## Concept Title: Return

**Description**: Explains teaches how to calculate return and different kinds of returns like Return on Equity (ROE), ROIC (Return on Invested Capital) and Payback Period

**Explanation**

We already know that return is the compensation for bearing risk. The question now is how do we determine an appropriate return? In order to answer this question we have to understand how we can break down risk into smaller components.

In any venture, risk has two components.

- The first is uncertainty, which determines the extent of deviation that can possibly occur from expected outcomes. The more uncertain future outcomes are, the higher the upswings and downswings, therefore the higher the risk.
- The second component is fixed costs. Irrespective of what happens on the revenue side, the firm will incur expenses which it will have to pay. To take an extreme view, these costs are certain.
- The balancing of these two components, certainty (in terms of fixed costs)

and uncertainty, should result in an opportunity where there is only a small probability (chance) that the fixed costs over a number of years will be higher than expected revenues over the same period.

One factor, which determines what the appropriate return should be, is this balance between fixed costs and uncertainty. Additional factors include:

- The return is on comparable opportunities available in the market,
- The number of comparable opportunities available for investment, and
- The ease at which the firm can raise money to invest in a project.

### Appropriate versus Expected Return

It is important to be able to differentiate between appropriate return and expected return at this point in time. Appropriate return is what you would expect to get paid for taking on the risk, while expected return is the return the project will pay you on average. Before we can determine an appropriate return, we still need to measure what the expected return would be. The two don’t have to be the same and you can tweak the terms of your investment to lower or raise both appropriate and expected return.

There are a number of approaches to measure returns. We present some of them below:

We will use a simple example for illustration 100 dollars are invested today. One year later, the 100 dollars are paid back. In addition a compensation of 50 dollars is also paid as a return on the initial investment. For the time being, let’s assume that the interest rate or discount rate (more on this later) is zero.

### i. **Return on Equity (ROE)**

What is the initial investment? 100 dollars. Do we fully own the 100 dollars that were invested? Yes. Then the equity in this investment is 100 dollars.

The absolute return is the total amount returned (150 dollars) minus the initial investment of 100 dollars, which in this case is 150 – 100 = 50 dollars.

The percentage return is the absolute return (50) divided by the initial investment (100). That turns out to be 50/100 = 50%.

The return on equity in this case is the same as percentage return, which is 50%.

If the interest or discount rate was non-zero then these amounts and figures would be adjusted for one year’s interest*. *

Return on equity is the same as return on investment if the original investment did not have any borrowed money. The following topic explains the difference in return on equity and return on invested capital.

### ROE Examples

#### Example # 1

** **Barbara has the opportunity to invest in a start-up for electronic newspaper. For every $100 that she is willing to invest, she will get back a gross amount of $150 . What is her Return On Equity (ROE)?

**Solution **To arrive at ROE we simply divide her net profit by the equity she invests. In this case:

ROE = 50/100 = 50.0%

#### Example # 2

As a financial analyst at a well known Investment Bank, your job is to tell clients what’s good for their business. A client has just asked you for advice on whether he should undertake this new high tech project that offers him a return of 25%. Of course being on top of your job as usual, you know that the ? for such a project is 2. You read in the Wall Street Journal that morning that the rate for US Treasury’s was currently at 6%. What advice would you give your client?

Assume the market risk premium to be 8%.

You need to calculate the required return on equity, and decide whether this project meets that requirement or not. You know that:

Req. ROE = [Risk free rate] + Beta * [Risk premium]

where: Risk free rate = 6% (using US treasuries as a proxy)

Risk premium (given) = 8%

Beta =2

Thus: Req. ROE = 6% + 2*(8%) = 22.00%

Hence, we should undertake this project as it gives a return that exceeds your required return.

### ii. **Return on Invested Capital (ROIC) & ROE**

Let’s make it more interesting. You are so sure of the opportunity that you don’t want to limit yourself to just making 50 dollars. You ask one of your friends if he will lend you 300 dollars. And, you promise to pay him back 330 dollars after one year, where the first 300 dollars is his principal and the next 30 dollars is his return.

Everything else remains the same. We make 50 dollars on every 100 dollars invested. The total investment is 400 dollars (100 equity + 300 friend’s loan). At the end of first year, we receive the 400 dollars principal and the 200 dollars profit. Out of the 200 dollars profit, we pay 30 dollars to our friend as return or compensation for putting his money at risk and are left with a net total of 170 dollars.

Let’s summarize. Original equity investment = 100 dollars. Net profit = 170 dollars. Return on equity = 170/100 = 170%. How did the jump from 50% to 170% happen? This is the benefit of leverage (the practice of putting borrowed money to work for you). Obviously the borrowed money comes at a price and the price you pay has a direct effect on the profits you generate. It is just a matter of more than off-setting the price with the returns coming in.

