## Holding Period Return

Earlier in this chapter, we noted that the total return from an investment consists of current cash income and capital gain (or loss). We take into account both of these components while calculating the return. **Holding period return** is such a measure of investment return that considers both current cash income and capital gain income.

The **holding period**, here, refers to the time period for which the investment return is calculated. Most analysts use an investment horizon of one year or less as the holding period. For example, if you buy shares of common stock today and then sell the stock at the end of a year after realizing cash dividend, your holding period is one year and the rate of return you realize during one year of investment is called the holding period return. Thus, holding period return is the total rate of return from an investment over a single period of the investment horizon. We use the following equation to calculate the holding period return:

**Current income + Capital gain (loss) /Beginning investment value **

Current income refers to the cash income such as dividend on common stock investment and interest on a bond investment. Capital gain (or loss) results from the change in investment value at the end as compared to the beginning. It is simply a difference between the sales value of the investment at the end and the purchase value of the investment at the beginning of the period.

It should be noted that all of the investment returns are not realized in cash. Especially, capital gains are realized only when the investment is sold off. Though not realized, we need to incorporate the unrealized return as well to work out the holding period return.

Further, it should also be noted that holding period return can be calculated from historical data. Such holding period return is called observed holding period return or ex-post holding period return. It can also be calculated from forecast data for future periods. It is called the expected holding period return or er-ante a holding period return.

## Internal Rate of Return

The holding period return we discussed in the previous section is an appropriate measure of investment return if the investment is held for less than or equal to one year of the period. For a longer holding period, HPR is not appropriate as it does not consider the time value of money. Thus, the **internal rate of return** (IRR), simply called ‘yield’ is an alternative measure used to express the annualized rate of return on investment withholding period of more than one year.

IRR or yield is a return measure that recognizes the concept of the time value of money. Further, the IRR method also considers cash flows (deposits and withdrawals) that occur within the investment horizon, therefore, it is also known as cash flow weighted rate of return. Conceptually, IRR is the discount rate at which the present value of benefits from an investment is equal to the present value of the cost of investment.

The internal rate of return is compared against the required return to conclude the performance of an investment. If IRR is greater than or equal to the required return, the investment performance is said to be satisfactory. Such investments are worth investing in from the viewpoint of the time value of money as well. In contrast, if IRR is lower than the required return we do not accept such investment as it erodes investor wealth. In the following section, we explain the procedure of calculating the internal rate of return for several types of cash flows.

**IRR OR YIELD FOR A SINGLE CASH FLoW**: If an investment produces only one cash flow or benefit over its life, the calculation of IRR or yield is simple. In this case, IRR or yield is the discount rate at which the present value of future single cash flow of investment is equal to the investment cost. It is worked out using the following equation: **PV= FVn /(1+ IRR)n **