Discount rate: what is it, where to apply and how to calculate

What is a discount rate, what is it for and how to calculate it.We talk about this in our review of the Moscow Exchange Index IMOEX2373.26 -2,6% Index SPB100 Index SPB100 705,31 -0.82%82%82%

In this article you will learn

What it is How it appeared How to calculate Intuitive methods for determining the rate Calculation models based on risk premiums Analytical calculation methods How it is applied What is the discount rate

The discount rate  is a reference value, expressed as a percentage, used for a comparative assessment of the effectiveness of investments.

For example, you need to choose whether to put money in a bank with a deposit rate of 12% for a period of five years with annual interest payments or buy bonds   maturing in nine years with an 8.5% coupon paid twice a year and with a current price of 91% of face value . How will you choose, given that the inflation rate is about 8%?

Analyst deals with valuation (Photo: Shutterstock)

To solve these problems, a technique is used, which is called. With the help of discounting, you can compare future cash flows and choose the most profitable from several investment options. And the discount rate is the key element used in the discounting technique.

The correct calculation of the discount rate will allow you to:

evaluate the effectiveness of investments in relation to reliable deposits; compare investment options with different investment durations; compare the return on investment of instruments with different degrees of risk.

The discount rate depends on many factors: the level of inflation, the investment options available to the investor, the risk of investments, the cost of your capital, etc. But not all external factors can be reliably taken into account in the rate.

How did the discount rate come about?

Initially, the discount rate was applied when discounting promissory notes. When accepting a bill of exchange for payment, the bankers knew the amount they would receive when they presented the bill for redemption. But in order for them to earn money themselves, the bankers paid the bearer money at a discount - a discount. And the interest rate at which their income was measured was called the discount rate or the discount rate. The amount that was paid to the bearer of the bill was calculated precisely with the help of discounting - knowing how much he would receive in the future and taking into account the current level of interest rates, the banker determined the current value of money.

This technique turned out to be so universal and useful that it has become widely used in evaluating and comparing the effectiveness of investments in different instruments or projects. When discounting, an investor, like a banker when discounting promissory notes, recalculates the value of the money that he will receive in the future, and at completely different times, to the current value. He, as it were, projects the value of money from the future onto the plane of the present. And the central link in the calculations is the discount rate.

What is a bill and how to use it Banking and finance , Central Bank , Credit , Deposit

How to calculate the discount rate

When calculating the discount rate, it is very important to determine the rate that will allow you to correctly bring the future value of income and expenses to the current one. To do this, it is necessary to take into account both the general level of interest rates and the risk factors of investing in individual instruments.

When calculating the discount rate, you need to take into account

The level of risk-free rates. Risk premiums.

Risk-free rates  are interest rates for instruments with a minimum level of risk for an investor. Usually such instruments are bonds of the central government - OFZ in RUSSIA, US Treasuries in the usa , etc. The rates on deposits of systemically important banks can also be taken into account as risk-free rates. Sometimes the key rate of central banks can be considered as the risk-free rate.

The level of risk-free rates is fundamental - it determines the minimum level of all discount rates.

Risk  premiums are premiums on the level of risk-free rates that should be taken into account when investing in individual instruments or projects. These can be general factors - the level of inflation, the premium for country risk; or factors that take into account the risk of investing in individual instruments - industry risk premium, individual risk premium (depending on the reliability of the issuer, instrument or project).

Taking into account risk premiums will allow you to fine-tune the discounting tool to avoid mistakes in comparing different investments.

When calculating the discount rate, various methods and methods are used, which can be combined into the following main groups:

Intuitive methods; Models based on risk premiums; Analytical models Intuitive methods

This group includes

Actually an intuitive method. expert method.

The intuitive method  is a way of determining the discount rate based on the subjective view of the investor. Simply put, when an investor estimates the discount rate almost by eye. For example, he argues like this: “I can put money on a deposit in a reliable bank at 12-15%. Then I will compare the effectiveness of other investments with this level of rates.”

The expert method  is essentially the same intuitive method, only the final value of the discount rate is derived as a cumulative consensus of several experts with one or another level of validity of their opinions.

Analysts confer (Photo: Shutterstock)

Risk premium models

Risk premium models include, for example, models such as

Model of cumulative construction; CAPM capital asset model.

