Present Value.html

Present Value

Present value (PV) calculations provide the basis for valuation analysis and pricing of financial instruments such as bonds and stocks. Present value refers to the current value of money—either paid or received—in the future. It is what investors will pay today for future cash flows. PV calculations are the inverse of FV calculations. You learned earlier that: FV = PV (1 + r)n. Dividing both sides by (1 + r)n yields: FV/(1 + r)n = PV (1 + r)n/(1 + r)n. The interest factors cancel, and the equation is now: PV = FV/(1 + r) n Example: What is the present value of receiving $9,000 in seven years if alternative investments yield (opportunity cost is) 6%?

Solution Using the PV formula:

PV = 9,000 / (1+.06)7 = 9,000 / (1.06)7 = 9,000 / 1.5036303 = 5985.51 Using a financial calculator: Input: FV = 9,000, I = 6, N = 7, PMT = 0 Compute: PV = 5985.51 With Microsoft Excel, use the function (fx)PV: =PV(rate, nper, pmt, [fv],[type])(don't enter spaces).

where:

• rate is the interest rate per period (if given an annual rate, divide by 12 for monthly rate; write rate, decimal or %)
• nper is the number of periods (if given years, multiply by 12 to determine monthly values)
• pmt is payment per period and is used in annuity calculations
• fv is the future value
• type is for the timing of the payment; 0 = end of period (most common and the default, if you leave the value blank), 1 = beginning of period

The formula to solve the above problem is:

=PV(6%,7,,-9000) by convention, an outgoing payment is indicated by a negative value (otherwise the result will be negative in Microsoft Excel). =PV(6%,7,,-9000) = $5,985.51 Sometimes there may be numerous cash flows rather than just one value. The present value of a set of cash flows (PMT) occurring at different points in time is simply the sum of the present values for the cash flows, as shown: PV = PMT1/(1 + r)1+ PMT2 /(1 + r)2+ PMT3 /(1 + r)3+ … + PMTt/(1 + r)t

Future Value.html

Future Value

Future value (FV) refers to the amount of cash to be received or paid at a future date.

For a Single-period

Potential investments offer a rate of return of 9% per period. Given an initial investment of $2,000, how much cash would be available at the end of one period?

The investment will return the principal $2,000, plus 9% of $2,000 or $2,180, which is calculated as follows:

• FV = (2,000 + 1,000 * 0.09) = 2,000 (1 + .09) = 2,000 (1.09) = 2,180
• The FV for one period is:
• FV = initial investment * (1 + interest rate)
• The equation is: FV = PV (1 + r)

where,

• FV = Future value
• PV = Present value

To continue with the above example, what will the investment be worth after four periods assuming that the accrued amount can be reinvested at a rate of 9%? FV = 2,000 (1.09)4 = 2,000 (1.09)4 = 2000 * 1.4115816 = 2823.16 After four periods the value of the investment will be $1,411.58. Although the above method correctly calculates the future value, it is inefficient because you need to multiply $1,000 with 1.09 four times. What if the investment was for 50 periods instead of 4?

 

Example: Albert plans to retire in 15 years. Will he be able to afford a $200,000 condominium when he retires if he invests $100,000 in a 15-year certificate of deposit (CD) that pays 6% interest, compounded annually? Solution: Yes, he will be able to purchase the condominium because he should have $100,000 (1.06) 15 = 239,655.82 when he retires.

Using a financial calculator:

Input: PV = -100,000

Note: Cash inflows are represented by a plus sign and cash outflows are represented by a minus sign. Albert invests $100,000 in the CD, and this is a cash outflow. The result will be a positive value because Albert will receive that amount.

I = 6 N = 15 PMT = 0 Compute: FV = $239,655.82

Using Excel:

Use the function (fx) FV:

=FV(rate, nper, pmt, [pv], [type])(don't enter spaces)

where:

• rate is the interest rate per period (if given an annual rate, divide by 12 for monthly rate; write rate as decimal or %)
• nper is the number of periods (if given years, multiply by 12 to determine monthly values)
• pmt is payment per period and is used in annuity calculations (put a comma to leave this blank for other calculations)
• pv is the present value
• type is for the timing of the payment; 0 = end of period (most common and the default, if you leave the value blank), 1 = beginning of period

Time Value of Money.html

Time Value of Money

The main elements of time value of money (TVM) are money (cash), interest, and time. Money can be received or given in two main ways. The first is as a one-time amount—either an inflow or outflow, today or tomorrow. This is a lump sum. If we are determining the value today, it is a present value. If we are talking about a value to be received or paid in the future, it is a future value. Second, the money might be received in a series of cash flows over time, such as an annuity or a payment. This is a series of cash flows. The flow or stream may be an even amount each period, or uneven. Finally, money may come in as a combination of a series of cash flows and a lump sum. For example, a bond, debt issued by corporations or governments, has periodic cash flows, interest payments, and a lump sum—the principal or par value of the bond.

The interest element represents the opportunities cost of using money. John Maynard Keynes, an economist, suggested we hold money for three motives: transactions, precautionary, and speculative. That is, we hold money because we need it for making purchases in the short term, to have in case of emergencies, or to have in case we find a “good deal.” Interest is the way we recognize that compensation is needed for waiting until the future to use money. We have to pay for getting the money sooner or be compensated for waiting until later. An interest rate is the interest payment divided by the principle or balance of a loan. The interest payment may be received annually, semiannually, monthly, and so on. You may earn interest on interest and principal. This is compounding, or the inverse of discounting. When you deposit money in the bank and earn interest over time you are receiving compound interest.

The time element in TVM affects the value of money based on how many periods the money is used and whether the payment is received at the beginning or the end of each period. Periods can be annual, monthly, daily, or any combination thereof.

Most of us want more of things now rather than later. You have heard the expression “time is money.” What is the meaning of this? Economists call this concept a positive time preference—we prefer things now as opposed to later. This preference gives rise to the concept of time value of money.

A positive time preference influences the value of money today versus the value of money tomorrow. Because we prefer now, we want to be compensated for waiting until tomorrow. We value things less that are in the future relative to things that might happen in a short time period. In other words, we discount the future. Furthermore, the time value of money also represents the cost of using money and the money itself.

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