = $5,000,000 + $400,000 + $151,700 = $5,551,700.
- 1] =
- Compute the present worth of net benefit
The present worths are: Savings, PW = $300,000/0.06 = $5,000,000; devaluation of prop-
erty, PW = $100,000. Then PW of net benefit = $5,000,000 - $100,000 = $4,900,000. - Determine whether the dam is feasible
Since BIC ratio = $4,900,000/$5,551,700 < 1, the dam is not feasible.