part 2 2-2 present value-single amount

2. Present value -single amount

In recent years, the sports pages have been filed with stories of athletes who receive multi-million dollar contracts for signing with sports organizations. Perhaps you have wondered how the new york yankees(纽约洋基) or Los ANGELES LAKERS(洛杉矶湖人队) can afford to pay such fantastic sums. The answer may lie in the concept of present value a sum payable in the future is worth less today than the stated amount.

The present value is the exact opposite of the future value. For example, earlier we determined that the future value of 1000 for four periods at 10 percent was 1464.1 we could reverse the process to state that 1464.1 received four years into the future. With a 10 percent interest of discount rate, is worth only 1000 today its present value. A timeline for this problem is presented as follows:

You will notice that this timeline looks similar to the first one. In fact, only the direction of the arrow is reversed. This reflects the close relationship between present values and futures. The figure depicts this relationship. When the interest rate is 10%, 1000 at the time zero has the same value as 1464.1 at time 4. also, every point along the line in above figure shows the value at other points in time. Every value along the line has the same value(present value) at a different time, given that i is equal to 10%.

The formula for present value is derived from the original formula for future value:(略)

The present value can be determined by finding the mathematical solution to this formula:

To help you feel comfortable with the various methods of writing the present value formula, here are several alternatives that all have the same algebraic meaning:

PV=FV(1+I)-N=FV/(1+I)N

WITH a little practice,you will be completely comfortable using formula above, but we will also cover the use of spreadsheet functions.

Let’s consider the present value version of the above problem:what is the present value of 1464.1 if it is discounted at 10% for 4 years?

Interest rate-single amount(一次款项利率的确定）

Thus far, we have seen that we can solve for the present value in formula by rewriting the equation to isolate PV on the left side of the equation to form Formula 3. both formula 1 and 2 use the same four variables. In fact, if we know any three of these variables,We can always solve for the fourth. Suppose we want to know the return on an investment that we have made, and we know the future value, present value, and the number of compounding periods. The return on the investment would be the interest rate that relates all of these variables.

I=?

When we substitute the values from our previous example, we find(演示)i=?

In this chapter, we examine the three basic types of financial statements the  income statement, the balance sheet, and the statement of cash flows with particular attention paid to the interrelationships among these three measurement devices. As special preparation for finance students, we briefly examine income tax considerations affecting financial decisions.