Payback Period = A +B/C
Where,
A = Last period with a negative cumulative cash flow
B = Absolute value of cumulative cash flow at the end of the period A
C = Total cash flow during the period after A
Computation of payback period for project A:
Period |
Cash flow |
‘Cumulative cash flow |
0 |
($30) |
($30) |
1 |
$5 |
($25) |
2 |
$10 |
($15) |
3 |
$15 |
$0 |
4 |
$20 |
$20 |
Payback period for Project A = 2 + $ 15/$15 = 2 + 1 = 3 years
Computation of payback period for project B:
Period |
Cash flow |
Cumulative cash flow |
0 |
($30) |
($30) |
1 |
$20 |
($10) |
2 |
$10 |
$0 |
3 |
$8 |
$8 |
4 |
$6 |
$14 |
Payback period for Project B = 1 + $ 10/$10 = 1 + 1 = 2 years
---------------------------------------------------
Discounted Payback Period = A +B/C
Where,
A = Last period with a discounted negative cumulative cash flow
B = Absolute value of discounted cumulative cash flow at the end of the period A
C = Total discounted cash flow during the period after A
Computation of discounted payback period for Project A:
Period |
Cash flow(CA) |
Computation of PV Factor |
PV Factor @ 10 % (F) |
Discounted cash Flow(CA x F) |
Discounted ‘Cumulative cash flow |
0 |
($30) |
1/(1+0.1)^0 |
1 |
($30) |
($30) |
1 |
$5 |
1/(1+0.1)^1 |
0.909090909090909 |
$4.55 |
($25.45) |
2 |
$10 |
1/(1+0.1)^2 |
0.826446280991735 |
$8.26 |
($17.19) |
3 |
$15 |
1/(1+0.1)^3 |
0.751314800901578 |
$11.27 |
($5.92) |
4 |
$20 |
1/(1+0.1)^4 |
0.683013455365071 |
$13.66 |
$7.74 |
Discounted Payback period for Project A = 3 + $ 5.92/$ 13.66 = 3 + 0.433382 = 3.433382 or 3.43 years
Computation of discounted payback period for Project B:
Period |
Cash flow (CB) |
Computation of PV Factor |
PV Factor @ 10 % (F) |
Discounted cash Flow (CB x F) |
Discounted ‘Cumulative cash flow |
0 |
($30) |
1/(1+0.1)^0 |
1 |
($30) |
($30) |
1 |
$20 |
1/(1+0.1)^1 |
0.909090909090909 |
$18.18 |
($11.82) |
2 |
$10 |
1/(1+0.1)^2 |
0.826446280991735 |
$8.26 |
($3.55) |
3 |
$8 |
1/(1+0.1)^3 |
0.751314800901578 |
$6.01 |
$2.46 |
4 |
$6 |
1/(1+0.1)^4 |
0.683013455365071 |
$4.10 |
$6.55 |
Discounted Payback period for Project B = 2 + $ 3.55/$ 6.01 = 2 + 0.590682 = 2.590682 or 2.59 years
---------------------------------------------------------------------------------
PV factor for period n = 1/ (1+r) n
Where r is rate of interest and n is the number of period
Multiply PV factor with the cash flow of respective year to get discounted cash flow. Discounted Cumulative cash flow in year 0 is the discounted cash flow or initial layout of the project. Add the discounted cash flow of year 1 with discounted cash flow year 0 to get discounted cumulative cash flow in year 1. With this discounted cumulative cash flow of year 1, add discounted cash flow of year 2 and get the discounted cumulative cash flow of year 2 and so on.
Project A Discounted Payback Period:
If excel sheet is like below table, insert formulas as:
A |
B |
C |
D |
E |
F |
|
1 |
Time period |
0 |
1 |
2 |
3 |
4 |
2 |
Cash Flow |
($30) |
$5 |
$10 |
$15 |
$20 |
3 |
Disc. Cash Flow |
=B2*(1/(1.1)^0) |
=C2*(1/(1.1)^1) |
=D2*(1/(1.1)^2) |
=E2*(1/(1.1)^3) |
=F2*(1/(1.1)^4) |
4 |
Disc. Cum. Cash Flow |
=B3 |
=B4+C3 |
=C4+D3 |
=D4+E3 |
=E4+F3 |
5 |
||||||
6 |
Discounted payback period A |
=E1 + (-E4/F3) |
This will display as:
A |
B |
C |
D |
E |
F |
|
1 |
Time period |
0 |
1 |
2 |
3 |
4 |
2 |
Cash Flow |
($30) |
$5 |
$10 |
$15 |
$20 |
3 |
Disc. Cash Flow |
-30 |
$4.55 |
$8.26 |
$11.27 |
$13.66 |
4 |
Disc. Cum. Cash Flow |
-30 |
$(25.45) |
$(17.19) |
$(5.92) |
$7.74 |
5 |
||||||
6 |
Discounted payback period A |
3.43 |
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