Question

You are considering buying a company for $325,000. If you expect the business to earn $113,000 per year, how long is the discounted payback period if your MARR is 10%? (in years, round to one decimal place) Please answer it by hand not using excel

Answer 1

Discounted payback period is time(years) to recover initial cost by periodic future cash flow in present value terms.

Provided,

Initial Cost (I) = $325,000

Annual Cash Inflow (A) = $113,000

MARR(i) = 10%

Now, we compute the cumulative present value of annual cash flows till it crossed the initial cost.

Year	Cash Flow	Present value of Cash flow	Cum. Cash Flow
0	-$325,000	-$325,000	-$325,000.00
1	$113,000	113. 000 (1 + 0.1)1 = $102, 727.27	(-$325,000.00+$102,727.27) = -$222,272.73
2	$113,000	113.000 1400g = $593 388 47	(-$222,272.73+$93,388.43)= -$128,884.28
3	$113,000	113.000 (1+013 = $84.898.57	(-$128,884.28+$84,898.57)= -$43,985.73
4	$113,000	113,000 (1 + 0.1)4 = $77, 180,52	(-$43,985.73+$77,180.52)= $33194.80

With above calculation, we can say Initial cost is fully recovered between year 3 and Year 4.

Thus,

Discounted payback period:

-Cum. PV cash flow year 3 = 3+ - PV Cash flow in year 4

=3+- --43.985.73) 77.180.52

=3+ 43.985.73 77.180.52

=3+0.57

= 3.57 years

Hope this will help, please do comment if you need any further explanation. Your feedback would be highly appreciated.