Determining the Internal Rate of Return IRR

Probably the truest measure of a project’s rate of return is its Internal Rate of Return. The IRR is that interest rate that exactly balances the discounted value of future net cashflows with the investment required to develop the project or enterprise. The higher the interest rate (discount rate) needs to be in order that future net cashflows exactly offset the upfront investment, the higher the IRR is and the better the project is, at least in terms of return on investment.

The IRR can be found by solving the following equation by trial and error (computers do it using an iterative process).

In the simplest model, if a student loans a Professor $1,000 and the Professor pays it back in three years with interest of, say, $150 per year, we have:

Year Investment/Cashflow (from the Student’s POV)

0 -$1,000
1 $150
2 $150
3 $1,150

The IRR can be found by solving the following equation by trial and error (not much trial or error here):

$1,000 – $150/(1+irr)^1 – $150/(1+irr)^2 – $1,150/(1+irr)^3 = 0

or IRR = 15% p.a.

Now, I have done survey after survey (not scientifically, I may add) of my students over the years and I haven’t yet found any students willing to lend their (poor) Professor $1,000 in return for $150 per year of interest. They usually aren’t interested until the money gets to be around $200 a year and most of them are looking for even more, $300 or $400 in interest per year. This implies that their Internal Rates of Return are in the 20 to 40% p.a. range.

Some work I did earlier on rates of return for students pursuing an architecture degree suggested that their IRRs are in the range of just 14%*. There could be a number of factors at work here including the possibility that architects (unlike more hard headed engineers like me or business students) are somewhat ‘other directed’ (a nice way of saying they are taking their architecture degrees for reason other than the big bucks).

(* Please see: A Case Study of the Perceived Value of An Architecture Degree, Carleton University, Ottawa, Canada, https://www.eqjournal.org/?p=1061.)

In any event, it is well known that personal discount rates tend to fall as people get older because: a. they have usually have more money as they get older and a greater supply of money implies that its price will fall, and b. their willingness to take risks drops so that they would rather have it in T-bills than startups by the time most people are in their 60s, 70s or 80s.

Just as IRRs tend to decrease with age, they tend to drop as companies become larger. Mega corporations tend to have minimum expectations for their IRRs (on their equity) of around 20 to 22% p.a. Entrepreneurs and startups usually require much higher IRRs than this because so many things can and do go wrong that they have to aim high just so they don’t go oob (out of business).

When the Disney Company acquired an expansion franchise in the NHL in the early 1990s, there was some concern that Disney could afford to ‘buy’ players and push up salaries even faster than they were already going up. Executives from that Company reassured Expansion Committee members that every Disney investment including sports teams had to meet certain minimum investment criteria and this shouldn’t be a concern. The Mighty Ducks of Anaheim began play within a couple of years thereafter and Mike Eisner, then CEO of Disney, was true to his word.

If you download the spreadsheet for a Rental Home Builder posted at:https://www.old.dramatispersonae.org/IRR/SampleIRR2.xls, you will see that if an investor/builder/developer puts down, say, 25% equity on each unit, he or she will see a 22% p.a. IRR. But if they put down just 5%, the IRR on their equity jumps to 56% p.a. In both cases, the IRR of the project hasn’t changed—it remains 10.8%. What this tells you is that the IRR for a project (or enterprise) is made up of a series of IRRs on equity and debt. In this case, the capital structure is simple—there are just two components: the investor/builder/developer’s equity and the bank’s mortgage debt.

So the IRR for the Project (at 10.8%) is like the ‘weighted’ average of the IRR on Equity (22%, or 56% in the case using greater leverage) and the IRR on Debt (in this case, this equals the interest rate on the mortgage, which is 6%). For more complex projects, you can have many components in the capital structure—equity, structured equity, debenture debt, secured debt, sub debt, capital lease, unsecured debt and so forth. Each tranche will have its own cashflow profile and IRR.

You might ask how can Banks afford to lend money at 6% when the above graph suggests that mega corps want minimum IRRs of 20 to 22% p.a.? Well, just ask yourself how much interest you are getting on your savings account. If the answer is less than 1% (in fact, after you calculate all the fees you pay your Bank, it is probably negative), then you can figure it out for yourself. Bottom line, the Banks use OPM (Other People’s Money) mixed in with a little of their own so that their IRRs on their equity are among the best on the planet. Don’t worry about your Bank’s rate of return, worry about your own.

(Recently, I have added a similar spreadsheet for an investor or sitting owner (owner occupier) of industrial condos. See: https://www.old.dramatispersonae.org/IRR/SampleIRR2-commercial.xls.

Again, I did two cases: one where you buy/invest in one industrial condo with 25% down and a second case where you buy five units with 5% down. In all probability, in the commercial space, you might more realistically do a case where you buy one with 40% down or two with 20% down since LTV (Loan to Value) ratios tend to be lower than in the residential area.

