Present Value (PV)

(noun)

The value of the money today.

Related Terms

Examples of Present Value (PV) in the following topics:

  • The Relationship Between Present and Future Value

    • Present value (PV) and future value (FV) measure how much the value of money has changed over time.
    • The FV is calculated by multiplying the present value by the accumulation function.
    • On the other hand, the present value (PV) is the value on a given date of a payment or series of payments made at other times.
    • The process of finding the PV from the FV is called discounting.
    • If there are multiple payments, the PV is the sum of the present values of each payment and the FV is the sum of the future values of each payment.

  • Calculating Present Value

    • Calculating the present value (PV) is a matter of plugging FV, the interest rate, and the number of periods into an equation.
    • Finding the present value (PV) of an amount of money is finding the amount of money today that is worth the same as an amount of money in the future, given a certain interest rate.
    • Calculating the present value (PV) of a single amount is a matter of combining all of the different parts we have already discussed.
    • If it is compound interest, you can rearrange the compound interest formula to calculate the present value.
    • Distinguish between the formula used for calculating present value with simple interest and the formula used for present value with compound interest

  • Defining NPV

    • Net Present Value (NPV) is the sum of the present values of the cash inflows and outflows.
    • The net present value (NPV) is simply the sum of the present values (PVs) and all the outflows and inflows:
    • Also recall that PV is found by the formula $PV=\frac { FV }{ { (1+i) }^{ t } }$ where FV is the future value (size of each cash flow), i is the discount rate, and t is the number of periods between the present and future.
    • NPV = 0: The PV of the inflows is equal to the PV of the outflows.
    • There is no difference in value between the value of the money earned and the money invested.

  • Single-Period Investment

    • The time value of money framework says that money in the future is not worth as much as money in the present.
    • The value of the money today is called the present value (PV), and the value of the money in the future is called the future value (FV).
    • In order to find the PV, you must know the FV, i, and n.
    • That means that the PV is simply FV divided by 1+i.
    • Therefore, the PV is i% less than the FV.

  • Present Value of Payments

    • The formula for calculating a bond's price uses the basic present value (PV) formula for a given discount rate .
    • The bond price can be summarized as the sum of the present value of the par value repaid at maturity and the present value of coupon payments.
    • The present value of coupon payments is the present value of an annuity of coupon payments.
    • The present value is calculated by:
    • ${ PV }_{ A }={ PMT }_{ i }\cdot \left( 1-\frac { 1 }{ { (1+i) }^{ n } } \right)$

  • Single-Period Investment

    • What is the value of a single-period, $100 investment at a 5% interest rate?
    • PV=100 and i=5% (or .05) so FV=100(1+.05).
    • The amount of time between the present and future is called the number of periods.
    • As you know, if you know three of the following four values, you can solve for the fourth:
    • You want to know the value of your investment in the future, so you're solving for FV.

  • Present Value, Multiple Flows

    • The PV of multiple cash flows is simply the sum of the present values of each individual cash flow.
    • The PV of multiple cash flows is simply the sum of the present values of each individual cash flow .
    • You now have two present values, but both are still in the future.
    • The sum of all these present values is the net present value, which equals 65,816.04.
    • The PV of an investment is the sum of the present values of all its payments.

  • Calculating Annuities

    • So far, we have addressed ways to find the PV and FV of three different types of annuities:
    • The PV of a perpetuity is the payment size divided by the interest rate:
    • The PV of an annuity with the payments at the beginning of each period:
    • The PV of an annuity with the payments at the end of each period:
    • For example, note that the PV of an annuity-due is simply 1+i times the PV of an ordinary annuity.

  • Calculating the Yield of an Annuity

    • The yield of an annuity is commonly found using either the percent change in the value from PV to FV, or the internal rate of return.
    • Just as for a single payment, this method calculated the percentage difference between the FV and the PV.
    • Since annuities include multiple payments over the lifetime of the investment, the PV (or V1 in is the present value of the entire investment, not just the first payment.
    • The IRR is the interest rate (or discount rate) that causes the Net Present Value (NPV) of the annuity to equal 0.
    • That means that the PV of the cash outflows equals the PV of the cash inflows.

  • Calculating Perpetuities

    • The present value of a perpetuity is simply the payment size divided by the interest rate and there is no future value.
    • There is no end date, so there is no future value formula.
    • There is, however, a PV formula for perpetuities .
    • The PV is simply the payment size (A) divided by the interest rate (r).
    • The PV of a growing perpetuity is represented as $PVGP \ = \ {A \over ( i - g )}$ .