

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:
А_{1} = А + A × r = A (1 + r),
Where:А_{2} = A_{1} (1 + r) = А (1 + r) (1 + r) = A (1 + r)^{2},
Accordingly, for n years the formula takes the form:
А_{n} = A_{n1} (1 + r)^{n} = A(1 + r)(1 + r)...(1 + r)_{n1} = A (1 + r)^{n}, 
[1] 
А_{month} = A (1 + r)^{1/12} ≈ A (1 + r)^{0,083}
А_{quarter} = A (1 + r)^{1/4} = A (1 + r)^{0,25}
А_{halfyear} = 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 = A_{n} / (1 + r)^{n}
And if we consider (instead of "А") a continuous discounted cash flow for n years (CF_{n}, we can deduce from formula [1] the following formula – for total discounted cash flow (DCF):
DCF = ∑ CF_{n} / (1 + r)^{n}
Where: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 "riskfree" 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.
