Question

A company is planning to invest $70,000 (before tax) in a personnel training program. The $70,000 outlay will be charged off as an expense by the firm this year (year 0). The returns from the program in the form of greater productivity and a reduction in employee turnover are estimated as follows (on an after-tax basis): Years 1–10: $14,000 per year Years 11–20: $21,000 per year The company has estimated its cost of capital to be 12 percent. Assume that the entire $70,000 is paid at time 0 (the beginning of the project). The marginal tax rate for the firm is 40 percent. Compute the project's net present value. Use Table II and Table IV to answer the question. Round your answer to the nearest dollar.

TABLE II Present Value Interest Factor (PVIF) ($1 at i % per period for n periods); PVIF PV = FV, (PVIF,.) (1 + i)" Period n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 24 25 30 40 50 60 1% 1.000 0.990 0.980 0.971 0.961 0.951 0.942 0.933 0.923 0.914 0.905 0.896 0.887 0.879 0.870 0.861 0.853 0.844 0.836 0.828 0.820 0.788 0.780 0.742 0.672 0.608 0.550 7% 1.000 0.935 0.873 0.816 0.763 0.713 0.666 0.623 0.582 0.544 0.508 0.475 0.444 0.415 0.388 0.362 0.339 0.317 0.296 0.276 0.258 0.197 0.184 0.131 0.067 0.034 0.017 9% 1.000 0.917 0.842 0.772 0.708 0.650 0.596 0.547 0.502 0.460 0.422 0.388 0.356 0.326 0.299 0.275 0.252 0.231 0.212 0.194 0.178 0.126 0.116 0.075 0.032 0.013 0.006 13% 1.000 0.885 0.783 0.693 0.613 0.543 0.480 0.425 0.376 0.333 0.295 0.261 0.231 0.204 0.181 0.160 0.141 0.125 0.111 0.098 0.087 0.053 0.047 0.026 0.008 0.002 0.001 2% 3% 4% 5% 6% 1.000 1.000 1.000 1.000 1.000 0.980 0.971 0.962 0.952 0.943 0.961 0.943 0.925 0.907 0.890 0.942 0.915 0.889 0.864 0.840 0.924 0.889 0.855 0.823 0.792 0.906 0.863 0.822 0.784 0.747 0.888 0.838 0.790 0.746 0.705 0.871 0.813 0.760 0.711 0.665 0.853 0.789 0.731 0.677 0.627 0.837 0.766 0.703 0.645 0.592 0.820 0.744 0.676 0.614 0.558 0.804 0.722 0.650 0.585 0.527 0.788 0.701 0.625 0.557 0.497 0.773 0.681 0.601 0.530 0.469 0.758 0.661 0.577 0.505 0.442 0.743 0.642 0.555 0.481 0.417 0.728 0.623 0.534 0.458 0.394 0.714 0.605 0.513 0.436 0.371 0.700 0.587 0.494 0.416 0.350 0.686 0.570 0.475 0.396 0.331 0.673 0.554 0.456 0.377 0.312 0.622 0.492 0.390 0.310 0.247 0.610 0.478 0.375 0.295 0.233 0.552 0.412 0.308 0.231 0.174 0.453 0.307 0.208 0.142 0.097 0.372 0.228 0.141 0.087 0.054 0.305 0.170 0.095 0.054 0.030 15% 16% 17% 18% 1.000 1.000 1.000 1.000 0.870 0.862 0.855 0.847 0.756 0.743 0.731 0.718 0.658 0.641 0.624 0.609 0.572 0.552 0.534 0.516 0.497 0.476 0.456 0.437 0.432 0.410 0.390 0.370 0.376 0.354 0.333 0.314 0.327 0.305 0.285 0.266 0.284 0.263 0.243 0.225 0.247 0.227 0.208 0.191 0.215 0.195 0.178 0.162 0.187 0.168 0.152 0.137 0.163 0.145 0.130 0.116 0.141 0.125 0.111 0.099 0.123 0.108 0.095 0.084 0.107 0.093 0.081 0.071 0.093 0.080 0.069 0.060 0.081 0.069 0.059 0.051 0.070 0.060 0.051 0.043 0.061 0.051 