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The objective of any investor is to maximize expected returns from his investments, subject to various constraints, primarily risk. Return is the motivating force, inspiring the investor in the form of rewards, for undertaking the investment. The importance of returns in any investment decision can be traced to the following factors:

• It enables investors to compare alternative investments in terms of what they have to offer the investor.
• Measurement of past returns enables the investors to assess how well they have done.
• Measurement of historical returns also helps in estimation of future returns.

 

Why are we discussing the return so much? The value of the security to an investor is directly proportional to the return that he is expected to get from that security. Higher the return expected, higher is the value. But what are we going to do with the value of the security? Well, value of the security is the price that you are going to pay for that security. This means that the present value of the security is that value which is dependent on the return from the security and the risk profile of that security. Now let us go further on return.

 

The Components of Return

 

Return is basically made up of two components:

• The periodic cash receipts or income on the investment in the form of interest, dividends, etc. The term yield is often used in connection with the component of return. Yield refers to the income derived from a security in relation to its price, usually its purchase price.
• The appreciation (depreciation) in the price of the asset is referred to as capital gain (loss). This is the difference between the purchase price and the price at which the asset can be, or is, sold.

 

Measuring the Rate of Return

 

The rate of return is the total return the investor receives during the holding period (the period when the security is owned or held by the investor) stated as a %age of the purchase price of the investment at the beginning of the holding period. In other words it is the income from the security in the form of cash flows and the difference in price of the security between and the end of the holding period expressed as a %age of the purchase price of the security at the beginning of the holding period.  Hence, total return can be defined as:

 

Total Returns = Cash Payments received + Price change over the period

                                                Purchase price of the asset

 

The price change over the period is the difference between the beginning (or purchase) price and the ending (or sales) price.  This can be either positive (sales price exceeds purchase price) or negative (purchase price exceeds sales price).

The general equation for calculating the rate of return for one year is shown below:

                                      K =  [D_t + (P_t - P_t-1)]

                                                       P_t-1

                   where K     =   Rate of Return

                    P_t   =     Price of the security at time "t" i.e., at the end of the holding period.

                    P_t-1   =   Price of the security at time "t-1" i.e., at the beginning           of  the
                                    holding period or purchase price.

                    D_t   =    Income or cash flows receivable from the security at time "t".

 

Rate of Return of a Bond

 

In case of bonds, instead of dividends, the investor is entitled to payments of interest annually or semi-annually. The investor also benefits if there is an appreciation in the value of bond, otherwise there is the redemption of the bond at par value or at premium.

 

Using the present value formula developed above we can say that:

 

Here interest amount is individually brought to its present value or we can apply the annuity factor table to get its present value. The principal amount is brought to its present value when it is due.

Or to use the tables the change would be:

Present Value = Interest Amount * (Present Value Annuity Factor_n,i)

                                      + Principal Amount * (Present Value Interest Factor_n,i)

Example

A bond is paying 10 % interest per annum and is going to mature in the next two years  At maturity it will pay its principal amount of Rs 100. If the expected return on bonds today are (i) 7 %, (ii) 10 % and (iii) 15 %, what value would you pay for the bond today.

Solution

Using the above formula for situation 2), we can say that

Or to use the tables the change would be:

Present Value = 10 * (PVAF_2,0.1)

                                      + 100 * (PVIF_2,0.1)

Substituting the values we find that

Present Value = 100

This is no magic. When you are getting a 10 % return and also expect a 10 % return, the price you would pay would equal the par value of the bond. This means that if we expect higher return i.e. 15% in situation (iii) above, the price that we would be willing to pay for a bond returning only 10 % would be less than the par value. Similarly, if we expect lower return, i.e., 7% in situation (i) above, the price that we would be willing to pay for a bond returning 10 % would be higher than the par value. Can you find out the values for these two cases?

There are five variables in this case: (1) present value, (2) future value, (3) interest amount paid, (4) return expected and (5) time period. Properties of mathematics say that if any four of these five variables are given, you can always find the value of the fifth variable.

 

A stocks rate of return

 

In case of shares the first component is "D_t" which is nothing but the income in cash from dividends and the second component is the price change (appreciation and depreciation).

 

This means that the price you are willing to pay for a share today is a function of the dividends that you expect to receive and the present value of the expected future share price.

 

But what if you are going to hold the share to maturity and not sell. Then your only return is the dividend amount. This means that this perpetual dividend is what you would use to value the share. So you simply use the perpetuity formulas mentioned above for constant or growing dividends.

 

Finding out the present value of the share seems easy-Doesn't it! Now comes the tedious question, what return do you expect from the security? Now every security has a different risk profile and you being a rational human being would expect a return that is commensurate with the risk that you are going to bear. So let us devote some time to understand the nature of risk and then how do we use this knowledge to reach the desired rate of return on the share.