Time Value Of Money

 

1.0 INTRODUCTION

One of the fundamental concepts in finance is that money has a ‘time value’. This is to say that money in hand today is worth more than money expected to be received in the future. The purpose of

this note is to introduce you to the concept, terminology and mathematics of the time value of money. Understanding this note is crucial to understanding all sorts of solutions to financial problems in personal finance, investment, banking, insurance, etc. 

2.0 OBJECTIVES By the end of this note, you should be able to:

·         explain the term ‘time value of money’

·         identify the worth of a present value to the future value of money

·         calculate the present and future values of money. 

3.0 MAIN CONTENT

3.1 Definition and Meaning of Time Value of Money

The time value of money clearly shows that a naira paid out or earned today, is not equal to a naira paid out or earn one year from now. The reason is simple; a naira that you received today can be invested such that you will have more than a naira at some future time. Money now is worth than money in the future, even after adjusting for inflation. This is because a naira now can earn interest or other appreciation until the time the naira in the future would be received.

The idea that money available now is worth than the same amount in the future is due to its potential earning capacity. This core principle of finance holds that available money can earn interest; any amount of money is worth more the sooner it is received.   

3.2 Reasons why a Present Value is Worth More Than a Future Value

Various reasons could be suggested as to why a present N1 is worth more than a future N1.

a. The businesses world is full of risk and uncertainty and although there might be the promise of money to come in the future, it can never be certain that the money will be received until it has actually been paid.

 b. An individual attaches more weight to current pleasures than to future ones, and would rather have N1 in a years time. A justification of this is based on individuals who have the choice of consuming or investing their wealth. However, it has been argued that the return from investment must be sufficient to persuade individuals to prefer to invest now.

 c. Money is invested now to make profits (more money or wealth) in the future. 

3.3 Determining the Present/Future Values of Money

 If you are given N100 and you deposited it in the bank at 10 per cent interest per annum for 2 years, then your:

present value = N100

future value = N121

We shall find out how to get both present and future value on monthly and annual basis.

To determine our values we will use the formula:

FV = PV (1 +i )ⁿ

FV = Future value

PV = Present value

i = the interest rate per period

 n = the number of compounding periods 

a. Determine future value compounded annually

What is the future value of N500 in 7 years if the interest rate if 5%?

 i = 0.05

 n = 7

PV = 500

To get the future value

FV = PV (1 + i)⁷

FV = N500 (1+0.05)⁷

FV = N500 (1.407100)

FV = N703.55 

b. To determine the future value compounded monthly

What is the future value of N500 in 5 years if the interest rate is 5% (i=0.05 divided by 12, because there are 12 months per year)

n = 84 (i.e. 7 x 12 (months in a year)

FV = N500 (1+ 0.0041666)⁸⁴

N500 (1.0041666)⁸⁴

N500 (1.418028)

N709.014 

c. Determine present value compounded annually

You can go backwards too. If I will give you N1, 000 in 5 years, how much money should you give me now to make it fair to me? You think a good interest rate would be 6%.

 I=0.06

FV = PV (1 +i)ⁿ

N1000 = PV (1 + 0.06)⁵

N1000 = PV (1.338)

    N          =    PV

 1.338

PV= N747.38

 So, if you give me N747.38 today, in five years time, I will give you N1000 assuming there is a six per cent interest rate on your money. 

d. Determine present value compounded monthly here is how to determine the present value using the above question again, but this time with monthly compounding instead of annual compounding. We should note that with monthly compounding, we divide the interest rate by 12. This is because there are 12 months in a year.

FV = PV (1 +i)n

N1000 = PV (1 + 0.06)60

N1000 = PV (1+ 0.005)

N1000 = PV (1.348) N

 = PV

1.348

PV= N741.83

 i=0.06/12 = 0.05

n=5 x 12 =60  

4.0 CONCLUSION

 This note has highlighted the importance of time value of money. It has also demonstrated the procedure for estimating the time value of money with examples.

 5.0 SUMMARY

 The note has explained to us the meaning of ‘time value of money’. This concept of time value of money was discussed along with illustrations of both present and future values of money. The reasons why the present values are more important than future value were discussed. The note also shed light on the importance of the time value of money to financial decision in the Organization. 

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