growth rate

(noun)

The percentage by which the payments grow each period.

Examples of growth rate in the following topics:

  • Expected Dividends and Constant Growth

    • Valuations rely heavily on the expected growth rate of a company; past growth rate of sales and income provide insight into future growth.
    • Valuations rely very heavily on the expected growth rate of a company.
    • One must look at the historical growth rate of both sales and income to get a feeling for the type of future growth expected.
    • Calculating the future growth rate requires personal investment research.
    • It assumes that dividends will increase at a constant growth rate (less than the discount rate) forever.

  • Assessing Internal Growth and Sustainability

    • What is its sustainable growth rate?
    • Sustainable Growth Rate = (750,000/5,000,000) x (1-0.80).
    • Sustainable Growth Rate = 3%
    • The internal growth rate is a formula for calculating maximum growth rate that a firm can achieve without resorting to external financing.
    • Therefore, a more commonly used measure is the sustainable growth rate.

  • Relationships between ROA, ROE, and Growth

    • What is the company's ROA and internal growth rate?
    • What is the company's ROE and sustainable growth rate?
    • ROA = 500,000/3,000,000 = 17% Internal growth rate = 17% x 80% = 13% ROE = 17% x (3,000,000/1,500,000) = 34% Sustainable growth rate = 34% x 80% = 27.2%
    • In terms of growth rates, we use the value known as return on assets to determine a company's internal growth rate.
    • This is the maximum growth rate a firm can achieve without resorting to external financing.

  • Long Run Growth

    • Over long periods of time even small rates of growth, like a 2% annual increase, have large effects.
    • A growth rate that averaged 1.97% over 178 years resulted in a 32-fold increase in GDP by 2008 .
    • The large impact of a relatively small growth rate over a long period of time is due to the power of compounding.
    • A growth rate of 2.5% per annum leads to a doubling of the GDP within 29 years, while a growth rate of 8% per annum (an average exceeded by China between 2000 and 2010) leads to a doubling of GDP within 10 years.
    • Growth in GDP can be significant, especially when annual growth rates are fairly consistent.

  • Exponential Growth and Decay

    • Exponential growth occurs when the growth rate of the value of a mathematical function is proportional to the function's current value.
    • Exponential growth occurs when the growth rate of the value of a mathematical function is proportional to the function's current value.
    • Exponential decay occurs in the same way, providing the growth rate is negative.
    • The formula for exponential growth of a variable $x$ at the (positive or negative) growth rate $r$, as time $t$ goes on in discrete intervals (that is, at integer times 0, 1, 2, 3, ...), is:
    • For example, with a growth rate of $r = 5 \% = 0.05$, going from any integer value of time to the next integer causes $x$ at the second time to be $1.05$ times (i.e., $5\%$ larger than) what it was at the previous time.

  • Valuing Nonconstant Growth Dividends

    • When a stock has a significantly higher growth rate than its peers, it is sometimes assumed that the earnings growth rate will be sustained for a short time (say, 5 years), and then the growth rate will revert to the mean.
    • To do this, one takes the average P/E and average growth for a comparison index, uses the current (or forward) P/E of the stock in question, and calculates what growth rate would be needed for the two valuation equations to be equal.
    • This gives you an estimate of the "break-even" growth rate for the stock's current P/E ratio.
    • Subsequently, one can divide this imputed growth estimate by recent historical growth rates.
    • Describe the limitations of valuing a company with dividends that have a nonconstant growth rate

  • Population Growth

    • Namely, it is given by the formula $P(r, t, f)=P_i(1+r)^\frac{t}{f}$ where $P{_i}$ represents the initial population, r is the rate of population growth (expressed as a decimal), t is elapsed time, and f is the period over which time population grows by a rate of r.
    • It is the Population Growth Rate ($PGR$).
    • A positive growth rate indicates an increasing population size, while a negative growth rate is characteristic of a decreasing population.
    • A growth rate of 0 means stagnation in population size.
    • If the current rates of births and deaths hold, the world population growth can be modeled using an exponential function.

  • Arguments in Favor and Opposed to Economic Growth

    • Over the long-run economists might look at the per-capita rate of GDP growth (the growth of the ratio of GDP to the population).
    • With a small growth rate, a country will experience a substantial increase in power over the long-run.
    • For example, a growth rate of 2.5% per annum leads to a doubling of the GDP within 29 years.
    • In contrast, a growth rate of 8% per annum leads to a doubling of the GDP within 10 years.
    • For example, in a country with low inequality, a country with a growth rate of 2% per head and 40% of the population living in poverty can halve the poverty in 10 years.

  • Generation Time

    • In many types of cancer, the rate at which tumors shrink following chemotherapy is related to the rate of tumor growth before treatment.
    • If growth is not limited, doubling will continue at a constant rate so both the number of cells and the rate of population increase doubles with each consecutive time period.
    • The slope of this line is the specific growth rate of the organism, which is a measure of the number of divisions per cell per unit time.
    • The actual rate of this growth (i.e. the slope of the line in the figure) depends upon the growth conditions, which affect the frequency of cell division events and the probability of both daughter cells surviving.
    • This basic batch culture growth model draws out and emphasizes aspects of bacterial growth which may differ from the growth of macrofauna.

  • Determinants of Long-Run Growth

    • It is measured as the percentage rate change in the real gross domestic product (GDP) .
    • In countries with high development and industrialization, labor force participation is high because of low birth and death rates.
    • As a result, more jobs would be available and the employment rate would also increase.
    • A high rate of population growth will cause less capital per worker, lower productivity, and lower GDP growth.
    • Economic growth is the percentage rate increase in the GDP.