Last month, we went back to school and discussed some useful financial calculations incorporated within Microsoft Excel formulas. This month, we are going to continue the school day and, along the way, weave in the theme of renovation being covered throughout this issue of * Properties*. Both fit perfectly for me; I teach a course at the University of Denver and just finished writing a question for the midterm exam, as follows:

An investor is contemplating installing an automated ticketing system in their parking garage. If continued to be operated with a manned attendant, the garage is expected to produce $100,000 next year and anticipated to grow $2,500 annually in subsequent years as a result of planned increases in the parking rate. The reversion value at the end of five years is expected to be $1,200,000.

The automated system is anticipated to cost $250,000 but income will increase to $125,000 in the first year, as a result of no longer needing an attendant and thus realizing lower expenses. Annual increases are projected to remain the same, $2,500 per year, and the reversion value at the end of five years is expected to be $1,500,000, based on the higher income level.

Using a discount rate of 10%, which alternative should the investor choose?

This is a classic renovation analysis – should the investor keep on keeping on, as-is, and not incur the upfront expense which will result in lower annual cash flows and lower reversion. Or should the renovation be completed, which will result in a significant upfront expense but higher annual cash flow and higher reversion. Who’s ready to go back to school?

We are going to use a three-step approach to solve this problem, dragging in our old friend the CCIM T-bar to help. The first step is to model the cash flows associated with doing nothing. The present value (PV) component would be zero, as no initial money is being spent. The payment (PMT) component would start at $100,000 in the first year and increase $2,500 each subsequent year of the holding period. And the future value (FV) would be $1,200,000. *Figure 1 *represents the T-bar for these cash flows. The second step is to model the cash flows associated with making the renovation. The PV component would be ($250,000), reflecting the cost of installing the automation system. The PMT component would start at $125,000 in the first year and increase $2,500 each subsequent year of the holding period.

And the FV would be $1,500,000, which is the anticipated value of the garage at the end of the holding period. *Figure 2 *represents the T-bar for these cash flows.

The third step is to calculate the net present value (NPV) of each T-bar, using the 10% target rate. You’ll need a financial calculator to perform this function (unless you were paying attention to last month’s column). Once completed, you will discover the “as-is” scenario has a NPV of $1,141,339 while the “renovate” scenario has a NPV of $1,172,385. At this point, the decision is simple; based on the assumptions provided, it is worth it to pursue the renovation.

We are not done yet – the university students also have a related bonus question, so why shouldn’t you? We can take this analysis one step further by using a concept known as “IRR of the differential.” Calculating it is straightforward and is the IRR of the difference between the renovated series of cash flows less the as-is series of cash flows. As you can see in *Figure 3*, the PV of ($250,000) is found by subtracting the PV of the renovated T-bar (*Figure 2*) minus the as-is T-bar (*Figure 1*). The PMT in year one in *Figure 3 *is found by subtracting the year one PMT of the renovated T-bar minus the as-is T-bar. Lather, rinse, repeat for the cash flows in years two through five and the reversions. Plug these into a financial calculator (unless, again, you were paying attention to last month’s column) and we come up with an IRR of the differential of 13.08%.

But the bonus question on this insidious mid-term exam doesn’t ask for the IRR of the differential. C’mon, these are graduate students! It asks what this concept means – because to me, this is the most important number on the board. And I’ll save you the grief. From a purely mathematical perspective, 13.08% is the exact rate at which the NPV of the as-is scenario and the NPV of the renovate $1,500,000, which is the anticipated value of the garage at the end of the holding period. *Figure 2 *represents the T-bar for these cash flows.

scenario are equal. You are welcome to try it but, trust me, you will come up with an NPV of $1,015,465-ish for either scenario if you use a discount rate of 13.08%. But mathematics doesn’t pay the bills, understanding the practical application is what’s important. The 13.08% discount rate is considered the point of indifference or cross-over point. At that exact rate, there is no difference between the as-is and the renovate scenario. They are equivalent decisions. But at any rate less than 13.08%, the decision swings to the renovate scenario and the lower the rate, the more pronounced the renovate decision becomes. Conversely, at any discount rate greater than 13.08%, the decision swings to the as-is scenario and the higher the rate, the more pronounced the as-is decision becomes.

Gang, our business is all about under- standing and quantifying risk, and the concept of IRR of the differential is a hallmark example. The break-even risk versus return for this proposed renovation is 13.08%. If you believe the risk associated with this proposed renovation demands a return greater than this point of indifference, you are better off to not spend the money and keep on keeping on. But if you perceive a low degree of risk associated with the renovation, and are good earning a return at some rate less than this break-even rate, you are better off to spend the money. And if you liked second period, just wait to see what we have in store for third period!

by Alec Pacella for ** Properties Magazine**, November 2022