Machinery's Handbook, 31st Edition
EVALUATING INVESTMENTS 153 Example, Annual Cost Considering Salvage Value: If in the previous example the sal vage value of the equipment installed was $5,000 at the end of 10 years, what is the effect on the annual cost of the proposed investment of $15,000? Solution: The only item in the annual cost of the previous example that will be affected is the capital recovery amount of $2,442. The following formula gives the amount of annual capital recovery when salvage value is considered: A P L – ( ) i 1 i + ( ) n 1 i + ( ) n – 1 -------------- Li AE + + =
15000 – 5000 ( ) ---------------------- 5000 + (0.10)(1 + 0.10) 10
=
+
5100
= 7227.45
(0.10)
(1 + 0.10) 10 – 1 This amount is $315 less than the previous annual cost of $7,542 for the proposed investment. Rate of Return.— This is the estimated interest rate produced by an investment. Rate of return ( ROR ) is the interest rate at which benefits are equivalent to costs. It is defined as the interest rate paid on the unpaid balance of a loan in such a way that the payment schedule makes the unpaid loan balance equal zero when the final payment is made. It may be com - puted by finding the interest rate in such a way that the estimated expenditures are equal to the capital gain. Net Present Worth = 0, or equivalently, PW of benefits - PW of costs = 0 1 ROR + ( ) n – 1 ROR 1 ROR + ( ) n --------------------- AR AE – ( ) L 1 ROR + ( ) n + --------------- P = The rate of return can only be calculated through trial and error. To find out the present worth, a reasonable interest rate is selected and the present worth is calculated. Then another rate is chosen and the present worth is calculated. The value of the ROR is interpo- lated or extrapolated to find the zero value of present worth. Benefit-Cost Ratio.— This is the ratio of present worth of benefit to present worth of cost. This method is applied to municipal project evaluations where benefits ( B ) and costs ( C ) accrue to different segments of the community. A project is considered acceptable if the ratio equals or exceeds 1. For fixed input, B / C ≥ 1 is maximized, and for fixed output, B / C ≥ 1 is maximized, and if neither input nor output is fixed, to compute the incremental benefit-cost ratio ( D B / D C ), choose D B / D C ≥ 1. Example: To build a bridge over a river costs $1,200,000, with benefits of $2,000,000, and disbenefits of $500,000. (a) What is the benefit-cost ratio? (b) What is the excess of benefits over costs? Solution: (a) The benefit-cost ratio B / C is regarded as ( B – D )/ C . Here B = benefits, D = disbenefits, and C = cost. (b) The excess of benefits over cost = 2,000,000 – 1,200,000 – 500,000 = 300,000. Payback Period.— This is the period required to obtain benefits or cost savings equal to the initial investment made. For example, if a piece of equipment costs $10,000 and the company can obtain cost savings of $2,500 per year by procuring that equipment, the payback period can be said to be $10,000 divided by $2,500, which is 4 years. Payback period is a quick way of evaluating whether an investment is worth making. For example, a plant manager who has a payback period of 5 years in her mind might think the $10,000 investment is worth making. Payback period ignores the rate of interest or assumes that rate to be 0%. Also, payback period ignores benefits coming in a non-linear manner over the life of the equipment. Benefit-cost ratio: (2,000,000 – 500,000)/1,200,000 = 1.25 As the ratio is greater than 1, the project is worth undertaking.
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