# Question 3.15: Proposal X requires an initial capital outlay of Rs 2,00,000......

Proposal X requires an initial capital outlay of Rs 2,00,000, with no salvage value, and will be depreciated on a straight line basis for tax purposes. The earnings before depreciation and taxes (EBDT) during its 5 year life are:
The corporate tax rate is 35 per cent and the company evaluates its capital budgeting projects at 12 per cent cost of capital. Advise the company whether the project should be accepted.
(i) when there is no inflation and (ii) when there is inflation at the rate of 15 per cent per annum, and its stated gross earnings are also expected to grow at this rate of inflation.

 5 4 3 2 1 $Year$ Rs 52,000 Rs 60,000 Rs 80,000 Rs 76,000 Rs 70,000 EBDT
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$\,$  Since the net present value is positive, the project is worth accepting in a non-inflationary scenario.
$\,$  In the inflationary situation, EBDT are expected to grow at 15 per cent. As per Table A-1 (showing compound sum of one rupee), EBDT values can be determined (reflecting 15 per cent compound rate of growth). Depreciation amount remains unchanged. As a result, taxable profits as well as taxes go up.
Detailed computations are shown in Table 3.4.
$\,$  Since CFAT are inflated sums, they are to be deflated at the rate of inflation (15 per cent) to determine real cash flows. Table 3.5 contains relevant calculations in this regard.
$\,$  It may be observed that real cash flows are substantially lower than nominal cash flows. This is caused on account of the fact that increased income (as depreciation charges do not change) is subject to higher amount of taxes; corporate tax rate is more than twice (35 per cent) the inflation rate (15 per cent). The NPV of real cash inflows is shown in Table 3.6.
$\,$  Since the NPV is negative under inflationary situations, the investment proposal is not acceptable. Similar conclusions follow based on the internal rate of return method. The IRR based on real CFAT is 11 per cent—lower than the cost of capital (12 per cent).
$\,$  It is apparent, therefore, that inflation results both in lower cash flows and lower real rates of return. Example 3.15 is important in that it highlights that corporate firms (conscious of protecting the real purchasing power of their owners) may go for unprofitable investment projects, affecting the shareholders wealth adversely. In brief, the example underlines the significance of incorporating the inflation factor in evaluating capital budgeting decisions, in particular for business firms interested in real returns.
$\,$  Consistency warrants that the real cost of capital should be used to discount real cash inflows after taxes and the nominal cost of capital should be employed for nominal CFAT. This point is illustrated in Example 3.16.

Determination of NPV (when there is no Inflation)
$\,$                                                                                                      $(Amount\>is \>in\> thousand\> rupees)$

 $Total\>PV$ $(Col.\>6 × 7)$ $\,$ $PV$ $factor$ $\,$ $CFAT$ $(Col.\>5 + 3)$ $\,$ $EAT$ $(Col. 4\>× 0.65)$ $\,$ $Taxable$ $income$ $(Col.\>3– 2)$ $Depreciation$ $(200 ÷ 5)$ $\,$ $EBDT$ $\,$ $\,$ $Year$ $\,$ $\,$ 8 7 6 5 4 3 2 1 53.13 0.893 59.5 19.5 30 40 70 1 50.53 0.797 63.4 23.4 36 40 76 2 46.99 0.712 66.0 26.0 40 40 80 3 33.71 0.636 53.0 13.0 20 40 60 4 27.10 0.567 47.8 7.8 12 40 52 5 211.46 Gross present value 200.00 Less cash outflows 11.46 Net present value

Table 3.4 Determination of CFAT in Inflationary Situation

$\,$                                                                                                      $(Amount\>is \>in\> thousand\> rupees)$

 $CFAT$ $(Col.\>7 + 5)$ $\,$ $EAT$ $(Col.\>6 × 0.65)$ $\,$ $Taxable$ $income$ $(Col.\>4 – 5)$ $Depreciation$ $\,$ $\,$ $Revised$ $EBDT$ $(Col.\>2 × 3)$ $Compound$ $Factor$ $at\>0.15$ $EBDT$ $\,$ $\,$ $Year$ $\,$ $\,$ 8 7 6 5 4 3 2 1 66.32 26.32 40.50 40 80.50 1.150 70 1 79.31 39.31 60.47 40 100.47 1.322 76 2 93.09 53.09 81.68 40 121.68 1.521 80 3 82.21 42.21 64.94 40 104.94 1.749 60 4 81.97 41.97 64.57 40 104.57 2.011 52 5

