Let’s revisit South Side Brewery and the stage for the musicians’ project. Recall that the company expects revenue to increase by $6,000 per month due to increased alcohol sales and expenses (cost of the bands) to increase by $4,000 per month. Therefore, net cash inflows are projected to be $24,000 per year for the life of the project. The cost to build the stage with a lighting and sound system is $120,000. It will be good for at least 8 years.
We already know that the simple payback period will be 5 years (5 * $24,000 = $120,000).
1. What is the Internal Rate of Return?
Using Excel, we find that the IRR is 11.815%.
2. What is the NPV if we use a 10% WACC/hurdle rate?
| Description | Amount | Factor | Total |
|---|---|---|---|
| Year 1 | $ 24,000 | 0.9090 | $ 21,816 |
| Year 2 | 24,000 | 0.8260 | $ 19,824 |
| Year 3 | 24,000 | 0.7510 | $ 18,024 |
| Year 4 | 24,000 | 0.6830 | $ 16,392 |
| Year 5 | 24,000 | 0.6210 | $ 14,904 |
| Year 6 | 24,000 | 0.5640 | $ 13,536 |
| Year 7 | 24,000 | 0.5130 | $ 12,312 |
| Year 6 | 24,000 | 0.4670 | $ 11,208 |
| Total present value of cash inflows | Single Line$ 128,016 | ||
| Initial investment | $ (120,000) | ||
| Net present value of project | Single Line$ 8,016Double line |
What is the NPV at 10% if we use an annuity table since all of the cash flows are equal?
| Present Value of Ordinary Annuity 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 | 1.970 | 1.942 | 1.913 | 1.886 | 1.859 | 1.833 | 1.808 | 1.783 | 1.759 | 1.736 | 1.690 | 1.647 | 1.626 | 1.605 | 1.566 | 1.528 |
| Period 3 | 2.941 | 2.884 | 2.829 | 2.775 | 2.723 | 2.673 | 2.624 | 2.577 | 2.531 | 2.487 | 2.402 | 2.322 | 2.283 | 2.246 | 2.174 | 2.106 |
| Period 4 | 3.902 | 3.808 | 3.717 | 3.630 | 3.546 | 3.465 | 3.387 | 3.312 | 3.240 | 3.170 | 3.037 | 2.914 | 2.855 | 2.798 | 2.690 | 2.589 |
| Period 5 | 4.853 | 4.713 | 4.580 | 4.452 | 4.329 | 4.212 | 4.100 | 3.993 | 3.890 | 3.791 | 3.605 | 3.433 | 3.352 | 3.274 | 3.127 | 2.991 |
| Period 6 | 5.795 | 5.601 | 5.417 | 5.242 | 5.076 | 4.917 | 4.767 | 4.623 | 4.486 | 4.355 | 4.111 | 3.889 | 3.784 | 3.685 | 3.489 | 3.326 |
| Period 7 | 6.728 | 6.472 | 6.230 | 6.002 | 5.786 | 5.582 | 5.389 | 5.206 | 5.033 | 4.868 | 4.564 | 4.288 | 4.160 | 4.039 | 3.812 | 3.605 |
| Period 8 | 7.652 | 7.325 | 7.020 | 6.733 | 6.463 | 6.210 | 5.971 | 5.747 | 5.535 | 5.335 | 4.968 | 4.639 | 4.487 | 4.344 | 4.078 | 3.837 |
| Period 9 | 8.566 | 8.162 | 7.786 | 7.435 | 7.108 | 6.802 | 6.515 | 6.247 | 5.995 | 5.759 | 5.328 | 4.946 | 4.772 | 4.607 | 4.303 | 4.031 |
| Period 10 | 9.471 | 8.983 | 8.530 | 8.111 | 7.722 | 7.360 | 7.024 | 6.710 | 6.418 | 6.145 | 5.650 | 5.216 | 5.019 | 4.833 | 4.494 | 4.192 |
| Period 11 | 10.368 | 9.787 | 9.253 | 8.760 | 8.306 | 7.887 | 7.499 | 7.139 | 6.805 | 6.495 | 5.938 | 5.453 | 5.234 | 5.029 | 4.656 | 4.327 |
| Period 12 | 11.255 | 10.575 | 9.954 | 9.385 | 8.863 | 8.384 | 7.943 | 7.536 | 7.161 | 6.814 | 6.194 | 5.660 | 5.421 | 5.197 | 4.793 | 4.439 |
| Period 13 | 12.134 | 11.348 | 10.635 | 9.986 | 9.394 | 8.853 | 8.358 | 7.904 | 7.487 | 7.103 | 6.424 | 5.842 | 5.583 | 5.342 | 4.910 | 4.533 |
| Period 14 | 13.004 | 12.106 | 11.296 | 10.563 | 9.899 | 9.295 | 8.745 | 8.244 | 7.786 | 7.367 | 6.628 | 6.002 | 5.724 | 5.468 | 5.008 | 4.611 |
$24,000 * 5.335 = $128,040 (slightly different than the $128,016 in the prior calculation due to rounding of the factor).
3. And the profitability index?
128/120 = 1.07. Slightly above 1.0, so an acceptable (although not fantastic) investment.
There is no singular “right” way to make a capital decision, and remember that there will always be qualitative factors at play. For instance, a college campus may charge fees for a parking structure, but they may not cover costs, resulting in an IRR less than the normal hurdle rate or even a negative cash flow, but the project may be approved anyway because it contributes to the larger plan of increasing enrollment and being able to handle the increased capacity. In addition, there may be emergency projects, such as replacing a machine that unexpectedly broke down, that do not go through the normal process and analysis.
However, for most projects, the process should resemble the process laid out in this module:
Phase 1 – Screening
- Begin with the larger picture
- Identify and evaluate potential opportunities
- Screen opportunities
Phase 2 – Analysis
- Estimate operating and implementation costs
- Estimate cash flow
- Assessment
Phase 3 – Implementation
- Select the project
- Implement the project
- Re-evaluate the decision
It is important to remember, too, that part of Phase 3 – Implementation is to review the actual results in order to gather information for subsequent projects. How close were the projected cash flows? (It’s human nature to overestimate revenues and underestimate expenses.) What costs were omitted? (Often, the effect of a capital project on the operating budget is overlooked or underestimated.) What parts of the decision-making process went smoothly, and what parts were overly difficult? These and a host of other questions inform and improve the process. An evaluation also holds managers accountable for projected results and provides feedback on how the project is going.
Finally, here is a brief summary of how to use differential analysis to present alternatives to management.
You can view the transcript for “Differential Analysis – Concepts” here (opens in new window).
