Question

14. [6 marks] You are trying to decide between manufacturing a part using a standard milling machine or a CNC machine. The Standard Mill option will cost $5,000 in capital, have an annual operating cost of $2,000, and annual benefits of $4,000. The CNC Mill will cost $16,000 in capital, but have an annual operating cost of only $750 and an annual benefit of $4,000. Your interest rate is 12% per year. The Standard Mill has a useful life of 5 years, the CNC Mill has a useful life of 10 years. The standard mill will have a salvage value of $2000 at the end of its life. a] Which alternative should you select based on a Present Value analysis? [6 marks]

Answer 1

$PV = CF_{0} + \frac{CF_{1}}{(1+r)^{1}} + \frac{CF_{2}}{(1+r)^{2}} + ... + \frac{CF_{n}}{(1+r)^{n}}$

where,

PV is Present Value

CF_n is the Cash Flow in the n^th period

r is the discounting factor (here, interest rate)

for Standard mill -

Standard Mill 12% Rate Time Period Cashflow Present Value Cost Maintainance Revenue -$5,000.00 $0.00 $0.00 -$5,000.00 -$5,000.00 0 $1,785.71 $0.00 -$2,000.00 $4,000.00 $2,000.00 1 $0.00 -$2,000.00 $4,000.00 $2,000.00 $1,594.39 2 $0.00 -$2,000.00 $4,000.00 $2,000.00 $1,423.56 3 $0.00 -$2,000.00 $4,000.00 $2,000.00 $1,271.04 4 $2,000.00 -$2,000.00 $4,000.00 $4,000.00 $2,269.71 5 $3,344.41 Presnt Value

initially (period 0), the company incur a cost of buying the Mill and later in the last year (period 5) company get the salvage value on selling the mill. During its operations, it generates and revenue of $4000 and takes a maintenance cost of $2000 every year. Thus calculating the cash flows (as in the above table) gives the present value as $3441.41.

Similarly for CNC Mill -

Standard Mill 12% Rate Time Period Cost Cashflow Present Value Maintainance Revenue -$16,000.00 $0.00 $0.00 -$16,000.00 -$16,000.00 $0.00 -$750.00 $4,000.00 $3,250.00 $2,901.79 1 $0.00 -$750.00 $4,000.00 $3,250.00 $2,590.88 2 $0.00 -$750.00 $4,000.00 $3,250.00 $2,313.29 3 $3,250.00 $0.00 -$750.00 $4,000.00 $2,065.43 4 $0.00 -$750.00 $4,000.00 $3,250.00 $1,844.14 5 $0.00 -$750.00 $4,000.00 $3,250.00 $1,646.55 6 $0.00 -$750.00 $4,000.00 $3,250.00 $1,470.13 7 $0.00 -$750.00 $4,000.00 $3,250.00 $1,312.62 8 $4,000.00 $0.00 -$750.00 $3,250.00 $1,171.98 $0.00 -$750.00 $4,000.00 $3,250.00 $1,046.41 10 $2,363.22 Presnt Value

we get a present value of $2363.22.

Thus based on present value analysis, it is better to buy the Standard Mill rather than CNC Mill as it has greater present value.