The following present value factors are provided for use in this problem.

periods present value of $1 at 12% present value of an annuity of $1 at 12%
1 0.8929 0.8929
2 0.7972 1.6901
3 0.7118 2.4018
4 0.6355 3.0373

cliff co. wants to purchase a machine for $50,000, but needs to earn an 12% return. the expected year-end net cash flows are $18,000 in each of the first three years, and $22,000 in the fourth year. what is the machine's net present value?

$7,213.40

Explanation:

The computation of the net present value is shown below:

= Present value of all yearly cash inflows after applying discount factor - initial investment

where,  

Initial investment is $50,000

And, the present value till 3 year would be

= Annual cash flows × PVIFA factor for 3 years at 12%

= $18,000 × 2.4018

= $42,232.40

And, the present value for fourth year would be

= Annual cash flows × present value factor

= $22,000 × 0.6355

= $13,981

So, the total present value would be

= $43,232.40 + $13,981

= $57,213.40

Since the annual cash flows are same for the three years so we use the PVIFA table

Refer to the PVIFA table

Now put these values to the above formula

So, the value would be equal to

= $57,213.40 - $50,000

= $7,213.40

y=mx+b is the right slope of velocity carry the 4 over

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