Question

Suppose a company has proposed a new 4-year project. The project has an initial outlay of $70,000 and has expected cash flows of $20,000 in year 1, $23,000 in year 2, $29,000 in year 3, and $35,000 in year 4. The required rate of return is 12% for projects at this company. What is the discounted payback for this project? (Answer to the nearest tenth of a year, e.g. 3.2)

Answer 1

Discounted Project payback period

Discounted Payback period = 3.60 years

When the annual cash flows are not uniform, the cumulative cash inflows from operations must be calculated for each year. The payback period shall be corresponding period when total of cumulative cash inflows is equal to the initial capital investment. However, if exact sum does not match then the period in which it lies should be identified. After that we need to compute the fraction of the year.

Initial capital investment = $70,000

Cash flows

Year	Cash flow	Present value factor @ 12%	Present value	Cumulative cash flow
(I)	(II)	(III)	(IV) = (II *III)	(V)
1	$20,000	0.8929	$17,858	$17,858
2	$23,000	0.7972	$18,336	$36,194
3	$29,000	0.7118	$20,642	$56,836
4	$35,000	0.6355	$22,243	$79,079

Payback period in this case will lie between year 3 and year 4. Since up to 3 years a sum of $56,836 shall be recovered, balance of $13,164 shall be recovered in the part (Fraction) of 4^th year, Computation is as follows

            = (Balance recoverable ÷ Cash flow of year 4)

= ($ 13,164 ÷ $ 22,243)

= 0.5918

            = 0.60 years (rounded)

Payback period = 3.60 years (rounded)

Amount of $56,836 is recovered in 3 years time and amount of $13,164 is recovered in 0.60 year therefore total payback = 3.60 years

Note

Present value = Cash flow * present value factor

Calculation of present value factor

Present value factor = 1/ (1+R) ^N

R = Discount Rate (i.e. = 12%)

N = No of years

E.g. for year 2 Discount Factor = 1/ (1.12)²

                                                                ⁼ 1/ (1.12) (1.12)

                                                = . 0.7972