The investment data of Prudent Company, launching a new product and having the cost of capital as 12 per cent, is as follows:
\, Assuming an inflation rate of 5 per cent, determine NPV of the project by using both the nominal rate of discount and the real rate of discount.
Amount | Particulars |
Rs 7,00,000 | Investment |
5,00,000 | CFAT: Year 1 |
4,00,000 | 2 |
2,00,000 | 3 |
1,00,000 | 4 |
1,00,000 | 5 |
\, The nominal rate of discount (n) is obtained by compounding the real rate (r) and inflation rate (i).^5
In equations terms, it is
\, (1 + n) = (1 + r) (1 + i) (3.8)
or (1 + r) = (1 + n)/ (1 + i). (3.8.1)
Accordingly, the value of r is 6.67 per cent as shown below:
\, (1 + r) = 1.12/1.05 = 1.0667
or r = 0.0667 or 6.67 per cent.
\, Since the discount rate now to be used is the real discount rate, the CFAT should also be adjusted for inflation so that they too are expressed in real terms. In operational terms, CFAT will be deflated by inflation rate, ie, 5 per cent. While Table 3.7 shows real/ deflated CFAT, NPV of real CFAT is provided in Table 3.8.
\, It is important to note that ‘real’ cash flows discounted at the ‘real’ discount rate yield the identical amount of NPV that is obtained by discounting ‘nominal’ cash flows by the ‘nominal’ discount rate. When estimates of CFAT and cost of capital include inflation, they are said to be expressed in nominal terms; in contrast, when such estimates exclude the impact of inflation, they are said to be shown in real terms.
Apparently, for correct analysis, these estimates should either be stated in nominal or real terms. In operational terms, it implies that capital budgeting decisions should either reckon the inflation factor in CFAT, as well as the cost of capital, or exclude it completely.
NPV using Nominal Rate of Discount
Total\>PV | PV\>factor\>at\>0.12 | CFAT | Year |
Rs 4,46,500 | 0.893 | Rs 5,00,000 | 1 |
3,18,800 | 0.797 | 4,00,000 | 2 |
1,42,400 | 0.712 | 2,00,000 | 3 |
63,600 | 0.636 | 1,00,000 | 4 |
56,700
|
0.567 | 1,00,000 | 5 |
10,28,000 | Total present value | ||
7,00,000
|
Less cash outflows | ||
3,28,000 | Net present value |
Table 3.7 Real Cash Flows
Real\>CFAT | Deflation\>factor\>at\>0.05 | CFAT | Year |
Rs 4,76,000 | 1/(1.05) = 0.952 | Rs 5,00,000 | 1 |
3,62,800 | 1/(1.05)2 = 0.907 | 4,00,000 | 2 |
1,72,800 | 1/(1.05)3 = 0.864 | 2,00,000 | 3 |
82,300 | 1/(1.05)4 = 0.823 | 1,00,000 | 4 |
78,400 | 1/(1.05)5 = 0.784 | 1,00,000 | 5 |
Table 3.8 NPV Using Real Rate of Discount
Total\>PV | PV\>factor\>at\>6.67\%^a | Real\>CFAT | Year |
Rs 4,46,488 | 0.938 | Rs 4,76,000 | 1 |
3,18,901 | 0.879 | 3,62,800 | 2 |
1,42,387 | 0.824 | 1,72,800 | 3 |
63,536 | 0.772 | 82,300 | 4 |
56,761
|
0.724 | 78,400 | 5 |
10,28,073 | Total present value | ||
7,00,000
|
Less cash outflows | ||
3,28,073^b | Net present value |
a. Based on interpolation as per Table A – 3.
b. Difference in NPV of Rs 73 (Rs 3,28,073 – Rs 3,28,000) between the two discount rates (nominal and real) is on account of rounding off the values. Both the approaches provide the same answer.
