# Question 3.RQ.34: Strong Company wants to launch a new product, suggested by i......

Strong Company wants to launch a new product, suggested by its marketing department. For this purpose a new machine is to be purchased. The relevant data processed in this regard is as follows:
$\,$  The company uses 13 per cent as required cost of capital (nominal) to evaluate new projects. The rate of inflation during the period is expected to be 6 per cent. Determine NPV of the machine using both the nominal as well as real rate of discount, and comment on the results.

 Rs 20,00,000 Cost of new machine 6,00,000 CFAT: year 1 7,00,000 2 8,00,000 3 5,00,000 4 4,00,000 5
Step-by-Step
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Determination of real discount rate
$\,$        $r$  = (1 + $n$  )/ (1 + $i$  ) – 1
$\,$           = (1.13/1.06) – 1 = 1.066 – 1= 0.066 or 6.6%

$\,$  Both the methods give identical results. The project is acceptable as NPV is positive. (The minor difference in the NPV under the two methods is on account of rounding off the values).

$NPV \>using\> nominal\> rate \>of \>discount$
 $Total\>PV$ $PV\>factor\>at\>0.13$ $CFAT$ $Year$ Rs 5,31,000 0.885 6,00,000 1 5,48,100 0.783 7,00,000 2 5,54,400 0.693 8,00,000 3 3,06,500 0.613 5,00,000 4 2,17,200 0.543 4,00,000 5 21,57,200 Total present value 20,00,000 Less cost of new machine 1,57,200 Net present value
$NPV\> using \>real \>rate \>of \>discount$
 $Total\>PV$ $\,$ $PV\>factor\>at\>6.6\%$ $\,$ $Real\>CFAT$ $\,$ $Deflated\>factor\>at$ $0.06\>as\>per\>Table\>A-3$ $CFAT$ $\,$ $Year$ $\,$ Rs 5,30,720 0.938 Rs 5,65,800 0.943 6,00,000 1 5,48,240 0.880 6,23,000 0.890 7,00,000 2 5,54,400 0.825 6,72,000 0.840 8,00,000 3 3,06,504 0.774 3,96,000 0.792 5,00,000 4 2,17,228 0.727 2,98,800 0.747 4,00,000 5 21,57,092 Total present value 20,00,000 Less cost of new machine 1,57,092 Net present value

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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