Question

A)

Consider the following investment project with a required return of 10 percent:

Year	Cash Flows
0	-51652
1	14891
2	13845
3	13942
4	14886

What is the payback period for this project? (Round your answers to 2 decimal places. (e.g., 32.16))

B)

An investment has an installed cost of $52572. The cash flows over the four-year life of the investment are projected to be $20399, $23594, $20582, and $11317.

If the discount rate is zero, what is the NPV? (Round your final answer to the nearest dollar amount . Omit the "$" sign and commas in your response. For example, $123,456.78 should be entered as 123457.)

Answer 1

Pay Back Period is the period in which the cost of investment is recovered by the the profits or cash inflows.

(A)Pay back Period without discounting:

Note below part of solution is for understanding purpose only. 'See Payback Period after discounting cash flows @10%' below for the solution of your question.

If we do not apply any formula then we can feel that we need to recover $51652. First year we get 14891 and second year 13845 up to second year we have got 28736 which is very less than 51652 so if we add another year cash inflow i.e. 13942 we have got in total $42678 still we need to cover $8974 more. Now out of 4th year cash flow i.e.14886 we need only 8974. If we apply unitary method now,

to recover 14886 we need 1year

to recover $1 we need 1year/14886

to recover 8974 we need 1year/14886*8974

=..60285year year or 7.2342 months or 220 Days

Hence in total we shall require 3year 220 days to recover $51652.

Payback Period after discounting cash flows @10%

A	B	C	D	E
Year	Cash flows	Discounting factor [1/(1+.r)^n	Discounted cash flow(B*C)	Cumulative Discounted Cash Flow
0	-51652	1	-51652	-51652
1	14891	0.909090909	13537.27273	-38114.72727
2	13845	0.826446281	11442.14876	-26672.57851
3	13942	0.751314801	10474.83095	-16197.74756
4	14886	0.683013455	10167.3383	-6030.409262

We can see that cost could not be recovered in four years so discounted pay back period shall be more than 4 years.(Exact payback period shall depend on the cash flows after 4th year) Cumulative discounted cash flow of 4th year shows that there is a Negative Net Present Value of 6030.409

(B) .Discounting at 0 % means no discounting at all.

  

Year	Cash flow	Cumulative Cash flow
1	20399	20399
2	23594	43993
3	20582	64575
4	11317	75892

We need to take the year in which the cumulative cash flow is highest but not more than Investment amount.

In year year 2nd the cumulative cash flow is 43993 hence 2nd year shall be called completed year(for our formula).

52572-43993=8579 is the required cash flow.(for our formula)

Formula:

Pay back Period =Completed years+(365/Next year cash flow*Required Cash flow)

2years and 48.49days or 2years 49days.

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