Wouldn't you expect that the solution below
would factor in the year 4 salvage value into the net
cash flow? Did they ignore the SV b/c they did not
actually say when the asset life is, nor whether year 4
did or did not have the salvage value? Or perhaps are
they assuming that, since we did not reach the end of
year 4, there is no CF to be included?

Question CPA-05833

A company purchases an item for $43,000.
The salvage value of the item is $3,000. The cost of
capital is 8%.

Pertinent information related to this
purchase is as follows:

Net cash flows Present value factor at 8%

Year 1 $10,000 0.926

Year 2 15,000 0.857

Year 3 20,000 0.794

Year 4 27,000 0.735

What is the discounted payback period in
years?

a. 3.10

b. 3.25

c. 2.90

d. 3.14

Choice "b" is correct. The discounted
payback period of 3.25 years is computed as follows:

Net Present value

cash flows factor at 8% Product
Cumulative

Year 1 $10,000 x 0.926 = 9,260 9,260

Year 2 15,000 x 0.857 = 12,855 22,115

Year 3 20,000 x 0.794 = 15,880 37,955

Year 4 27,000 x 0.735 = 19,845

The cumulative payback after three years is
$37,955. The portion of the fourth year needed to fully
pay back the

investment is computed as the ratio of the
amount remaining to be recovered to the amount collected
in the fourth

year as follows:

(43,000 - 37,955)

÷

19,845 = .252

The discounted payback period is,
therefore:

Years 1-3 3.00 years

Year 4 .25 years

Total 3.25 years

Choice "a" is incorrect. This solution only
anticipates payback of the capital investment net of
salvage.

Choice "c" is incorrect. This solution does
not apply the discount factors

Choice "d" is incorrect, per the above.