Still the principles are the same: more leverage increases your return on equity under certain conditions. Your total return (wealth effect) is again made up of three components: cash on cash return (money you make every month assuming your mortgage and other payments are less than your rents), inflation (all inflation in real estate values go to the equity owner assuming your marketplace is not going through a recession) and forced savings (paydown of mortgage either by sitting owner or tenants).

Establishing Sales Goals Using a Reverse IRR Model

The Reverse IRR Model* helps you establish monthly goals for your new enterprise that, if (when) achieved, will also allow you to pay your bills and make a profit too. You want to make a profit not so you can take a trip to Vegas but so you can reinvest in your business and in new technologies, new products, new services, more staff, more staff training and so forth.

(You can download this model from:https://www.old.dramatispersonae.org/IRR/ReverseIRRAcmePromotions.xls.)

Visualize Your Goals, Then Achive Them: One Step at a Time

People are really good at reaching goals once they set them. If you are involved in a timed race, you always want to go second or near the end when you know everyone else’s times. Then you have a goal, you can break it down into intervals and WIN.

Same thing for business. It does you no good to say, I want $150k in sales my first year. What you need to say is, I need $12,500 a month in sales or $625 a day, every day for the 20 working days in each month.

Visualization is key. Put up a sign “N = ?” in your office and at home and every day focus on it and drive N up. (N can be sales, number of customers, number of products shipped, whatever. It is the basic metric for your business.)

Don’t think that, oh well, I didn’t make $625 in sales today, I’ll make it up at month’s end. It doesn’t work that way. If you miss today’s target, it means you have to sell $1,300 tomorrow or $1,925 the day after and pretty soon, you and your business are toast.

The Reverse IRR Model is based on the assumption that, going in, you are likely to know your costs more accurately that what your revenues are likely to be. Revenue estimates, whether based on marketing surveys you did or a guesstimate you came up with as to what percentage of the total market you think you are going to get, can be highly unreliable. So goal setting based on what your expected costs will be plus an allowance for profitability based on some type of target you have established, is probably as good a mechanism to establish your future revenue stream as any.

The Power of Leverage/Using Other People’s Money

Note also the power of using OPM (Other People’s Money) or leverage (aka debt). It increases the IRR on your equity and it allows you to ration your use of a limited amount of capital to do more of whatever it is you are planning on doing.

Leverage is usually interpreted (especially by Banks) as increasing risk but as you can see in the rental home example we used above, it may be that if you develop five rental units instead of one, your risks (and your Bank’s exposure to you as well) may go down not up despite higher gearing.

Archimedes Understood the Power of Leverage

If you use your equity to build five units instead of one (i.e., you are putting 5% down on each unit instead of 25% and financing the rest), and if one tenant leaves, you will have a 20% vacancy rate instead of 100%. The free cashflow you are earning from the other four (still occupied) units can assist you in paying the mortgage for the vacant fifth unit.

If the average vacancy rate for each unit over a ten year period is, say, 10%, then the probability that all five units would be vacant at the same time is pretty low (0.1 to the power of five or just .001%). So, as entrepreneurs, we can argue (with our Bank) for more leverage not less.

Obviously, the Bank will say:

1. If you put down more equity, they will be looking at a better debt to equity ratio and that means if asset values tumble, their loans are protected by your equity since in a Bankruptcy, Foreclosure or Power of Sale proceeding, the secured creditor (the Bank) gets paid first.

2. If you only had one unit instead of five and it becomes vacant, your income from other sources may be enough to cover your loan payments* but if you had to cope with all five units suddenly becoming vacant, you could be under water in a hurry.

(* This is known as the cashflow coverage for your loan; i.e., your free cashflow as calculated by the Bank must be significantly greater than your monthly mortgage obligations or they won’t make the loan. The Bank will usually only include half the rental income you are receiving and will deduct from your employment and other income, your other monthly obligations like home mortgage and car payments.)

This is what I like to call the ‘nuclear bomb scenario’ or what other people call the Banks’ ‘belt and suspenders’ approach to lending. Banks generally only like to lend money to people who don’t need it (i.e., people who have enough of their own cash to start a project without any Bank lending).

From your POV, your cash-on-cash returns are much higher if you build five units. The spreadsheet shows if you leverage your $37,500 in equity into five rental properties (with 5% down on each unit), you have a cash return of $254,052.85 over five years as compared to $89,291.00 if you can only build one unit (with a down payment of 25%).

So leverage has the strange effect of being more risky (at least from the Bank’s POV) but ultimately lets you pay off all your debt obligations much faster than if you used less leverage; i.e., bought only one rental property.

Bottom line, you need a sophisticated, motivated lender before you can do highly leveraged deals.

@ProfBruce