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# Time Value of Money Definitions

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As a financial manager you will often have to compare cash payments which occur at different dates. To make optimal decisions, you must understand the relationship between a dollar today [present value] and a dollar in the future [future value].

Future value is the amount to which an investment will grow after earning interest. Interest can be of two types: i) simple interest, and ii) compound interest.

1) How would you define time value of money in your own words? Please provide a brief definition of time value of money in your own words.

2) To what extent is it important for financial managers to understand the concept of time value of money? Why? Please explain your reasoning in two to three paragraphs.

If you do not know how to use calculator, please use the tables to answer question 3, 4, 5, and 6.
Brealey, R.A., Myers, S.C., & Allen, F. (2005). Principles of corporate finance, 8th Edition. The McGraw?Hill. Retrieved May, 2012, from http://jcooney.ba.ttu.edu/fin3322/Brealey%20Files/Appendix%20A%20-%20Present%20Value%20Tables.pdf

3) Calculate the future value of the followings:
a. \$190,537.19 if invested for six years at a 8% interest rate
b. \$231,891.22 if invested for four years at a 9% interest rate
c. \$310,891.12 if invested for nine years at an 5% interest rate
d. \$420,520.22 if invested for fifteen years with a 1% interest rate

4) Calculate the present value of the followings:
a. \$552,126.17 to be received four years from now with a 3% interest rate
b. \$125,003.21 to be received three years from now with an 8% interest rate
c. \$621,567.35 to received nine years from now with a 14% interest rate
d. \$93,000.05 to be received eleven years from now with a 2% interest rate

5) Suppose you are to receive a stream of annual payments (also called an "annuity") of \$225,891.12 every year for five years starting at the end of this year. The interest rate is 7%. What is the present value of these five payments? Please use Table 3 [http://jcooney.ba.ttu.edu/fin3322/Brealey%20Files/Appendix%20A%20-%20Present%20Value%20Tables.pdf]

6) Suppose you are to receive a payment of \$337,891.24 at the end of each year for seven years. You are depositing these payments in a bank account that pays 6% interest. Given these seven payments and this interest rate, how much will be in your bank account in seven years? If you do not know how to use calculator, please use Table [http://www.principlesofaccounting.com/ART/fv.pv.tables/fvofordinaryannuity.htm]
Please include the references used to obtain information/response

#### Solution Preview

1) How would you define time value of money in your own words? Please provide a brief definition of time value of money in your own words.

The time value of money can be simply expressed by "a dollar at present is worth more than a dollar in the future." The major reasons are (1) money can earn interest and (2) there is a risk with the money that is not spent.

Therefore, the time value of money can be defined as the compensation for the risk of unspent money and the interest that the money could earn.

2) To what extent is it important for financial managers to understand the concept of time value of money? Why? Please explain your reasoning in two to three paragraphs.

The concept of time value of money is important for financial managers in business planning, as they need to compare current and future cash flows.

For example, in order to decide whether an investment in a particular project is worthwhile, a financial manager needs to compare the related costs and returns. The investment is profitable only when its return rate is greater than the interest rate to be paid. The interest payment in this case actually measures the time value of money.

Another example is the comparison ...

#### Solution Summary

The time value of money definitions are examined. The relationship between a dollar today and a dollar in the future are provided.

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