In such a situation is ROE still an appropriate measure? The sane answer is no. Which is why we look at Return on Invested Capital. This is the return on all investments, irrespective of original ownership.

What is the initial investment? 400 dollars.

The absolute return is the total amount returned by the investment (600 dollars) – the initial investment (400). Which in this case is 600 – 400 = 200 dollars.

The percentage return is the absolute return (200) divided by the initial investment (400). That turns out to be 200 / 400 = 50%.

The return on invested capital is the same as percentage return, which is 50%.

If the interest or discount rate was non-zero then these amounts and figures would be adjusted for one year’s interest, as mentioned earlier*.*

What is the key takeaway? In highly leveraged situations, such as the one that we just observed, return on total investment (popularly known as Return on Invested Capital or ROIC) is a more appropriate measure of return than ROE.

### iii. **Payback period**

Payback is the time period required to return the initial investment. In both of the above cases the initial investment is returned a year later. Therefore, the payback period is one year.

## Exam Questions for ROE, ROIC & Payback Period

### Test problem # 1

Nirav invests $200 in his dyed T-shirt business. This includes the $50 Nirav borrows from his brother. 6 months later, he has a return of 75%. What does the figure 37.5 represent? His

- Equity
- Absolute Return or Return on Investment
- Percentage Return
- Return on Equity

### Test problem # 2

Adriana Gonzales invests $100 in a venture. She gets the following returns:

What is the payback period?

- 1 year
- 2 years
- 3 years
- 4 years

### Test problem # 3

Lets suppose that we have an investment opportunity that requires a minimum 100 dollar investment. The investment promises us $50 every year for the next 4 years. Since we have only $50 in cash, we decide to borrow the rest of the amount, i.e. $50, from our friend who will not charge us anything for it, as long as we return the money within 2 years. What is our return on equity (ROE) on this investment? Return on invested capital (ROIC)? Payback period for this investment? Can we return the money in time? For simplicity, ignore the time value of money i.e. discount rate = 0%.

### Solution to Test problem # 3:

Well let’s recap the information given in the question:

- Minimum investment requirement = $ 100.0
- Equity = $50.0
- Debt = $50.0

Total invested capital is simply the sum of any debt and capital invested. Hence:

T*otal. invested cap * 50 + 50 = $ 100.0

Then ignoring the time value of money, net profit is simply the sum of the stream

of payments, minus our original investment

*Net profit* = (50 + 50 + 50 + 50) – 100 = $ 100

Therefore, the ROIC, which is simple the net profit divided by the total invested capital, is:

*ROIC* = 100 / 100 = 100%

And the ROE, which is simply the net profit divided by the equity invested, is:

*ROE* = 100 / 50 =200%

We define the payback period is as the amount of time taken to get back the original investment, which in this case was $100. Looking at the stream of payments we can see that:

*Payback period =*2 years.

Hence we can also return his $50 dollars in time (which we actually get back in 1 year).

### Test problem # 4

Lets suppose now that we have an alternate investment opportunity to the one described in *Example 3*. This second investment requires of minimum investment of only $50 dollars, and pays $125 dollars at the end of year 4. Which investment would you chose? What would your answer be if you required the payback period to be 3 years maximum? Again for simplicity, ignore the time value of money.

### Solution to Test problem #4

Well let’s recap the information given in the question:

- Minimum investment requirement = $50.0
- Equity = $50.0
- Debt = $ –

Now using the formulas stated above:

Total Invested Cap. = 50 + 0 = $50.0

Net Profit = 0 + 0 + 0 + 125 – 50 = $ 75.00

ROIC = 75 / 50 =150%

ROE= 75 / 50 = 150%

Payback period =4years

Note: As our invested capital consists of equity only, ROIC = ROE.

To analyze which investment to choose, lets look at the percentages we have calculated. Investment 1 (from example 1) has a higher ROE than investment 2. However that can be misleading. **Always compare investments using ROIC**.

Here we see that investment 2 has a higher ROIC (150% compared to the 100% of investment 1) and hence would be a better investment for us. Would our answer change if we required our payback period to be a maximum of 3 years? Note: Companies often have alternate cash flow needs, to make interest payments for example. Therefore it is important to not only look at the overall return of the investment, but also the structure of the cashflow. The answer to our question would be yes! Investment 2 has a payback period of 4 years which exceeds our payback requirement. We would, therefore, choose investment 1 which has a payback of 2 years (less than our required time).

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