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Investment analysis

Discounting (Present Value, PV)
Determining the level of the discount rate
Model weighted average cost of capital – WACC
Methods of calculation of indicators of investment effectiveness in simple examples
Types of cash flows
Features of the calculation of cash flows in Budget-Plan Express
Settings of calculation parameters
The present value of cash flow postnumbero and prenumerando
Cash Flow Forecast

Investment analysis. Discounting (Present Value, PV)


Deducing of the formula of discounted money (Present Value, PV)

Discount is the determination of the value of future cash flows. Discount is the basis for calculating the cost of money taking into account the time factor.

To derive the discount formula, for starters, let us recall the calculation of annuities using the formula of complex rent. The same money, as you know, have different values over time. The use of interest in calculating the value of money is associated with the notion of financial rent, when the value of money depends on the percentage and duration of their use. For example, the cost of money (payments for a loan) in a year can be calculated as:

    А1 = А + A × r = A (1 + r),

    Where:
    А – Current value of money
    А1 – The future (in a year) cost of money
    r – annual percentage (coefficient)

    Then, in two years, the value of money can be calculated by the formula:

    А2 = A1 (1 + r) = А (1 + r) (1 + r) = A (1 + r)2,

    Accordingly, for n years the formula takes the form:

    Аn = An-1 (1 + r)n = A(1 + r)(1 + r)...(1 + r)n-1 = A (1 + r)n,    

    [1]

This formula [1] is known as the formula for calculating rent annuities (by complex percent). It is easy to understand that, for example, payments in intermediate periods are calculated as follows:

    Аmonth = A (1 + r)1/12A (1 + r)0,083
    Аquarter = A (1 + r)1/4 = A (1 + r)0,25
    Аhalf-year = A (1 + r)1/2 = A (1 + r)0,5 … and so on

Discounted cash flows are calculated using the reverse of complex rents. To do this, output the number A from the formula [1] - the cost of future money:

    A = An / (1 + r)n

And if we consider (instead of "А") a continuous discounted cash flow for n years (CFn, we can deduce from formula [1] the following formula – for total discounted cash flow (DCF):

    DCF = ∑ CFn / (1 + r)n

    Where:
    CFn – cash flow for n periods;
    r – discount rate (for example, weighted average cost of capital, WACC can be used as the discount rate);
    n – is the number of periods by which cash flows are calculated.

Now the coefficient r is the discount rate coefficient. In assessing the effectiveness of projects (business plans), the discount rate is a kind of risk level, beyond which investment indicators are calculated, sometimes called the discount rate barrier or "risk-free" rate. These concepts do not always coincide. Barrier rate, or the effective barrier rate is the interest rate that determines the minimum expected return on investment for a particular investor. If the expected return on investment is less than the barrier rate, the investment does not make sense.



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