Table 3.5 Determination of Real Cash Flows

$\,$                                                                                                      $(Amount\>is \>in\> thousand\> rupees)$

 $Real\>cash\>inflows$ $(CFAT)\>(Col.\>2 × 3)$ $Discount/\>Deflated\>factor\>at$ $0.15\>as\>per\>Table\>A – 3$ $CFAT$ $\,$ $Year$ $\,$ 4 3 2 1 57.70 1/1.15 = 0.870 66.32 1 59.96 1/ (1.15)² = 0.756 79.31 2 61.25 1/(1.15)³ = 0.658 93.09 3 47.02 1/(1.15)$^4$ = 0.572 82.21 4 40.74 1/(1.15)$^5$ = 0.497 81.97 5

Table 3.6   NPV of Real CFAT

 $Total\>PV\>(Col.\>3 x 4)$ $PV\>factor\>at\>12\%$ $Real\>CFAT$ $Year$ 4 3 2 1 51.53 0.893 57.70 1 47.79 0.797 59.96 2 43.61 0.713 61.25 3 29.90 0.636 47.02 4 23.10 0.567 40.74 5 195.93 Gross present value 200.00 Less cash outflows (4.07) Net present value

Table A-1   The Compound Sum of One Rupee

 $10\%$ $9\%$ $8\%$ $7\%$ $6\%$ $5\%$ $4\%$ $3\%$ $2\%$ $1\%$ $Year$ 1.100 1.090 1.080 1.070 1.060 1.050 1.040 1.030 1.020 1.010 1 1.210 1.188 1.166 1.145 1.124 1.102 1.082 1.061 1.040 1.020 2 1.331 1.295 1.260 1.225 1.191 1.158 1.125 1.093 1.061 1.030 3 1.464 1.412 1.360 1.311 1.262 1.216 1.170 1.126 1.082 1.041 4 1.611 1.539 1.469 1.403 1.338 1.276 1.217 1.159 1.104 1.051 5 1.772 1.677 1.587 1.501 1.419 1.340 1.265 1.194 1.126 1.062 6 1.949 1.828 1.714 1.606 1.504 1.407 1.316 1.230 1.149 1.072 7 2.144 1.993 1.851 1.718 1.594 1.477 1.369 1.267 1.172 1.083 8 2.358 2.172 1.999 1.838 1.689 1.551 1.423 1.305 1.195 1.094 9 2.594 2.367 2.159 1.967 1.791 1.629 1.480 1.344 1.219 1.105 10 2.853 2.580 2.332 2.105 1.898 1.710 1.539 1.384 1.243 1.116 11 3.138 2.813 2.518 2.252 2.012 1.796 1.601 1.426 1.268 1.127 12 3.452 3.066 2.720 2.410 2.133 1.886 1.665 1.469 1.294 1.138 13 3.797 3.342 2.937 2.579 2.261 1.980 1.732 1.513 1.319 1.149 14 4.177 3.642 3.172 2.759 2.397 2.079 1.801 1.558 1.346 1.161 15 4.595 3.970 3.426 2.952 2.540 2.183 1.873 1.605 1.373 1.173 16 5.054 4.328 3.700 3.159 2.693 2.292 1.948 1.653 1.400 1.184 17 5.560 4.717 3.996 3.380 2.854 2.407 2.026 1.702 1.428 1.196 18 6.116 5.142 4.316 3.616 3.026 2.527 2.107 1.753 1.457 1.208 19 6.727 5.604 4.661 3.870 3.207 2.653 2.191 1.806 1.486 1.220 20 7.400 6.109 5.034 4.140 3.399 2.786 2.279 1.860 1.516 1.232 21 8.140 6.658 5.436 4.430 3.603 2.925 2.370 1.916 1.546 1.245 22 8.954 7.258 5.871 4.740 3.820 3.071 2.465 1.974 1.577 1.257 23 9.850 7.911 6.341 5.072 4.049 3.225 2.563 2.033 1.608 1.270 24 10.834 8.623 6.848 5.427 4.292 3.386 2.666 2.094 1.641 1.282 25 17.449 13.267 10.062 7.612 5.743 4.322 3.243 2.427 1.811 1.348 30 28.102 20.413 14.785 10.676 7.686 5.516 3.946 2.814 2.000 1.417 35 45.258 31.408 21.724 14.974 10.285 7.040 4.801 3.262 2.208 1.489 40 72.888 48.325 31.920 21.002 13.764 8.985 5.841 3.781 2.438 1.565 45 117.386 74.354 46.900 29.456 18.419 11.467 7.106 4.384 2.691 1.645 50
