present value

Examples of present value in the following topics:

• Present Value of Payments

  • The bond price can be calculated using the present value approach.
  • 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:
  • Bond price is the present value of coupon payments and face value paid at maturity.

• Discounted Cash Flow Approach

  • This finds discounted present values (DPV).
  • These present values are summed to give the net present value (NPV) of the asset.
  • -- To find the discounted present value of an asset, it is necessary to sum the discounted present value of each future cash flow (FV) at any time period (t) in years from the present time, using the appropriate interest rate (i).
  • -- Use this equation to find the present value of a future terminal value.
  • To find the discounted present value of an asset, it is necessary to sum the discounted present value of each future cash flow (FV) at any time period (t) in years from the present time, using the appropriate interest rate (i).

• 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

• Impact of Payment Frequency on Bond Prices

  • Bond prices is the present value of all coupon payments and the face value paid at maturity.
  • In other words, bond price is the sum of the present value of face value paid back at maturity and the present value of an annuity of coupon payments.
  • For bonds of different payment frequencies, the present value of face value received at maturity is the same.
  • However, the present values of annuities of coupon payments vary among payment frequencies.
  • Bond price is the present value of all coupon payments and the face value paid at maturity.

• 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.
  • The value does not include corrections for inflation or other factors that affect the true value of money in the future.
  • 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.
  • 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.

• Defining NPV

  • Net Present Value (NPV) is the sum of the present values of the cash inflows and outflows.
  • Since cash flows occur over a period of time, the investor knows that due to the time value of money, each cash flow has a certain value today .
  • 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.
  • There is no difference in value between the value of the money earned and the money invested.

• Deciding to Refund Bonds

  • The decision of whether to refund a particular debt issue is usually based on a capital budgeting (present value) analysis.
  • The principal benefit, or cash inflow, is the present value of the after-tax interest savings over the life of the issue.
  • Step 1: Calculate the present value of interest savings (cash inflows):
  • Net present value of refunding = Present value of interest savings - Present value of net investment

• MVA and EVA

  • Market Value Added (MVA) is the difference between the current market value of a firm and the capital contributed by investors.
  • If the MVA is positive, the firm has added value.
  • where: MVA is market value added, V is the market value of the firm, including the value of the firm's equity and debt, and K is the capital invested in the firm.
  • The firm's market value added, or MVA, is the discounted sum (present value) of all future expected economic value added: MVA = Present Value of a series of EVA values.
  • MVA is the present value of a series of EVA values.

• Par Value at Maturity

  • Par value is stated value or face value, with a typical bond making a repayment of par value at maturity.
  • Par value, in finance and accounting, means the stated value or face value.
  • From this comes the expressions at par (at the par value), over par (over par value) and under par (under par value).
  • Below is the formula for calculating a bond's price, which uses the basic present value (PV) formula for a given discount rate .
  • Bond price is the present value of coupon payments and the par value at maturity.

• Market Value vs. Book Value

  • Book value is the price paid for a particular asset, while market value is the price at which you could presently sell the same asset.
  • Market value is often used interchangeably with open market value, fair value, or fair market value.
  • In accounting, book value or carrying value is the value of an asset according to its balance sheet account balance.
  • If the asset is valued on the balance at market value, then its book value is equal to the market value.
  • Market value is the asset's worth if it were to be exchanged in the open market in an arm's length transaction; it can also be derived based on the asset's present value of the expected cash flows it will generate.