Table A-3 The Present Value of One Rupee
10\% | 9\% | 8\% | 7\% | 6\% | 5\% | 4\% | 3\% | 2\% | 1\% | Year |
.909 | .917 | .926 | .935 | .943 | .952 | .962 | .971 | .980 | 0.990 | 1 |
.826 | .842 | .857 | .873 | .890 | .907 | .925 | .943 | .961 | 0.980 | 2 |
.751 | .772 | .794 | .816 | .840 | .864 | .889 | .915 | .942 | .971 | 3 |
.683 | .708 | .735 | .763 | .792 | .823 | .855 | .888 | .924 | .961 | 4 |
.621 | .650 | .681 | .713 | .747 | .784 | .822 | .863 | .906 | .951 | 5 |
.564 | .596 | .630 | .666 | .705 | .764 | .790 | .837 | .888 | .942 | 6 |
.513 | .547 | .583 | .623 | .665 | .711 | .760 | .813 | .871 | .933 | 7 |
.467 | .502 | .540 | .582 | .627 | .677 | .731 | .789 | .853 | .923 | 8 |
.424 | .460 | .500 | .544 | .592 | .645 | .703 | .766 | .837 | .914 | 9 |
.386 | .422 | .463 | .508 | .558 | .614 | .676 | .744 | .820 | .905 | 10 |
.350 | .388 | .429 | .475 | .527 | .585 | .650 | .722 | .804 | .896 | 11 |
.319 | .356 | .397 | .444 | .497 | .575 | .625 | .701 | .789 | .887 | 12 |
.290 | .326 | .368 | .415 | .469 | .530 | .601 | .681 | .773 | .879 | 13 |
.263 | .299 | .340 | .388 | .442 | .505 | .577 | .661 | .758 | .870 | 14 |
.239 | .275 | .315 | .362 | .417 | .481 | .555 | .642 | .743 | .861 | 15 |
.218 | .252 | .292 | .339 | .394 | .458 | .534 | .623 | .728 | .853 | 16 |
.198 | .231 | .270 | .317 | .371 | .436 | .513 | .605 | .714 | .844 | 17 |
.180 | .212 | .250 | .296 | .350 | .416 | .494 | .587 | .700 | .836 | 18 |
.164 | .194 | .232 | .227 | .331 | .396 | .475 | .570 | .686 | .828 | 19 |
.149 | .178 | .215 | .258 | .312 | .377 | .456 | .554 | .673 | .820 | 20 |
.135 | .164 | .199 | .242 | .294 | .359 | .439 | .538 | .660 | .811 | 12 |
.123 | .150 | .184 | .226 | .278 | .342 | .422 | .522 | .647 | .803 | 22 |
.112 | .138 | .170 | .211 | .262 | .326 | .406 | .507 | .634 | .795 | 23 |
.102 | .126 | .158 | .197 | .247 | .310 | .390 | .492 | .622 | .788 | 24 |
.092 | .116 | .146 | .184 | .233 | .295 | .375 | .478 | .610 | .780 | 25 |
.057 | .075 | .099 | .131 | 174 | .231 | .308 | .412 | .552 | .742 | 30 |
.036 | .049 | .068 | .094 | .130 | .181 | .253 | .355 | .500 | .706 | 35 |
.022 | .032 | .046 | .067 | .097 | .142 | .208 | .307 | .453 | .672 | 40 |
.014 | .021 | .031 | .048 | .073 | .111 | .171 | .264 | .410 | .639 | 45 |
.009 | .013 | .021 | .034 | .054 | .087 | .141 | .228 | .372 | .608 | 50 |
20\% | 19\% | 18\% | 17\% | 16\% | 15\% | 14\% | 13\% | 12\% | 11\% | Year |
.833 | .840 | .847 | .855 | .862 | .870 | .877 | .885 | .893 | .901 | 1 |
.694 | .706 | .718 | .731 | .743 | .756 | .769 | .783 | .797 | .812 | 2 |
.579 | .593 | .609 | .624 | .641 | .658 | .675 | .693 | .712 | .731 | 3 |
.482 | .499 | .516 | .534 | .552 | .572 | .592 | .613 | .636 | .659 | 4 |
.402 | .419 | .437 | .456 | .476 | .497 | .519 | .543 | .567 | .593 | 5 |
.335 | .352 | .370 | .390 | .410 | .432 | .456 | .480 | .507 | .535 | 6 |
.279 | .296 | .314 | .333 | .354 | .376 | .400 | .425 | .452 | .482 | 7 |
.233 | .249 | .266 | .285 | .305 | .327 | .351 | .376 | .404 | .434 | 8 |
.194 | .209 | .225 | .243 | .263 | .284 | .308 | .333 | .361 | .391 | 9 |
.162 | .176 | .191 | .208 | .227 | .274 | .270 | .295 | .322 | .352 | 10 |
.135 | .184 | .162 | .178 | .195 | .215 | .237 | .261 | .287 | .317 | 11 |
.112 | .124 | .137 | .152 | .168 | .187 | .208 | .231 | .257 | .286 | 12 |
.093 | .104 | .116 | .130 | .145 | .163 | .182 | .204 | .229 | .258 | 13 |
.078 | .088 | .099 | .111 | .125 | .141 | .160 | .181 | .205 | .232 | 14 |
