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:

Description Amount
Year 1 $        60,000
Year 2           60,000
Year 3             55,000
Year 4             55,000
Year 5           50,000
Year 6 (includes the $40,000 proceeds from sale)             65,000

 

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

 

Year Amount Factor Total
Year 1 $       60,000 times the factor of    0.8700 = $52,200
Year 2   60,000     0.7560 $ 45,360
Year 3         55,000     0.6580 $ 36,190
Year 4           55,000     0.5720 $ 31,460
Year 5           50,000     0.4970 $ 24,850
Year 6           65,000     0.4320 $ 28,080
Total present value of cash inflows Single Line$   218,140

 

Then subtract the initial investment:

Description Amount
Initial investment $ (230,000)
Net present value of project Single Line$   (11,860)Double line

 

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.

Practice Question