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MGMT2023 Financial Management The University of the West Indies Mona

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The University of the West Indies Mona

MGMT2023 Financial Management The University of the West Indies Mona

After studying this chapter you should understand the following terms and concepts:
1. the time value of money (TVM) and how to solve problems involving present and future value using both the table and calculator methods; 2. ordinary annuities, annuities due and how to solve TVM problems including annuities; 3. compound interest, effective annual rates (EAR) and how to use them in TVM problems; 4. amortized loans (e.g. mortgage loans) and how they are calculated; 5. perpetuities, continuous compounding, multi-part problems, uneven streams, and imbedded annuity problems.
CHAPTER SUMMARY
This chapter concentrates on the concept of the time value of money–the idea that a dollar received today is more valuable than a dollar received at some point in the future. Problems involving the present and future value of individual amounts and of annuities are carefully explained and solved. The effect of the interest rate and interest rate compounding on the value of money is explained and demonstrated through various examples. The concepts expressed in this chapter are of vital importance to the understanding of the field of finance, and the student should carefully follow the instructions for problem-solving presented throughout the chapter.
CHAPTER REVIEW
1. The time value of money (TVM) is the concept that treats money as having two dimensions: (1) a dollar amount, and (2) a specific time at which the money is received or spent. The fundamental assumption underlying TVM is that “money received today is more valuable than money received at some point in the future, because today’s money can be invested and
Chapter 5
grow by earning interest for a longer period of time.” Closely related to this idea is the understanding that if a person wants to accumulate a particular amount of money at a future date, the interest rate paid on the original amount invested will determine how much must be invested in order for it to grow to the required future amount. The higher the interest rate received, the less money that must be originally invested to grow to the desired amount.
AMOUNT PROBLEMS
2. An amount refers to a single amount of money that will grow into a larger sum in the future because of earning interest. Amount problems involve two important and related concepts: present value and future value.
3. “Future value of an amount” problems determine how much an amount of money deposited today will be worth at some specified time in the future. The future value will be determined by how much is originally deposited; how long the money remains on deposit; and how often the interest will be paid and at what rate. This amount can be calculated by using the formula,
FVn = PV[FVFk,n]
where the future value factor (FVF) is determined by the interest rate per period (k) and the number of periods the amount is on deposit (n). These factors can be found in Table A-1 in the text. The formula can also be stated as
FUTURE VALUE OF AN AMOUNT = AMOUNT DEPOSITED  TABLE FACTOR
This is a simple problem to solve when only one sum of money is deposited, but the calculations become more complicated when multiple sums are involved. When more than one amount is involved, separate calculations must be performed for each amount, and then the answers are added together to get the future value of the various amounts.
4. The opportunity cost rate is defined as the rate of interest at which a person could have invested his or her money. The opportunity cost will vary from person to person depending upon his or her investment opportunities.
5. “Present value of an amount” problems compute the value of a specified future amount of money in today’s terms. If a person wants to have a certain amount of money in five years, he or she will want to know what must be invested today so that it will grow to the desired amount in the time available. The amount that must be deposited today is the present value of that future amount. The amount that must be deposited today will also depend upon the following: the value of the future amount, how long the money will remain on deposit, and how often interest will be paid and the rate of that interest.
As with future value calculations, present value amounts may be calculated by using the formula
PV = FVn(PVFk,n)
where the present value factor (PVF) is determined by the interest rate per period (k) and the number of periods the amount is on deposit (n). These factors can be found in Table A-2 in the text. The formula can also be stated as:

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MGMT2023 Financial Management The University of the West Indies Mona

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