Annual fuel saving ($) = 45,000 x 3 = 135,000
(1) Simple Payback period (PBP) is the time by when cumulative cash flows becomes zero.
Year | Cash flow ($) | Cumulative Cash Flow ($) |
0 | -10,00,000 | -10,00,000 |
1 | 1,35,000 | -8,65,000 |
2 | 1,35,000 | -7,30,000 |
3 | 1,35,000 | -5,95,000 |
4 | 1,35,000 | -4,60,000 |
5 | 1,35,000 | -3,25,000 |
6 | 1,35,000 | -1,90,000 |
7 | 1,35,000 | -55,000 |
8 | 1,35,000 | 80,000 |
PBP lies between years 7 and 8.
PBP = 7 + (Absolute value of cumulative cash flow, year 7 / Discounted cash flow, year 8)
= 7 + (55,000 / 135,000)
= 7.41 years
(2) Discounted payback period (DPBP) is the time by when cumulative discounted cash flows becomes zero.
Year | Cash flow ($) | PV Factor @20% | Discounted Cash Flow ($) | Cumulative Discounted Cash Flow ($) |
0 | -10,00,000 | 1.0000 | -10,00,000 | -10,00,000 |
1 | 1,35,000 | 0.8333 | 1,12,500 | -8,87,500 |
2 | 1,35,000 | 0.6944 | 93,750 | -7,93,750 |
3 | 1,35,000 | 0.5787 | 78,125 | -7,15,625 |
4 | 1,35,000 | 0.4823 | 65,104 | -6,50,521 |
5 | 1,35,000 | 0.4019 | 54,253 | -5,96,267 |
6 | 1,35,000 | 0.3349 | 45,211 | -5,51,056 |
7 | 1,35,000 | 0.2791 | 37,676 | -5,13,380 |
8 | 1,35,000 | 0.2326 | 31,397 | -4,81,983 |
9 | 1,35,000 | 0.1938 | 26,164 | -4,55,820 |
10 | 1,35,000 | 0.1615 | 21,803 | -4,34,016 |
11 | 1,35,000 | 0.1346 | 18,169 | -4,15,847 |
12 | 1,35,000 | 0.1122 | 15,141 | -4,00,706 |
13 | 1,35,000 | 0.0935 | 12,618 | -3,88,088 |
14 | 1,35,000 | 0.0779 | 10,515 | -3,77,573 |
15 | 1,35,000 | 0.0649 | 8,762 | -3,68,811 |
16 | 1,35,000 | 0.0541 | 7,302 | -3,61,509 |
17 | 1,35,000 | 0.0451 | 6,085 | -3,55,424 |
18 | 1,35,000 | 0.0376 | 5,071 | -3,50,354 |
19 | 1,35,000 | 0.0313 | 4,226 | -3,46,128 |
20 | 1,35,000 | 0.0261 | 3,521 | -3,42,607 |
21 | 1,35,000 | 0.0217 | 2,934 | -3,39,672 |
22 | 1,35,000 | 0.0181 | 2,445 | -3,37,227 |
23 | 1,35,000 | 0.0151 | 2,038 | -3,35,189 |
24 | 1,35,000 | 0.0126 | 1,698 | -3,33,491 |
25 | 1,35,000 | 0.0105 | 1,415 | -3,32,076 |
26 | 1,35,000 | 0.0087 | 1,179 | -3,30,896 |
27 | 1,35,000 | 0.0073 | 983 | -3,29,914 |
28 | 1,35,000 | 0.0061 | 819 | -3,29,095 |
29 | 1,35,000 | 0.0051 | 682 | -3,28,412 |
30 | 1,35,000 | 0.0042 | 569 | -3,27,844 |
31 | 1,35,000 | 0.0035 | 474 | -3,27,370 |
32 | 1,35,000 | 0.0029 | 395 | -3,26,975 |
33 | 1,35,000 | 0.0024 | 329 | -3,26,646 |
34 | 1,35,000 | 0.0020 | 274 | -3,26,371 |
35 | 1,35,000 | 0.0017 | 229 | -3,26,143 |
36 | 1,35,000 | 0.0014 | 190 | -3,25,952 |
37 | 1,35,000 | 0.0012 | 159 | -3,25,794 |
38 | 1,35,000 | 0.0010 | 132 | -3,25,661 |
39 | 1,35,000 | 0.0008 | 110 | -3,25,551 |
40 | 1,35,000 | 0.0007 | 92 | -3,25,459 |
41 | 1,35,000 | 0.0006 | 77 | -3,25,383 |
42 | 1,35,000 | 0.0005 | 64 | -3,25,319 |
43 | 1,35,000 | 0.0004 | 53 | -3,25,266 |
44 | 1,35,000 | 0.0003 | 44 | -3,25,221 |
45 | 1,35,000 | 0.0003 | 37 | -3,25,185 |
46 | 1,35,000 | 0.0002 | 31 | -3,25,154 |
47 | 1,35,000 | 0.0002 | 26 | -3,25,128 |
48 | 1,35,000 | 0.0002 | 21 | -3,25,107 |
49 | 1,35,000 | 0.0001 | 18 | -3,25,089 |
50 | 1,35,000 | 0.0001 | 15 | -3,25,074 |
As is seen, even after 50 years, cumulative discounted cash flows cannot be even nearer to zero (since at the high discount rate of 20%, the discount factor becomes very small). So DPBP can be taken as an infinite period and cannot be calculated precisely.
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