Present Value, Functions

Present Value (PV) concept refers to the current worth of a future sum of money or stream of cash flows, discounted at a specific interest rate. It reflects the principle that a dollar today is worth more than a dollar in the future due to its potential earning capacity.

PV = FV / (1+r)^n

where

FV is the future value,

r is the discount rate,

n is the number of periods until payment.

This concept is essential in finance for assessing investment opportunities and financial planning.

Functions of Present Value:

• Valuation of Cash Flows:

PV allows investors and analysts to evaluate the worth of future cash flows generated by an investment. By discounting future cash flows to their present value, stakeholders can determine if the investment is financially viable compared to its cost.

• Investment Decision Making:

In capital budgeting, PV is crucial for assessing whether to proceed with projects or investments. By comparing the present value of expected cash inflows to the initial investment (cost), decision-makers can prioritize projects that offer the highest returns relative to their costs.

• Comparison of Investment Alternatives:

PV provides a standardized method for comparing different investment opportunities. By converting future cash flows into their present values, investors can effectively evaluate and contrast various investments, regardless of their cash flow patterns or timing.

• Financial Planning:

Individuals and businesses use PV for financial planning and retirement savings. By calculating the present value of future financial goals (like retirement funds), individuals can determine how much they need to save and invest today to achieve those goals.

• Debt Valuation:

PV is essential for valuing bonds and other debt instruments. The present value of future interest payments and the principal repayment is calculated to determine the fair market value of the bond. This valuation helps investors make informed decisions about purchasing or selling bonds.

• Risk Assessment:

Present Value helps in assessing the risk associated with investments. Higher discount rates, which account for risk and uncertainty, lower the present value of future cash flows. This relationship allows investors to gauge the risk-return trade-off of different investments effectively.

Present Value of a Single Flow:

Used when we have a single future amount to be received after a certain time.

Formula:

PV = FV / (1+r)^n

Example:

You will receive ₹15,000 after 3 years. What is its present value if the discount rate is 10%?

PV = 15000(1+0.10)^3 = 15000 / 1.331 = ₹11,270

This applies when cash flows are not equal each year. Each amount is discounted separately.

Example:

You will receive ₹2,000 in Year 1, ₹3,000 in Year 2, and ₹4,000 in Year 3. Discount rate = 10%

Present Value of an Annuity (Ordinary Annuity):

Used when you receive equal payments at the end of each period for a specific number of years.

Example:

You will receive ₹2,000 every year for 3 years. Discount rate = 10%

PV = 2,000 × (1−(1+0.10)^−3 / 0.10) = 2,000 × 2.487 = ₹4,974