4.7 Discounting techniques – Present value (PV) of a future cash flow and series of future cash flows and discounting of annuity cash flows

Discounting techniques are used to calculate the present value of future cash flows by applying a discount rate that represents the time value of money. These techniques help determine the current value of future cash flows, considering the fact that money received in the future is worth less than the same amount received today. Here are the common discounting techniques:

1. Present Value (PV) of a Future Cash Flow: This technique calculates the present value of a single future cash flow. The formula for calculating the present value is:PV = FV / (1 + r)^nWhere: PV = Present value FV = Future value of the cash flow r = Discount rate (interest rate per compounding period) n = Number of compounding periods

   This formula discounts the future cash flow back to its present value, reflecting the time value of money.

2. Present Value (PV) of a Series of Future Cash Flows: When there are multiple future cash flows occurring over a period of time, the present value of the entire series can be calculated. Each future cash flow is discounted individually to its respective present value, and then the present values are summed to determine the total present value. The formula for calculating the present value of a series of future cash flows is:PV = CF₁ / (1 + r)^n₁ + CF₂ / (1 + r)^n₂ + … + CFₙ / (1 + r)^nₙWhere: PV = Present value of the series of cash flows CF₁, CF₂, …, CFₙ = Individual future cash flows n₁, n₂, …, nₙ = Number of compounding periods for each cash flow r = Discount rate (interest rate per compounding period)

   This technique discounts each future cash flow back to its respective present value, considering the time value of money.

3. Discounting of Annuity Cash Flows: Similar to the compounding of annuity cash flows, the present value of an annuity can be calculated using a simplified formula that accounts for the regularity of the cash flows. The formula for calculating the present value of an annuity is:PV = Pmt * [1 – (1 + r)^(-n)] / rWhere: PV = Present value of the annuity Pmt = Payment amount (equal cash flow) r = Discount rate (interest rate per compounding period) n = Number of compounding periods

   This formula discounts the regular annuity cash flows back to their present value, considering the time value of money.

These discounting techniques help in evaluating the present value of future cash flows, including single cash flows, series of cash flows, and annuity cash flows. By applying a discount rate, they adjust future cash flows to their current value, enabling better financial analysis, decision-making, and comparison of investment alternatives.

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