November 25

# Required Rate of Return: How Do You Calculate It?

By Andy Duncan

November 25, 2020

jargon, required rate of return

Hello, and welcome to a look at the required rate of return, here at Finlingo. The required rate of return is a deceptively simple concept, but one that's quite nuanced. Let's take a look at what's going on.

## How do you calculate the required rate of return?

First, we'll head over to Finlingo Island, a privately owned territory deep in the Pacific. On this fabulous Island, a new company has started up called Andy's Dodgy Jet-skis. Andy would like to borrow 100 Finlingo dollars for a measly two years.

Another much larger company, Sean's Luxury Yachts, also wants to borrow \$100 for the same two year period. Remarkably, you're an investor and have precisely 100 Finlingo dollars that you'd like to invest. I know, it's an incredible coincidence.

## Why required rate of return?

You need to know how much you want in return for lending your money.  Or for investing in shares.  Or real estate.  Any investment decision you make will take this into account.

Now, which companies should you lend your money to? And at what rate of return is acceptable on either of these two investments?

First, we need to examine a few possible things to calculate acceptable rates of return on both of these potential investments. We need two equations. The first is the nominal risk-free rate, which is made up of the real risk-free rate, plus the expected inflation rate.

Nominal risk-free interest rate = real risk-free interest rate + inflation premium

## What is a risk-free rate of return?

It’s the rate of return you earn when you’re guaranteed to get your money back.

The second equation we need is the required return. This is the nominal risk-free rate above, plus the default risk premium, the liquidity risk premium, and the maturity risk premium.  Here’s the formula for required rate of return:

Before we get to those last three premiums, let's break down the nominal risk-free rate. Let's say Finlingo Bank, the most reliable bank in the world, borrows money at a risk-free rate of 3%.

How do we make up that nominal risk-free you rate? Well, imagine that at the start of a year, the price of a small boat on Finlingo Island is exactly \$100. The following year, the boat costs \$101.

Why? Because gold is being mined continuously, globally, at the rate of about 1% a year compared to current global gold stocks held above ground. So we've got expected price inflation of 1% a year.

If you lend \$100 at a 1% return and get back \$101 a year later, in both cases, you'd only be able to buy the same small boat at either end of the time period. So you'd failed to gain any real increase in wealth at a 1% return, despite the nominal growth of 1% in money. The price inflation of 1% eats up all of your potential gains.

## Is the required rate of return the same as the expected rate of return?

Required rate of return vs expected rate of return can be explained simply.

The required rate of return is the absolute minimum return on investment you would accept for that investment to be worthwhile.  An expected rate of return is what you expect to collect when investing in a stock. So the required rate of return is the lowest possible rate that would make you put your hand in your pocket to invest, while the expected rate of return is what you hope to make once you’ve invested.

The required rate of return is also called the cost of capital.

## What is the minimum required rate?

That’s up to each investor individually.  But knowing the components of this calculation can help determine it.

Let's get back to the equation.

That 1% of expected price inflation makes up the second part of the equation. When Finlingo Bank offers a nominal risk-free rate of 3%, the real risk-free rate is just 2%. You decide you'd rather be a little more adventurous than just getting a risk-free return. So you look at two investments: either Andy's Dodgy Jet-skis or Sean's Luxury Yachts.

Let's get on then to the second equation. But now we can fill in the first part. The nominal risk-free rate for both Andy's company and Sean's company is the same. It's 3%.

What about this default risk premium? The jet-ski company is a startup, so it's got a very high chance of defaulting on its loan, and you might lose all of your stake money. So you decide Andy's default risk premium is 10%. Sean's company is much safer but still has some default risk. So you set his default risk premium to a much lower 3%.

## What is meant by liquidity risk?

Now we can do the liquidity risk.

Andy's company is tiny, so there'll be significant liquidity issues.  What does this mean? It means it will be challenging to sell your investment quickly whenever you want to sell. That’s because you're swimming in a pool of just a very few potential buyers. This difficulty in selling is especially real in any financial crisis.

Despite building jet-skis, Andy's dodgy jet-skis is a very illiquid company. You decide his liquidity premium is 4%. On the other hand, Sean's company is very liquid. It's large and stable and has a long record of consistently high profits over several decades. There are many buyers in his liquidity pool, so you make his liquidity risk premium just 1%.

Finally, when you tie up money for just two years, you're not taking on much maturity risk, but let's try to cover this on another diagram.

Sean's also offering a range of other bond investments. There's the two-year maturity bond we know about, a five-year maturity bond, and a 10-year maturity bond.

When your money is tied up for longer periods, you're missing out on other investment opportunities. The longer you lend money, the greater the return you need to make up for this loss of opportunity. Plus, you might just want your money back quickly to buy an ice cream cone. So you might decide on different maturity risk premiums of 1%, 3%, and 8% for these three different bonds. This driving force is, incidentally, what drives the normal shape of a standard yield curve, but that's a subject for another day.

Getting back to our investment choice, we decided that, for a two-year loan, we'll set a maturity risk premium of 1% on both Andy's Dodgy Jet-skis and Sean's Luxury Yachts.

## Add It All Up and Compare

We can now work out the required rates of return for both potential investments. For Andy's company, we need at least 18%. For Sean's, we need at least 8%. Andy does offer 18% on his bond, but Sean's only offering 7%. So you lend the money to Andy because you're getting an acceptable rate of return. And that's about it for the required rate of return.

We hope this conceptual look at the makeup of the required rate of return was helpful.  To see more, make sure you visit finlingo.com for more great stuff to help you on your banking journey!

Andy Duncan

Andy Duncan, CQF, is Finlingo's indispensable Chief Technical Officer. He's the creator of Finlingo's incomparable Infinite Question Engine and CFA® Total Recall app, soon to be available in the Apple App Store and Google Play Store.

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