For IRR and NPV calculations use the PV of an Annuity sheet below

Payback Method - Simplest - How long does it take to recover your investment?

Investment! Future cash flows or savings = years to recover investment

Internal Rate of Return - The percentage rate of return a project will earn.

Investment! Future cash flows or savings; then use the the table (present value of an annuity) to find the % rate of return In the table, use the years you are given in the exercise. follow the row down to the closest number calculated above and look at the heading to get the %

Net Present Value (NPV) - Does the project meet the hurdle rate?

Discount the future cash flows at the predetermined rate then subtract it from the cost of the investment, if the number is positive it will meet the rate of return, if not, it won't

Don't suffer ask questions if you get hung up

Exercises
1. An investment in a robotics system of $75,000 will save us a net total of $22,400 per year after tax in operational expenses including depreciation for 5 years.

Payback -

NPV @ 8% (hurdle rate)

IRR -

2. An investment of $100,000 in a new server and software system will net us a savings of $20,540 per year after tax including depreciation for the next 7 years.
Payback -

NPV @ 8% (hurdle rate)
IRR -

3. John needs a new production machine for operations.

The machine cost is $250,000

Estimated life is 7 years

Additional revenue is expected to be $30,000, net of tax, per year (based upon 1,000 additional widgets produced per run) Additional efficiency labor savings per time study is $17,600 per year Additional tax savings from depreciation based upon a tax rate of 35% calculated on a straight line basis

Payback –

NPV @ 8% (hurdle rate)

IRR - 

Present value interest factor of an (ordinary) annuity of $1 per period at i% for n periods, PVIFA(i,n). Period 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16% 17% 18% 19% 20% 1. 0.990 1.970 0.980 1.942 0.971 0.962 0.952 1.859 0.943 1.833 0.935 0.926 0.917 0.909 0.901 0.893 0.885 1.713 1.690 0.877 0.870 0.862 0.855 0.847 0.840 1.566 0.833 1.913 1.886 1.808 1.783 1.759 1.736 1.668 1.647 1.626 1.605 1.585 1.547 1.528 2.106 3 2.941 2.884 2.829 2.775 2.723 2.673 2.624 2.577 2.531 2.487 2.444 2.402 2.361 2.974 2.322 2.283 2.855 2.246 2.210 2.174 2.140 4 3.902 3.808 3.717 3.630 3.546 3.465 3.387 3.312 3.240 3.170 3.102 3.037 2.914 2.798 2.743 2.690 2.639 2.589 5 4.853 4.713 4.580 4.452 4.329 4.212 4.100 3.993 3.890 3.791 3.696 3.605 3.517 3.433 3.352 3.274 3.199 3.127 3.058 2.991 4.623 6 5.795 6.728 5.601 5.417 6.230 5.242 5.076 4.917 4.767 4.486 4.355 4.231 4.111 3.998 3.889 3.784 3.685 4.039 3.589 3.498 3.410 3.326 7 6.472 6.002 5.389 5.206 3.706 5,786 6.463 5.582 5.033 4.868 4.712 4.564 4.423 4.288 4.160 3.922 3.812 3.605 5.535 5.335 5.995 5.759 8 7.652 7.325 7.020 6.733 6.210 5.971 5.747 5.146 4.968 4.799 3.837 4.639 4.946 4.487 4.344 4.207 4.451 4.078 3.954 9 8.566 8.162 7.786 6.247 7.435 8.111 7.108 7.722 6.802 6.515 5.537 5.328 5.889 5.650 5.132 4.772 4.607 4.303 4.494 4.163 4.031 10 7.360 7.887 7.024 7.499 6.710 6.418 6.145 5.426 5.687 5.019 4.833 4.659 4.836 4.988 9.471 8.983 8.530 5.216 4.339 4.192 11 10.368 12 11.255 13 12.134 14 13.004 15 13.865 16 14.718 17 15.562 18 16.398 19 17.226 20 18.046 25 22.023 30 25.808 35 29.409 40 32.835 50 39.196 9.787 6.806 6,495 6.814 4.327 9.253 9.954 8.760 8.306 7.139 6.207 5.938 5.453 5.234 5.029 4.656 4.486 10.575 9.385 8.863 8.384 7.943 7.536 7.161 6.492 6.194 5.918 5.660 5.421 5.197 4.793 4.611 4.439 11.348 10.635 9.986 9.394 8.853 8.358 7.904 7.487 7.103 6.750 6.424 6.122 5.842 5.583 5.342 5.118 4.910 4.715 4.533 12.106 11.296 10.563 9.899 9.295 8.745 8.244 7.786 7.367 6.982 6.628 6.302 6.002 5.724 5.468 5.229 5.008 4.802 4.611 11.118 11.652 9. 108 9.447 8.061 7.606 8.313 7.824 6.811 6.462 6.974 6.604 6.142 6.265 12.849 11.938 4.675 10,380 10.838 11.274 9.712 10.106 8.559 7.191 5.847 5.575 5.954 5.668 5.324 5.405 5,475 5.092 4.876 4.938 5.162 5.222 13.578 12.561 8.851 7.379 7.549 4.730 14.292 14.992 15.678 13.166 9.122 12.166 12.659 7.120 7.702 7.250 7.839 10.477 9.763 8,544 8.756 8.022 6.729 6.373 6.047 5.749 4.990 5.033 4.775 13.754 11.690 10.059 10.336 9.372 9.604 6.467 6.550 10.828 5.534 5.273 8.201 8.365 6.840 6.128 5.818 4.812 14.324 14.877 13.134 12,085 11.158 8.950 7.366 6.938 6.198 5.877 5.584 5.316 5.070 4.843 4.870 4.948 16.351 13.590 15.622 12.462 11.470 10.594 9.818 9.129 8.514 7.963 7.469 7.025 6.623 6.873 6.259 5.929 5.628 5.353 5.101 5.195 5.235 19.523 17.413 14.094 12.783 11.654 10.675 9.823 9.077 8.422 7.843 7.330 6.464 6.097 5.766 5.467 22.396 19.600 17.292 15.372 13.765 12.409 8.055 6.566 11.258 11.665 10.274 9.427 8.694 7.496 7.003 6.177 5.829 5.517 4.979 24.999 21.487 18.665 16.374 14.498 12.948 10.567 9.644 B.855 8.176 7.586 7.070 6.617 6.215 5.858 5.539 5.251 4.992 27.355 23.115 19.793 17.159 15.046 13.332 11.925 10.757 9.779 8.951 8.244 7.634 7.105 6.642 6.233 5.871 5.880 5.548 5.258 4.997 31.424 25.730 21.482 18.256 15.762 13.801 12.233 10.962 9.915 9.042 8.304 7.675 7.133 6.661 6.246 5.554 5.262 4.999