TIME VALUE OF MONEY

TIME VALUE OF MONEY

To illustrate the time value of money, suppose an investor expects to receive $100 three years from now and that the investor can invest at a constant 5% annual investment rate. Based on the time value of money equation, the $100 to be received three years from now has a present value of $100/(1+.05)^3 = $86.38. Time value of money then suggests that at a 5% annual rate, $100 three years from now is equivalent to $86.38 today.

The longer it takes to collect all of the payments that are due on the note the discount will be more significant. Thus, time value of money concludes that, if there is an investment vehicle with a positive real rate of return, owning a dollar today is worth more than owning a dollar in the future. The time value of money concept has numerous applications in finance including but not limited to the valuation of annuities, bonds, and equities. Time value of money is also applied to solve calculations such as net present value and internal rate of return.

The time value of money states that by paying cash today to receive cash tomorrow, the seller’s note will have to get a discount because the lender/investor will have to wait to collect their money.  A note seller always has to take  discount to pay for his risk and the alternate fees, which may be charged against the paper.

The longer the lender has to  wait to get their money back, the less they can pay today.  The shorter the time before the lender can get his money, the more he is willing to pay today, though the seller’s note still must get a discount.

Whenever anyone pays cash today to receive cash at some future date, you have to get a discount because time erodes the value of the money.

Let me give you a simplified example of the time value of money. When someone has a baby, a frequent gift to the new child is a U.S. Savings Bond.  It’s a great gift, because it matures in twenty years, when the infant will be an adult, either in college or perhaps starting a family and setting up a household.

Suppose you buy the child a $100 savings bond.  Do you pay $100 for it?  No.  The bond is worth $100 at maturity, so you pay much less.  Would you pay $100 for that twenty-year bond now?  Would you pay $100 today to receive $100 in twenty years?   Of course you wouldn’t.  You’d pay maybe $50 or $60 dollars today.

This is exactly how the time value of money works in a very simple example, familiar to everyone.  It’s paying less for something today because you will get your money back at a future date.

When you buy a bond, the certificate states that it will pay a certain rate of compound interest.  The compound interest will result in the $100 payoff at maturity.  If you cash in the bond before maturity, you get less than the face amount of $100 because it will not yet have earned enough interest.

The time value of money, states that by paying cash today to receive cash tomorrow , the seller’s note will have to get a discount because the lender/investor will have to wait to collect their money.

The longer the lender has to wait to get their money back, the less they can pay today.

Whenever anyone pays cash today to receive cash at some future date, you have to get a discount because time erodes the value of the money.

Let me give you a simplified example of the time value of money.  When someone has a baby, a frequent gift to the new child is a U.S. Savings Bond.  It’s a great gift because it will mature in twenty years, when the infant will be an adult. either in college or perhaps starting a family and setting up a household.

Suppose you buy the child a $100.00 savings bond.  Do you pay $100.00 for it?  NO.  The bond is worth $100.00 at maturity, so you pay much less.  Would you pay $100.00 for that twenty year bond right now?  Of course you wouldn’t, you would probably pay $50.00 or $60.00 today.

This is exactly how the time value of money  works in a very simple example, familiar to everyone.  It’s paying less for something today because you will get your money back at a future date.

When you buy a bond, the certificate states that it will pay a certain rate of compound interest.  The compound interest will result in the $100.00 payoff at maturity.  If you cash in the bond before maturity, you will get less than the face amount, because it will not have earned enough interest.

Time value of money

A time value of money calculation is a calculation that solves for one of several variables in a financial problem.

In a typical case, the variables might be: a balance (the real or nominal value of a debt or a financial asset in terms of monetary units), a periodic rate of interest, the number of periods, and a series of cash flows. (In the case of a debt, cash flows are payments against principal and interest; in the case of a financial asset, these are contributions to or withdrawals from the balance.) More generally, the cash flows may not be periodic but may be specified individually. Any of the variables may be the independent variable (the sought-for answer) in a given problem. For example, one may know that: the interest is 0.5% per period (per month, say); the number of periods is 60 (months); the initial balance (of the debt, in this case) is 25,000 units; and the final balance is 0 units. The unknown variable may be the monthly payment that the borrower must pay.

For example, 100.00  invested for one year, earning 5% interest, will be worth £105 after one year; therefore, £100 paid now and 105.00  paid exactly one year later both have the same value to a recipient who expects 5% interest assuming that inflation would be zero percent. That is, 100.00  invested for one year at 5% interest has a future value of 105.00  under the assumption that inflation would be zero percent.

This principle allows for the valuation of a likely stream of income in the future, in such a way that annual incomes are discounted and then added together, thus providing a lump-sum “present value” of the entire income stream; all of the standard calculations for time value of money derive from the most basic algebraic expression for the present value of a future sum, “discounted” to the present by an amount equal to the time value of money. For example, the future value sum FV to be received in one year is discounted at the rate of interest r to give the present value sum PV:

PV = \frac{FV}{(1+r)}

Some standard calculations based on the time value of money are:

  • Present value: The current worth of a future sum of money or stream of cash flows, given a specified rate of return. Future cash flows are “discounted” at the discount rate; the higher the discount rate, the lower the present value of the future cash flows. Determining the appropriate discount rate is the key to valuing future cash flows properly, whether they be earnings or obligations

  • Present value of an annuity: An annuity is a series of equal payments or receipts that occur at evenly spaced intervals. Leases and rental payments are examples. The payments or receipts occur at the end of each period for an ordinary annuity while they occur at the beginning of each period for an annuity due

Present value of a perpetuity is an infinite and constant stream of identical cash flows

  • Future value: The value of an asset or cash at a specified date in the future, based on the value of that asset in the present

  • Future value of an annuity (FVA): The future value of a stream of payments (annuity), assuming the payments are invested at a given rate of interest.

 

 

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