Question

Compute the discounted payback statistic for Project C if the appropriate cost of capital is 7 percent and the maximum allowable discounted payback period is three years. (Do not round intermediate calculations and round your final answer to 2 decimal places.)

Project C
Time:	0	1	2	3	4	5
Cash flow:	–$1,400	$640	$600	$640	$380	$180

Should the project be accepted or rejected?

• accepted

• rejected

Answer 1

Discounted payback period

Discounted Payback period is nothing but the length of time taken for the initial cost of a project to equalise the discounted value of expected cashflows or the time taken to break-even from the amount of investment.

Discounted payback period for Project C

Present value factor of the cash flow may be calculated using the formula

PV= ( CF) / (1+r)^n

Where PV = Present value of cash flows
CF = Cash flows
   r = interest rate per period
   n = period of cash flow

Project C	Years	Cash flow	1/(1+r)^n	PV = CF * 1/(1+r)^n	Cumulative PV
	1	640	0.93	598.13	598.13
	2	600	0.87	524.06	1122.19
	3	640	0.82	522.43	1644.62
	4	380	0.76	289.90	1934.52
	5	180	0.71	128.34	2062.86

As you can see from the cumulative PV column, it is understood the initial cost of Project C has been recovered in 3 years, but still not the entire amount of discounted cash flows is allocated for investment. Thus the initial initial investment was recovered during 2 years and part of the third year and the discounted payback period may be calculated as follows:

Payback period = (2+( (1644.62 – 1400)/1644.62))

Payback period =(2+0.148740) = 2.15 years

Thus the discounted payback period is 2.15 years