Question

Precision Dyes is analyzing two machines to determine which one it should purchase. The company requires a rate of return of 15 percent and uses straight-line depreciation to a zero book value over the life of its equipment. Ignore bonus depreciation. Machine A has a cost of $462,000, annual aftertax cash outflows of $46,200, and a four-year life. Machine B costs $898,000, has annual aftertax cash outflows of $16,500, and has a seven-year life. Whichever machine is purchased will be replaced at the end of its useful life. Which machine should the company purchase and how much less is that machine's EAC as compared to the other machine's?

Answer 1

Answer:

Machine A EAC:  $ 208,723.12

Machine B EAC:  $ 232,343.62

Machina will be better as it has a lower equivalent cost

Explanation:

we will calcualte the net present value of the machines and from there the equivalent annual cost:

Net present value: investment + cash outflow

Machine A

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C 46,200

time 4 years

15% discount rate = 0.15

$46200 \times \frac{1-(1+0.15)^{-4} }{0.15} = PV$

PV $131,900

462,000 + 131,900 = $593,900

Now we calcualtethe PTM of a 4 years annuity which present value is 593,900

$PV \div \frac{1-(1+r)^{-time} }{rate} = C$

PV  $595,900.00

time 4

rate 0.15

$595900 \div \frac{1-(1+0.15)^{-4} }{0.15} = C$

$  208,723.123

Machine B will be the same procedure:

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C 16,500

time 7

rate 0.15

$16500 \times \frac{1-(1+0.15)^{-7} }{0.15} = PV$

PV $68,647

NPV = $966,647

$PV \div \frac{1-(1+r)^{-time} }{rate} = C$

PV  $966,647.00

time 7

rate 0.15

$966647 \div \frac{1-(1+0.15)^{-7} }{0.15} = C$

C  $ 232,343.624