MODULE ON INVESTMENT SELECTION. Article #5: ENJOYING THE CAKE WITHOUT EATING IT

In a previous article (Investment Selection Based on Returns) I said that the main advantage of the internal rate of return method is that it is very easy to understand. We all easily grasp what it means that an investment has a particular return (eg. 10% per year), and whether this is attractive when compared with the minimum return compatible with the risk of the project.

Moreover, the results obtained with the NPV approach are more difficult to interpret since these are absolute numbers whose meaning is unclear. In this article I explain the meaning of the NPV results. As usual I will resort to an example.

Imagine Albertico Limonta just inherited €90 thousand from his beloved grandmother. Albertico wants to mitigate his sorrow using the inheritance money to buy a sports car, a Lamborghini.

Just when he was about to buy the car Albertico is presented with a business opportunity. It consists in purchasing an apartment whose value is expected to be €112 thousand within a year. The deal is that the property can be purchased now for €90 thousand. The risk of this type of business requires a discount rate (minimum return) of 12%.

Let´s calculate the NPV of this investment ,

NPV = -€90000+€112000/1.12 = +€10000

 This is an attractive proposition because it yields a positive NPV of €10 thousand.

Albertico is very tempted to do the business but also wants to buy the Lamborghini. It seems that he will have to decide by one thing or another. Well, incredibly, he must not! Actually Albertico can benefit from the property deal and at the same time purchase the Lamborghini. Let's see how.

The first thing Albertico must do is set up a company that we will name Nauru Real Estate (NRE). Albertico transfers to the company the option to buy the property for €90 thousand and in return becomes its sole shareholder. After this, Albertico must find an investor who is willing to buy the shares of NRE.

Since the risk of this business requires a minimum return of 12%, and the apartment is estimated to be worth €112 thousand within a year, any investor will be willing to pay up to €100 thousand to own the apartment. By becoming the sole owner of NRE the new investor will have to pay €90 thousand for the property. So he will be willing to pay up to €10 thousand to buy the shares (giving him the right to buy the apartment).

Therefore, Albertico must sell the NRE shares for €10 thousand and buy the Lamborghini with the €90 thousand inherited from his grandmother. What is the result? Albertico gets the profit from the propertry deal and at the same time has the pleasure of buying the car. The magic of finance has allowed him to "enjoy the cake without eating it".

The NPV of €10 thousand represents the "value" of the investment opportunity. In other words, for how much a business deal can be sold to any investor willing to settle for a reasonable return commensurate with the risk being taken. This is how we should interpret the NPV.

This example also allows us to understand what the key assumption behind the NPV method is. For NPV to function a developed and transparent capital market must exist permiting the sale of investment opportunities to other investors with total freedom and without any barriers. Whenever this condition is not  met, the NPV rule is invalidated.

In my next article I will give an example of what happens when the NPV rule can not be applied.

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MODULE ON INVESTMENT SELECTION Article #4 INVESTMENT SELECTION BASED ON RETURNS

In a previous article (How to Know if an Investment is Better or Worse than Another?) I explained that the present value PV represents the sum you need to invest to get a certain amount at the end of a year, given a certain discount rate. The discount rate being the minimum return that is required for the investment according to its risk.

For example, €100 is the PV of €112 for a discount rate of 12% per year, because €100 is the amount you must invest to get €112 if the required return is 12%.

I also showed that net present value (NPV) results from subtracting the initial investment from the present value corresponding to the amount of money received in a year. If in the above example the amount initially invested was €90, the NPV would be €10 (€100 minus €90).

It was concluded that the NPV method was useful for deciding whether an investment was acceptable, and also to compare it with other investments involving different amounts and risks.

The procedure discussed in this article is an alternative to NPV that is also used to make investment decisions. It consists in calculating the return which corresponds to a NPV of zero. This return is called the "internal rate of return" (IRR). Then, this return is compared to the discount rate that would be required for investments of the same risk. If the IRR is greater than the required discount rate, the investment is acceptable because its return is superior to the minimum required. Otherwise, the investment should be rejected.

Continuing with our example, if we write the formula for its NPV:

NPV = -90 + 112/(1+r)

The IRR is calculated by solving the following equation:

0 = -90 + 112/(1+IRR) 

The result is 24.4%. Since this yield is higher than the discount rate of 12%, the investment should be accepted.

If the initial investment is now €110, the equation to be solved becomes,

0 = -110 + 112/(1+IRR)

And the IRR would be 1.8%. As this return is less than 12%, in this case the investment must be rejected.

The main advantage of the IRR is that it is easy to understand. Anyone grasps the meaning of the return on an investment, and that if this return is above the minimum required it must be accepted, or rejected otherwise. Moreover, the meaning of NPV is much murkier. How should we interpret that a NPV is +€8.6, or -€7.4? Is it too much? Is it too little? This is why the IRR has always been more popular than the NPV among investors.

However, the NPV rule never fails while IRR has two problems. The first is that its calculation is difficult when analyzing investments that extend for more than two years. Fortunately, since computers have been available this has ceased to represent a difficulty.

The second, and much more important, problem is that the IRR can lead to wrong decisions when comparing investments whose invested amounts differ, or where additional disbursements must be made beyond the initial moment.

That is why scholars have been fighting for years to propagate the NPV method among analysts. However, while the NPV method is increasingly used, IRR remains very popular.

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MODULE ON INVESTMENT SELECTION Article 3 THE RULE OF 72

This article short presents a mathematical curiosity that is very useful to calculate how long it takes for an investment to double in value given a certain rate of return. The only thing needed is to remember the number 72. Let's see.

 

If we expect a yield of 8% it will take nine years to double our money, just because 8 multiplied by 9 equals 72. That is, if we invest 100 now at an 8% return we will have 200 after 9 years. Similarly, if the return was 12%, six years would be needed to double our money, since 12 times 6 also make 72.

This simple rule assumes that the money invested is not touched until the end. That is, both the initial capital and the returns it produces are reinvested year after year until the original investment
is doubled.

The rule also works if we fix the number of years and want to know the corresponding return. For instance, what should be the return to double my money in 10 years? The answer is 7.2% (because 7.2 times 10 equal 72).

Interestingly, the rule does not have to be limited to money. For example: In how many years will the population of a country will double if population growth is 2% per year? It will take 36 years (2 multiplied by 36 make 72).

It is important to note that this is a rule of thumb that loses accuracy when yields rise above 16%. However it is still very practical when we want to do fast computations without resorting to a calculator.

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