Question 3.16: The investment data of Prudent Company, launching a new prod......

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
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\,  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
(Contd.)
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
(Contd.)
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

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