Machinery's Handbook, 31st Edition
EVALUATING INVESTMENTS 151 To include depreciation, the after tax depreciation recovery (ATDR) must be added to get the net present value. Example: A pharmaceutical company makes a product from a composition of chemi- cals. Two mixing processes, batch and continuous, are available. Process Continuous Batch Initial cost ( P ) $75,000 $35,000 Lifetime (years) ( n ) 10 10 Maintenance (per year) $5,000 $8,000 Capacity (units/year) 25,000 20,000 The company uses straight line depreciation, pays 40% of its net income as income tax, and has an after tax minimum attractive rate of return of 15%. The company can sell the product at $1.00 per unit. Which manufacturing process should the company invest in? Solution: Because the lifetimes of the batch and continuous processes are equal at 10 years each, we can make a comparison using the present worth method by applying the formulas for NPV and also for ATDR . NPV P – AR AE – ( ) 1 TR – ( ) 1 i + ( ) n – 1 i 1 i + ( ) n -------------- TR P L – n ------- 1 i + ( ) n – 1 i 1 i + ( ) n -------------- + + = Continuous
10
10
1
1+
– 1
– 1
+ 0.15
0.15
0.40 75000 10 --------
1 10 ------------------- 0.15 + 0.15
1 10 ------------------- 0.15 + 0.15
=
–75000 25000 1 × [ ] – 5000 ( ) 1 – 0.40 ( ) +
+
= –14775 + 15056 = 281
) n – 1 i 1 i + ( ) n --------------
n – 1 i 1 i + ( ) n --------------
P – AR AE – ( ) 1 TR – ( ) 1 i + ( +
TR P L – n -------
1 i + ( )
=
+
NPV
Batch
10
10
1
1+
+ 0.15
– 1
– 1
0.15
0.40 35000 10 --------
1+ 10 ------------------- 0.15 0.15
1+ 10 ------------------- 0.15 0.15
=
–35000 20000 1 × [ ( ) +
+
] –8000
1– 0.40 ( )
= 1135 + 7026 = 8161
Based on above calculations, the batch production process is selected because it gives a greater net present value ( NPV ) than the continuous process. Capitalized Cost.— In governmental analyses, there are some circumstances where a service is required for an infinite period of time, such as with roads, dams, and pipelines. Present worth of a project with an infinite life is known as capitalized cost (CC). Capital- ized cost is the amount of money at n = 0 needed to perpetually support projected expenses with earned interest only. Capitalized cost is the present sum of money that would need to be set aside now, at some interest rate, to yield the funds required to provide the service. CC = P + ( A )( P given A ) - ( L )( P given F ) + ( G )( P given G ) Without periodical replacement: CC P A i = + -- With 100% periodical replacement: CC P P L – 1 i + ( ) n – 1 -------------- A i -- + + = With periodical renovation cost: CC P RC 1 i + ( ) n – 1 -------------- A i -- + + = where CC = capitalized cost; P = initial cost; L = salvage value; A = annual cost; RC = renovation cost; i = interest rate; and, n = effective period of time.
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