## Net Present Value

### Learning Outcomes

• Calculate the net present value of a capital project

To calculate the net present value of a capital project, start with the nominal cash flows. We’ll be using the JuxtaPos scenario where management is considering adding a line of puzzles that necessitates a new machine that will cost $230,000 with an estimated useful life of six years and a residual value of$40,000. Management is using the weighted average cost of capital of 15% as a hurdle rate

Net annual cash flows are as follows:

-

Next, using Excel, a financial calculator, or a PV table (as shown below), calculate the net present value of each cash flow. Use the factors from the 15% column.

Present Value of $1 Periods 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12% 14% 15% 16% 18% 20% Period 1 0.990 0.980 0.971 0.962 0.952 0.943 0.935 0.926 0.917 0.909 0.893 0.877 0.870 0.862 0.847 0.833 Period 2 0.980 0.961 0.943 0.925 0.907 0.890 0.873 0.857 0.842 0.826 0.797 0.769 0.756 0.743 0.718 0.694 Period 3 0.971 0.942 0.915 0.889 0.864 0.840 0.816 0.794 0.772 0.751 0.712 0.675 0.658 0.641 0.609 0.579 Period 4 0.961 0.924 0.888 0.855 0.823 0.792 0.763 0.735 0.708 0.683 0.636 0.592 0.572 0.552 0.516 0.482 Period 5 0.951 0.906 0.863 0.822 0.784 0.747 0.713 0.681 0.650 0.621 0.567 0.519 0.497 0.476 0.437 0.402 Period 6 0.942 0.888 0.837 0.790 0.746 0.705 0.666 0.630 0.596 0.564 0.507 0.456 0.432 0.410 0.370 0.335 Period 7 0.933 0.871 0.813 0.760 0.711 0.665 0.623 0.583 0.547 0.513 0.452 0.400 0.376 0.354 0.314 0.279 Period 8 0.923 0.853 0.789 0.731 0.677 0.627 0.582 0.540 0.502 0.467 0.404 0.351 0.327 0.305 0.266 0.233 Period 9 0.914 0.837 0.766 0.703 0.645 0.592 0.544 0.500 0.460 0.424 0.361 0.308 0.284 0.263 0.225 0.194 Period 10 0.905 0.820 0.744 0.676 0.614 0.558 0.508 0.463 0.422 0.386 0.322 0.270 0.247 0.227 0.191 0.162 Period 11 0.896 0.804 0.722 0.650 0.585 0.527 0.475 0.429 0.388 0.350 0.287 0.237 0.215 0.195 0.162 0.135 Period 12 0.887 0.788 0.701 0.625 0.557 0.497 0.444 0.397 0.356 0.319 0.257 0.208 0.187 0.168 0.137 0.112 Period 13 0.879 0.773 0.681 0.601 0.530 0.469 0.415 0.368 0.326 0.290 0.229 0.182 0.163 0.145 0.116 0.093 Period 14 0.870 0.758 0.661 0.577 0.505 0.442 0.388 0.340 0.299 0.263 0.205 0.160 0.141 0.125 0.099 0.078 - Then subtract the initial investment: - This negative net present value tells us that the present value of all future cash flows, discounted at 15%, is less than the original price of the project, so it is as if we are spending$230,000 today and immediately receiving back only \$218,140. In other words, the company is losing money on this project.

Here is an NPV problem worked out on video:

You can view the transcript for “Net Present Value (NPV)” here (opens in new window).

Before we calculate the Internal Rate of Return (IRR) on this project, check your understanding of the NPV method.