Question

A machine shop is trying to decide which of two types of metal lathe to purchase. The more versatile Japanese lathe costs $32,000,and will generate an annual profit of$16,000 for three years. Its trade-in value after three years will be about $10,000. The more durable German lathe costs $42,000, and will increase profits by $12,000 per year for six years. Its trade-in value at that point is estimated at $15,000. Based on an NPV calculation at a 10% cost of capital, which lathe should be purchased?

Answer 1

First we will calculate the NPV of the Japanese lathe.
Following is the cash flow for the Japanese lathe:

Year	Cash Flow
0	-32000
1	16000
2	16000
3	16000
4	10000

NPV = -32000 + P*[ 1- (1+r)^-n ] / r + TV/ (1+r)ⁿ

where, P = $16000 ( used to calculate present value annuity)
TV = trade in value = $10000
r = 10%
n = 3 years

NPV = -32000 + 16000*[ 1 - (1+0.10)^-3 ] / 0.10 + 10000 / (1+ 0.10)³

          = -32000 + 16000* 2.4869 + 10000 / 1.331
       = -32000 + 39789.63 + 7513.15
       = $15302.78

NPV from German lathe is below:

NPV = -42000 + P*[ 1- (1+r)^-n ] / r + TV/ (1+r)ⁿ

where, P = $12000 ( used to calculate present value annuity)
TV = trade in value = $15000
r = 10%
n = 6 years

NPV = -42000 + 12000*[ 1 - (1+0.10)^-6 ] / 0.10 + 15000 / (1+ 0.10)⁶
         = - 42000 + 12000* 4.355 + 8467.11
      = $18730.24

Based on simple NPV calculation, German lathe should be purchased as it has higher NPV than Japanese lathe. However, since both have different project life , we need to bring the Japanese lathe to same 6 years use and determine the NPV.

Therefore, for a 3 year project it has NPV of $15303 at time 0, for another three years it will have same NPV but at time 3 years. We will now discount %15303 to time zero as below
NPV at time 0 = $15303 + $15303 / (1.10)^3
                        = 15303 + 11497
                       = $26800

Therefore, NPV of Japanese lathe is more and hence considering same time span we should purchase Japanese lathe