0.043 0.037 0.035 0.028 0.023 0.019 0.030 0.024 0.020 0.016 0.015 0.012 0.009 0.007 0.004 0.003 0.002 0.001 0.001 0.001 0.000 0.000 0.000 0.000 0.000 0.000 8% 1.000 0.926 0.857 0.794 0.735 0.681 0.630 0.583 0.540 0.500 0.463 0.429 0.397 0.368 0.340 0.315 0.292 0.270 0.250 0.232 0.215 0.158 0.146 0.099 0.046 0.021 0.010 20% 1.000 0.833 0.694 0.579 0.482 0.402 0.335 0.279 0.233 0.194 0.162 0.135 0.112 0.093 0.078 0.065 0.054 0.045 0.038 0.031 0.026 0.013 0.010 0.004 0.001 0.000 0.000 10% 1.000 0.909 0.826 0.751 0.683 0.621 0.564 0.513 0.467 0.424 0.386 0.350 0.319 0.290 0.263 0.239 0.218 0.198 0.180 0.164 0.149 0.102 0.092 0.057 0.022 0.009 0.003 28% 1.000 0.781 0.610 0.477 0.373 0.291 0.227 0.178 0.139 0.108 0.085 0.066 0.052 0.040 0.032 0.025 0.019 0.015 0.012 0.009 0.007 0.003 0.002 0.001 0.000 0.000 0.000 11% 1.000 0.901 0.812 0.731 0.659 0.593 0.535 0.482 0.434 0.391 0.352 0.317 0.286 0.258 0.232 0.209 0.188 0.170 0.153 0.138 0.124 0.082 0.074 0.044 0.015 0.005 0.002 32% 1.000 0.758 0.574 0.435 0.329 0.250 0.189 0.143 0.108 0.082 0.062 0.047 0.036 0.027 0.021 0.016 0.012 0.009 0.007 0.005 0.004 0.001 0.001 0.000 0.000 0.000 0.000 12% 1.000 0.893 0.797 0.712 0.636 0.567 0.507 0.452 0.404 0.361 0.322 0.287 0.257 0.229 0.205 0.183 0.163 0.146 0.130 0.116 0.104 0.066 0.059 0.033 0.011 0.003 0.001 36% 1.000 0.735 0.541 0.398 0.292 0.215 0.158 0.116 0.085 0.063 0.046 0.034 0.025 0.018 0.014 0.010 0.007 0.005 0.004 0.003 0.002 0.001 0.000 0.000 0.000 0.000 0.000 Period, 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 24 25 30 40 50 60 14% 1.000 0.877 0.769 0.675 0.592 0.519 0.456 0.400 0.351 0.308 0.270 0.237 0.208 0.182 0.160 0.140 0.123 0.108 0.095 0.083 0.073 0.043 0.038 0.020 0.005 0.001 0.000 19% 1.000 0.840 0.706 0.593 0.499 0.419 0.352 0.296 0.249 0.209 0.176 0.148 0.124 0.104 0.088 0.074 0.062 0.052 0.044 0.037 0.031 0.015 0.013 0.005 0.001 0.000 0.000 24% 1.000 0.806 0.650 0.524 0.423 0.341 0.275 0.222 0.179 0.144 0.116 0.094 0.076 0.061 0.049 0.040 0.032 0.026 0.021 0.017 0.014 0.006 0.005 0.002 0.000 0.000 0.000 40% 1.000 0.714 0.510 0.364 0.260 0.186 0.133 0.095 0.068 0.048 0.035 0.025 0.018 0.013 0.009 0.006 0.005 0.003 0.002 0.002 0.001 0.000 0.000 0.000 0.000 0.000 0.000

Answer 1

Year	cash flow	present value factor at 12% = 1/(1+r)^n r=12%	present value of cash flow = cash flow*present value factor
0	-70000	1	-70000
1	14000	0.893	12500
2	14000	0.797	11160.71
3	14000	0.893	12500
4	14000	0.797	11160.71
5	14000	0.893	12500
6	14000	0.797	11160.71
7	14000	0.893	12500
8	14000	0.797	11160.71
9	14000	0.893	12500
10	14000	0.797	11160.71
11	21000	0.893	18750
12	21000	0.797	16741.07
13	21000	0.893	18750
14	21000	0.797	16741.07
15	21000	0.893	18750
16	21000	0.797	16741.07
17	21000	0.893	18750
18	21000	0.797	16741.07
19	21000	0.893	18750
20	21000	0.797	16741.07
Net present value = sum of present value of (cash flow*present value factor at 12%)			225759