Management Department

Management Department
Finance Pre-MBA Dr Abdeldjelil Ferhat BOUDAH Business School Management Department 1

CHAPTER 5 TIME VALUE OF MONEY
Dr Abdeldjelil Ferhat BOUDAH

CHAPTER 5: TIME VALUE OF MONEY
Introduction 1- The role of time value in finance 2- Future value 3- Present value Conclusion Dr Abdeldjelil Ferhat BOUDAH

Introduction Financial manager must assess the firm’s value and decisions in light of both its present and future cash flows- both inflows and outflows. Dr Abdeldjelil Ferhat BOUDAH

1- The role of time value in finance Firms and individuals are always confronted with opportunities to earn positive rates of return on their funds, that is, interest rates which are always greater than zero. Taking a long-term view requires the financial manager to explicitly recognize the time value of money. Dr Abdeldjelil Ferhat BOUDAH

Future Versus Present Value Values and decisions can be assessed by using either future value or present value techniques. Dr Abdeldjelil Ferhat BOUDAH

Future value techniques are used to find future values, which are, typically, measured at the end of a project’s life. Present value techniques are used to find present values, which are, typically, measured at the start of a project’s life. Dr Abdeldjelil Ferhat BOUDAH

Time Line To understand how future value and present value can be computed, an horizontal time line is drawn as it is shown below: Years Dr Abdeldjelil Ferhat BOUDAH

Time Line Years -$ $ $ $ $ $ Cash flows Time lines are frequently used in finance to allow the analyst to fully understand the cash flows associated with a given investment. Dr Abdeldjelil Ferhat BOUDAH

Time Line The present value techniques uses discounting to find the present value of each cash flow at time zero and then sums them to find the investment’s present value. Dr Abdeldjelil Ferhat BOUDAH

Time Line years $ $ $ $ $ Cash flows Discounting : The application of discount factors to each year’s cash flows projections, alternatively, the present value based on the discount rate which is considered as the interest rate that the funds used for the project could earn elsewhere. Dr Abdeldjelil Ferhat BOUDAH

Time Line The present value techniques uses discounting to find the present value of each cash flow at time zero and then sums them to find the investment’s present value. Dr Abdeldjelil Ferhat BOUDAH

Time Line years $ $ $ $ $ Cash flows Present Value Dr Abdeldjelil Ferhat BOUDAH

Time Line The future value techniques uses compounding to find the future value of each cash flow at the end of the investment’s life and then sums them to find the investment’s future value. Dr Abdeldjelil Ferhat BOUDAH

Time Line years $ $ $ $ $ $ Cash flows Compounding means the compound interest, where the charge of the loan is calculated on the sum loaned plus any interest that has accrued in previous period. Dr Abdeldjelil Ferhat BOUDAH

Time Line years $ $ $ $ $ $ Cash flows Future value Dr Abdeldjelil Ferhat BOUDAH

Computational aids There are three computational aids: financial tables, hand-held business/calculators, and personal computers. Dr Abdeldjelil Ferhat BOUDAH

Computational aids Financial Tables Financial tables include future and present value interest factors which can be easily developed from the appropriate formulas and used to simplify time value calculations. (Figure 5.3) Dr Abdeldjelil Ferhat BOUDAH

2- Future value There are two main categories of future value: future value of a single amount and future value of an annuity. Dr Abdeldjelil Ferhat BOUDAH

2-1 Future value of a single amount Prior to any calculation of the future value, it should be so helpful to define the following terms: future value, compound interest, and principal. Dr Abdeldjelil Ferhat BOUDAH

Future value: the value of a present amount at future date found by applying compound interest over a specified period of time. Compound interest : interest earned on a given deposit that has become part of the principal at the end of a specified period. Principal: The amount of money on which interest is paid. Dr Abdeldjelil Ferhat BOUDAH

The calculation of future value of a single amount Where : = future value at the end of the period n C = initial principal k = annual rate of interest paid n = number of periods Dr Abdeldjelil Ferhat BOUDAH

Example: Jane Farber placed $800 in savings account paying 6 percent interest compounded annually, she wishes to determine how much money will in the account at the end of 5 years. Dr Abdeldjelil Ferhat BOUDAH

