Solution Manual
CHAPTER 5
The Time Value of Money
CHAPTER ORIENTATION
In this chapter the concept of a time value of money is introduced, that is, a dollar today is worth more than a dollar received a year from now. Thus if we are to logically compare projects and financial strategies, we must either move all dollar flows back to the present or out to some common future date.
CHAPTER OUTLINE
I. Compound interest results when the interest paid on the investment during the first period is added to the principal and during the second period the interest is earned on the original principal plus the interest earned during the first period.
A. Mathematically, the future value of an investment if compounded annually at a rate of i for n years will be
FVn = PV (l + i)n where n = the number of years during which the compounding occurs i = the annual interest (or discount) rate PV = the present value or original amount invested at the beginning of the first period FVn = the future value of the investment at the end of n years
1. The future value of an investment can be increased by either increasing the number of years we let it compound or by compounding it at a higher rate.
2. If the compounded period is less than one year, the future value of an investment can be determined as follows:
FVn = PV mn
where m = the number of times compounding occurs during the year
II. Determining the present value, that is, the value in today's dollars of a sum of money to be received in the future, involves nothing other than inverse compounding. The differences in these techniques come about merely from the investor's point of view.
A. Mathematically, the present value of a sum of money to be received in the future can be determined with
The Time Value of Money
CHAPTER ORIENTATION
In this chapter the concept of a time value of money is introduced, that is, a dollar today is worth more than a dollar received a year from now. Thus if we are to logically compare projects and financial strategies, we must either move all dollar flows back to the present or out to some common future date.
CHAPTER OUTLINE
I. Compound interest results when the interest paid on the investment during the first period is added to the principal and during the second period the interest is earned on the original principal plus the interest earned during the first period.
A. Mathematically, the future value of an investment if compounded annually at a rate of i for n years will be
FVn = PV (l + i)n where n = the number of years during which the compounding occurs i = the annual interest (or discount) rate PV = the present value or original amount invested at the beginning of the first period FVn = the future value of the investment at the end of n years
1. The future value of an investment can be increased by either increasing the number of years we let it compound or by compounding it at a higher rate.
2. If the compounded period is less than one year, the future value of an investment can be determined as follows:
FVn = PV mn
where m = the number of times compounding occurs during the year
II. Determining the present value, that is, the value in today's dollars of a sum of money to be received in the future, involves nothing other than inverse compounding. The differences in these techniques come about merely from the investor's point of view.
A. Mathematically, the present value of a sum of money to be received in the future can be determined with