What these models have in common is that the discount rate is derived as the sum of the risk-free rate and risk premiums.

Cumulative construction models  are a method of determining a discount rate in which all the risk premiums that can be determined for a particular instrument are added to the risk-free interest rate.

The formula for calculating the discount rate in a cumulative way looks like this:

where r0 is the risk-free rate,

r1, r2, rn are all risk premiums for the instrument being valued.

The CAPM (Capital Asset Pricing Model) is a method for determining the discount rate for the comparative evaluation of the effectiveness of investments in shares, in which a risk premium for an individual instrument is added to the risk-free interest rate, taking into account its β-coefficient.

The β-coefficient (Beta-coefficient) is a measure of the market risk of a stock, which shows the volatility of a stock's return relative to the market's average return. The β-coefficient numerically shows by what percentage the stock price of a security changes with an increase or decrease in the index by 1%. A positive ratio indicates that the stock is moving in the same direction as the market, while a negative ratio means that the stock is moving in the opposite direction from the general direction of the market.

β-coefficients are calculated and published by both analysts and trading platforms, such as the Moscow Exchange.

The formula for calculating the CAPM discount rate looks like this:

where r0 is the risk-free rate,

β is the β-coefficient,

rf is the average return of the stock market (stock index).

Analytical charts (Photo: Shutterstock)

Analytical Methods

Analytical methods - methods for calculating the discount rate, using elements of financial analysis. Analytical methods include

WACC Multiplicative Methods

WACC  is the Weighted Average Cost of Capital. WACC is used by companies to compare the effectiveness of investment projects.

As a rule, a company has two types of capital used - equity and debt. Equity is equal to the amount of funds owned by the company itself or due to its shareholders. Borrowed capital is the funds attracted by the company from outside (credits and loans). Borrowed capital does not come to the company for free - it must pay interest on loans and borrowings.

In the case when a company or an investor has only borrowed money, then the most important thing for them is that investment projects bring more than they have to pay on the loan. In this case, when evaluating investment projects, the loan rate adjusted for the income tax rate can be used as the discount rate.

But when a company has both own and borrowed capital, then the discount rate according to the WACC model is calculated as follows

where re is the cost of equity,

Se is the share of equity,

rd is the cost of borrowed capital,

Sd - share of borrowed capital

t is the income tax rate.

The cost of borrowed capital rd is the weighted average interest on existing loans and credits.

The cost of equity re can be determined either by the CAPM method described above, or in another way, for example, using the Gordon model.

The Gordon model for estimating the value of a company's equity assumes that the company pays dividends for the opportunity to use equity. This means that the cost of equity capital is determined by the ratio of the amount of dividends paid to the amount of money raised during the placement of shares.

As a result, the formula by which the cost of equity according to Gordon is calculated looks like this:

where DIV is the amount of annual expected dividends per share;

P is the placement price of shares;

fc - emission costs (in %);

g is the growth rate of dividends.

Multiplicative methods  are ways of calculating the discount rate based on different growth rates and other business factors.

It could be, for example

Rate calculation based on return on equity (ROE). When ROE is taken as the discount rate. Rate calculation based on return on assets (ROA). When ROA is taken as the discount rate. Calculation of the rate based on market multipliers. When the discount rate is taken as the value of profitability as the ratio of forecasted income to the current market value of the company. For example, the forecast value of net earnings per share (EPS) to the market value of shares or the forecast value of cash flow to capitalization

EPS: what is earnings per share and what does it give an investor EPS , Financial statements , Investments , Financial analysis , Multiples

How the discount rate is applied

As we wrote at the beginning, the discount rate is the key element used in the discounting technique.

Discounting is the reduction of the future value of cash flows to the present value at a discount rate.

One of the frequent results of discounting is the net present value of money.

Net present value (NPV, Net Present Value) - the difference between all cash inflows and outflows, reduced to the current time at a discount rate. This value shows the amount of cash that the investor expects to receive from the project, recalculated to date.

By comparing the NPV of investment options of different duration, the investor can choose the most profitable one.

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A debt security whose owner has the right to receive from the person who issued the bond its face value within a specified period. In addition, the bond implies the right of the owner to receive a percentage of its face value or other property rights. Bonds are the equivalent of a loan and are similar in principle to the lending process. Both governments and private companies can issue bonds.