The perpetual annuity is based on assumptions of constant growth and a constant discount rate and is used in business valuation in both the Income approach and the DCF (discounted cash flow) method.
The perpetual annuity is based on assumptions of constant growth and a constant discount rate and is used in business valuation in both the Income approach and the DCF (discounted cash flow) method.
In the DCF method, the perpetual annuity is used to estimate the value of the company after the end of a certain forecast period for an indefinite period in order to determine its present value. In the Income approach, the perpetual annuity is used to estimate the terminal value if the company's exact cash flows are difficult to predict for the indefinite future. The terminal value thus describes the value contribution of the period after the defined forecast period as a going concern value.
Cash flow (DCF approach) or income (Income approach) in perpetuity is considered an extremely value-sensitive parameter in the context of business valuation. In a 5-year detailed planning phase with a subsequent rough planning phase, it is not uncommon for the terminal value to account for more than 75% of the company value. In the valuation of SMEs with frequently shorter planning periods of only 3 years or with very ambitious growth plans, this value is often even higher than the 85% mark.
Calculating the perpetuity for business valuation is a simple mathematical matter. The valuer needs a "sustainable" cash flow or income, a growth rate and an appropriate discount rate for the value contribution.
Less trivial than the pure calculation is the determination of the three parameters mentioned above, as shown below. No explicit distinction is made between the DCF and Income approach, as both methods are based on the correct determination of the same influencing factors.
In the DCF approach, the cash flow corresponds to the free cash flow of the last forecast year; in the Income approach, it corresponds to the forecast income of the last year of the planning period.
The two variables, growth rate and capitalization rate, are not initially directly related to each other. On closer inspection, however, it becomes clear that both the discount rate and the growth rate have a common component: the general rate of price increase. According to accepted opinion in theory and practice, a discount rate is made up of the following components:
The growth rate of the perpetual annuity is also made up of several components:
Volume growth rarely plays a dominant role for established companies. For young, fast-growing companies, business expansion is conceivable for a longer period of time, but certainly not indefinitely. Increases in production efficiency are also limited, at least in the long term.
The growth rate is therefore always significantly influenced by the price increase on the income side and the price increase on the cost side. In the long term, however, both cannot deviate significantly from the general rate of price increases in the economy, i.e. the inflation rate, under the "going concern" premise.
Read more on the topic here: Sustainable growth rate
It becomes problematic when the valuation implicitly incorporates two different assumptions regarding long-term price increases. In a low interest rate environment, even experienced business valuers can make this mistake more quickly than expected.
On April 30, 2019, the value for the 30-year risk-free federal interest rate - calculated using the Svensson method and published on the Bundesbank's website - was 0.78 % p.a. It is not easy to say what proportion is due to the real interest rate and what proportion is due to inflation expectations. Negative real yields are certainly conceivable, and a liquidity premium in bond trading can also be assumed. Nevertheless, there is much to suggest that current inflation expectations do not correspond to the ECB's inflation target of 2.0%. In this respect, when determining the long-term growth rate, business valuers should not be overly generous with the component attributable to price increases.
The correct estimation of the cost of capital plays a decisive role in the present value, as it is used as the discount rate. Various factors such as the company's risk and market interest rates are taken into account. With smartZebra's cost of capital module, the cost of capital can be determined quickly and easily in accordance with common standards.
As companies cannot usually grow at a certain growth rate for all eternity, a growth discount is also included in the calculation. It is a measure of how much of the expected growth rate of the perpetuity is considered "risky" by the investor. It is typically determined using a growth model based on historical data and future forecasts. A common model is the Gordon Growth Model, which calculates the growth discount as the difference between the expected growth rate of the perpetuity and the discount rate. The inverse of this is the present value factor, which is also referred to as the excess return. The present value factor is used to calculate the present value of the perpetual annuity by multiplying it by the expected annual cash flow. This results in the annual present value, which is then discounted to a current present value.
Perpetuity is a critical component of business valuation, especially in the DCF and Income approach. Accurately determining the growth rate, discount rate and sustainable cash flow is crucial for a realistic valuation. smartZebra's tools and expertise can help to carry out these complex valuation processes efficiently and accurately.