$(Contd.)$
 $20\%$ $19\%$ $18\%$ $17\%$ $16\%$ $15\%$ $14\%$ $13\%$ $12\%$ $11\%$ $Year$ 1.200 1.190 1.180 1.170 1.160 1.150 1.140 1.130 1.120 1.110 1 1.440 1.416 1.392 1.369 1.346 1.322 1.300 1.277 1.254 1.232 2 1.728 1.685 1.643 1.602 1.561 1.521 1.482 1.443 1.405 1.368 3 2.074 2.005 1.939 1.874 1.811 1.749 1.689 1.630 1.574 1.518 4 2.488 2.386 2.288 2.192 2.100 2.011 1.925 1.842 1.762 1.685 5 2.986 2.840 2.700 2.565 2.436 2.313 2.195 2.082 1.974 1.870 6 3.385 3.379 3.185 3.001 2.826 2.660 2.502 2.353 2.211 2.076 7 4.300 4.021 3.759 3.511 3.278 3.059 2.853 2.658 2.476 2.305 8 5.160 4.785 4.435 4.108 3.803 3.518 3.252 3.004 2.773 2.558 9 6.192 5.695 5.234 4.807 4.411 4.046 3.707 3.395 3.106 2.839 10 7.430 6.777 6.176 5.624 5.117 4.652 4.226 3.836 3.479 3.152 11 8.916 8.064 7.288 6.580 5.936 5.350 4.818 4.334 3.896 3.498 12 10.699 9.596 8.599 7.699 6.886 6.153 5.492 4.898 4.363 3.883 13 12.839 11.420 10.147 9.007 7.987 7.076 6.261 5.535 4.887 4.310 14 15.407 13.589 11.974 10.539 9.265 8.137 7.138 6.254 5.474 4.785 15 18.488 16.171 14.129 12.330 10.748 9.358 8.137 7.067 6.130 5.311 16 22.186 19.244 16.672 14.426 12.468 10.761 9.276 7.986 6.866 5.895 17 26.623 22.900 19.673 16.879 14.462 12.375 10.575 9.024 7.690 6.543 18 31.948 27.251 23.214 19.748 16.776 14.232 12.055 10.197 8.613 7.263 19 38.337 32.429 27.393 23.105 19.461 16.366 13.743 11.523 9.646 8.062 20 237.373 38.591 32.323 27.033 22.574 18.821 15.667 13.021 10.804 8.949 21 55.205 45.923 38.141 31.629 26.186 21.644 17.861 14.713 12.100 9.933 22 66.247 54.648 45.007 37.005 30.376 24.891 20.361 16.626 12.552 11.026 23 79.496 65.031 53.108 43.296 35.236 28.625 23.212 18.788 15.178 12.239 24 95.395 77.387 62.667 50.656 40.874 32.918 26.461 21.230 17.000 13.585 25 237.373 184.672 143.367 111.061 85.849 66.210 50.949 39.115 29.960 22.892 30 590.657 440.691 327.988 243.495 180.311 133.172 98.097 72.066 52.799 38.574 35 1469.740 1051.642 750.353 533.846 378.715 267.856 188.876 132.776 93.049 64.999 40 3657.176 2509.583 1716.619 1170.425 795.429 538.752 363.662 244.629 163.985 109.527 45 9100.191 5988.730 3927.189 2566.080 1670.669 1083.619 700.197 450.711 288.996 184.559 50

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