.065 | .074 | .084 | .095 | .108 | .123 | .140 | .160 | .183 | .209 | 15 |
.054 | .062 | .071 | .081 | .093 | .107 | .123 | .141 | .163 | .188 | 16 |
.045 | .052 | .060 | .069 | .080 | .093 | .108 | .125 | .146 | .170 | 17 |
.038 | .044 | .051 | .059 | .069 | .081 | .095 | .111 | .130 | .153 | 18 |
.031 | .037 | .043 | .051 | .060 | .070 | .083 | .098 | .116 | .138 | 19 |
.026 | .031 | .037 | .043 | .051 | .061 | .073 | .087 | .104 | .124 | 20 |
.022 | .026 | .031 | .037 | .044 | .053 | .064 | .077 | .093 | .112 | 21 |
.018 | .022 | .026 | .032 | .038 | .046 | .056 | .068 | .083 | .101 | 22 |
.015 | .018 | .022 | .027 | .033 | .040 | .049 | .060 | .074 | .091 | 23 |
.013 | .015 | .019 | .023 | .028 | .035 | .043 | .053 | .066 | .082 | 24 |
.010 | .013 | .016 | .020 | .024 | .030 | .038 | .047 | .059 | .074 | 25 |
.004 | .005 | .007 | .009 | .012 | .015 | .020 | .026 | .033 | .044 | 30 |
.002 | .002 | .003 | .004 | .006 | .008 | .010 | .014 | .019 | .026 | 35 |
.001 | .001 | .001 | .002 | .003 | .004 | .005 | .008 | .011 | .015 | 40 |
.000 | .000 | .001 | .001 | .001 | .002 | .003 | .004 | .006 | .009 | 45 |
.000 | .000 | .000 | .001 | .001 | .001 | .001 | .002 | .003 | .005 | 50 |
30\% | 29\% | 28\% | 27\% | 26\% | 25\% | 24\% | 23\% | 22\% | 21\% | Year |
.769 | .775 | .781 | .787 | .794 | .800 | .806 | .813 | .820 | .826 | 1 |
.592 | .601 | .610 | .620 | .630 | .640 | .650 | .661 | .672 | .683 | 2 |
.455 | .466 | .477 | .488 | .500 | .512 | .524 | .537 | .551 | .564 | 3 |
.350 | .361 | .373 | .384 | .397 | .410 | .423 | .437 | .451 | .467 | 4 |
.269 | .280 | .291 | .303 | .315 | .328 | .341 | .355 | .370 | .386 | 5 |
.207 | .217 | .227 | .238 | .250 | .262 | .275 | .289 | .303 | .319 | 6 |
.159 | .168 | .178 | .188 | .198 | .210 | .222 | .235 | .249 | .263 | 7 |
.123 | .130 | .139 | .148 | .157 | .168 | .179 | .191 | .204 | .218 | 8 |
.094 | .101 | .108 | .116 | .125 | .134 | .144 | .155 | .167 | .180 | 9 |
.073 | .078 | .085 | .092 | .099 | .107 | .116 | .126 | .137 | .149 | 10 |
.056 | .061 | .066 | .072 | .079 | .086 | .094 | .103 | .112 | .123 | 11 |
.043 | .047 | .052 | .057 | .062 | .069 | .076 | .083 | .092 | .102 | 12 |
.033 | .037 | .040 | .045 | .050 | .055 | .061 | .068 | .075 | .084 | 13 |
.025 | .028 | .032 | .035 | .039 | .044 | .049 | .055 | .062 | .069 | 14 |
.020 | .022 | .025 | .028 | .031 | .035 | .040 | .045 | .051 | .057 | 15 |
.015 | .017 | .019 | .022 | .025 | .028 | .032 | .036 | .042 | .047 | 16 |
.012 | .013 | .015 | .017 | .020 | .023 | .026 | .030 | .034 | .039 | 17 |
.009 | .010 | .012 | .014 | .016 | .018 | .021 | .024 | .028 | .032 | 18 |
.007 | .008 | .009 | .011 | .012 | .014 | .017 | .020 | .023 | .027 | 19 |
.005 | .006 | .007 | .008 | .010 | .012 | .014 | .016 | .019 | .022 | 20 |
.004 | .005 | .006 | .007 | .008 | .009 | .011 | .013 | .015 | .018 | 21 |
.003 | .004 | .004 | .005 | .006 | .007 | .009 | .011 | .013 | .015 | 22 |
.002 | .003 | .003 | .004 | .005 | .006 | .007 | .009 | .010 | .012 | 23 |
.002 | .002 | .003 | .003 | .004 | .005 | .006 | .007 | .008 | .010 | 24 |
.001 | .002 | .002 | .003 | .003 | .004 | .005 | .006 | .007 | .009 | 25 |
.000 | .000 | .001 | .001 | .001 | .001 | .002 | .002 | .003 | .003 | 30 |
.000 | .000 | .000 | .000 | .000 | .000 | .001 | .001 | .001 | .001 | 35 |
.000 | .000 | .000 | .000 | .000 | .000 | .000 | .000 | .000 | .000 | 40 |
.000 | .000 | .000 | .000 | .000 | .000 | .000 | .000 | .000 | .000 | 45 |
.000 | .000 | .000 | .000 | .000 | .000 | .000 | .000 | .000 | .000 | 50 |