# Question 3.RQ.35: Royal Industries is considering to buy a moulding machine. T......

Royal Industries is considering to buy a moulding machine. The machine (having capital cost of Rs 20 lakh) is expected to have 4 years economic useful life with no salvage value; the company follows the straight line method of depreciation and the same is accepted for tax purposes. The expected CFAT (with corporate tax rate of 35 per cent) during its 4 years economic useful life are as follows:
$\,$  Inflation is expected to be 8 per cent per year and the machine’s cost of capital in real terms would be 10 per cent. Compute the NPV of purchasing this machine.

 4 3 2 $Year$ 1 Rs 4 lakh Rs 7 lakh Rs 10 lakh CFAT Rs 8 lakh
Step-by-Step
The 'Blue Check Mark' means that this solution was answered by an expert.

Since the cost of capital is stated in real terms, nominal CFAT need to be converted into real terms by deflating at inflation rate of 8 per cent. Relevant computations related to NPV are shown in Table.

Alternatively, nominal CFAT provided in the question can be discounted by nominal cost of capital (n).
We know            (1 + $n$) = (1 + $r$) (1 + $i$)
$\,$                                    $n = r + i + ri$
$\,$                                       = 0.10 + 0.08 + .008 = 0.188
$\,$                                       = 18.8 %

$\,$ (a) Based on interpolation as per Table A-3.
$\,$ (b) Difference in net present value computed by two methods (Rs 50,800
$\,$       and Rs 49,677) is due to approximation.
$\,$  In effect, both the methods yield identical results, both in terms of acceptance/rejection decision and in terms of net present value.

$Determination\> of\> NVP\> in\> real \>terms$
 $Total\>PV$ $PV\>factor\>at\>0.10$ $Real\>CFAT$ $Deflated\>factor\>at$ 0.08ª $CFAT$ $Year$ Rs 6,73,387 0.909 Rs 7,40,800 0.926 Rs 8,00,000 1 7,07,882 0.826 8,57,000 0.857 10,00,000 2 4,17,406 0.751 5,55,800 0.794 7,00,000 3 2,51,002 0.683 3,67,500 0.735 5,00,000 4 20,49,677 Total present value 20,00,000 Less cash outflows 49,677 Net present value

ªAs per Table A-3.

 $Total\>PV$ $PV\>factor\>at\>18.8\%^a$ $Nominal\>CFAT$ $Year$ Rs 6,73,600 0.842 Rs 8,00,000 1 7,09,000 0.709 10,00,000 2 4,17,200 0.596 7,00,000 3 2,51,000 0.502 5,00,000 4 20,50,800 Total present value 20,00,000 Less cash outflows 50,800$^\mathrm{b}$ 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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