Question

A resource firm is looking to purchase two machines for its extraction plant. The initial costs and net cash flows are captured in the table below. The company uses a discount rate (MARR) of 6 percent.

Table 2

Year	Machine A	Machine B
0	($72,000)	($51,660)
1	24,000	18,000
2	24,000	18,000
3	24,000	16,000
4	22,000	16,000
5	12,000	9,000

a)    Calculate the discounted payback period for Machine A and Machine B. If the discounted payback period was the only decision tool, which machine would the company select?

b) Calculate the net present value (NPV) of both machines if the firm uses a MARR of 6%. Which machine would be selected in this case? Explain.

Answer 1

Machine A

Intial Investment = $72,000

So our target here is $72,000

Year	Cashflow	PV Factor @ 6%	P.V. of cashflows	Cumulative P.V. of cashflows
1	24000	0.943	22632	22632
2	24000	0.890	21360	43992
3	24000	0.840	20160	64152
4	22000	0.792	17424	81576
5	12000	0.747	8964	90540

We can see that the cost of $72000 is covered between year 3 and year 4. To be more precise:

Cashflow is 17424 in 12 months

So a cashflow of 7848 will be in = (12/17424) *7848 = 5.4 months

So the discounted payback period for Machine A is 3 years 5.4 months.

NPV for Machine A = PV of cash inflows - PV of cash outflows = 90540-72000 =$18540

Machine B

Initial Investment= $51660

Year	Cash Flow	PV Factor @ 6%	PV of Cashflows	Cumulative PV of cashflows
1	18000	0.943	16974	16974
2	18000	0.890	16020	32994
3	16000	0.840	13440	46434
4	16000	0.792	12672	59106
5	9000	0.747	6723	65829

Here the cost of $51660 is recovered between year 3 and year 4. To be more precise:

Cashflow of 12672 is in 12 months

So a cashflow of 5226 will be in : (12/12672)*5226 = 4.95 months

So the discounted pay back period for machine B is 3 years 4.95 months.

NPV for machine B= 65829-51660 =$14169

Since the discounted payback period of Machine B is lower than that of Machine A therefore we will select machine B as per discounted pay back period criteria.

Since the NPV for machine A is greater than the NPV for machine B therefore we will select machine A as per the NPV critera.