Solution See financial tables Substituting C= $800, k= 0.06, and n = 5 into equation 1 gives the amount at the end of year 5: Dr Abdeldjelil Ferhat BOUDAH

2-2 Future value of an annuity An annuity is a stream of equal annual cash flows. These cash flows can be inflows of returns earned on investments or outflows of funds invested to earn future returns. There are two basic types of annuities, ordinary annuity, and the annuity due. Dr Abdeldjelil Ferhat BOUDAH

An Ordinary annuity is an annuity for which the payments occurs at the end of each period, whereas an annuity due is one for which the payments occur at the beginning of each period . Dr Abdeldjelil Ferhat BOUDAH

Example: Fran Abrams is attempting to choose the better of two annuities. Both are 5-year, $ 1,000 annuities, but the annuity A is an ordinary annuity , and annuity B is an annuity due. To better understand the difference between these annuities , she has listed their cash flows in table shown below as follows: Dr Abdeldjelil Ferhat BOUDAH

Annual cash flows End of year Annuity B (due) Annuity A (Ordinary) $ 1,000 $ 1,000 1 2 Dr Abdeldjelil Ferhat BOUDAH

Annual cash flows (Continuation) End of year Annuity B (due) Annuity A (Ordinary) 1,000 3 4 $ 5 $ 5000 Totals Dr Abdeldjelil Ferhat BOUDAH

The Future Value of $ year Ordinary Annuity Compounded at 7 Percent FV at the end of Year [(1)×(3)= (4)] FV IF From Table (3) Number of Years Compounded (2) Amount deposited (1) End of year 1,311 1.311 4 $1000 1 1,225 1.225 3 1,000 2 1,145 1.145 Dr Abdeldjelil Ferhat BOUDAH

The Future Value of $ year Ordinary Annuity Compounded at 7 Percent FV at the end of Year [(1)×(3)= (4)] FV IF From Table (3) Number of Years Compounded (2) Amount deposited (1) End of year 1,070 1.070 1 1,000 4 1.000 5 $ 5,751 $ 5000 Totals Dr Abdeldjelil Ferhat BOUDAH

The Future Value of $ year Annuity Due Compounded at 7 Percent FV at the end of Year [(1)×(3)= (4)] FV IF From Table (3) Number of Years Compounded (2) Amount deposited (1) End of year 1,403 1.403 5 $1000 1,311 1.311 4 1,000 1 1,225 1.225 3 2 Dr Abdeldjelil Ferhat BOUDAH

The Future Value of $ year Annuity Due Compounded at 7 Percent FV at the end of Year [(1)×(3)= (4)] FV IF From Table (3) Number of Years Compounded (2) Amount deposited (1) End of year 1.145 2 1,000 4 1,070 1.070 1 5 $ 6,154 $ 5000 Totals Dr Abdeldjelil Ferhat BOUDAH

3- Present value There are two main categories of present value: present value of a single amount, and present value of cash flow streams (PV of mixed stream and annuity). Dr Abdeldjelil Ferhat BOUDAH

3-1 Present Value of a single amount It is often useful to determine the present value of a future amount of money. So, the Present Value is the current dollar value of a future amount – the money that would have to be invested today at a given interest rate over a specified period to equal the future amount. Dr Abdeldjelil Ferhat BOUDAH

Present value, like future value, is based on the belief that a dollar today is worth more than a dollar that will be received at some future date. Dr Abdeldjelil Ferhat BOUDAH

The Concept of Present Value The Process of finding present values is often referred to as discounting cash flows. This process is actually the inverse of compounding interest. It is concerned with answering the questions: Dr Abdeldjelil Ferhat BOUDAH

“ If I can earn k percent on my money, what is the most I would be willing to pay now for an opportunity to receive FVn dollars n periods from today ? “ Dr Abdeldjelil Ferhat BOUDAH

Instead of finding the future value of present dollars invested at a given rate, discounting determines the present value of a future amount, assuming that the decision maker has an opportunity to earn certain rate, k , on the money. This annual rate of return is referred to as the discount rate, required return, cost of capital, or opportunity cost. Dr Abdeldjelil Ferhat BOUDAH

Example: An investor has been given an opportunity to receive $300 one year from now. If he can receive 6% on his investment in the normal course of events, what is the most he should pay now for this opportunity? Dr Abdeldjelil Ferhat BOUDAH

Answer Since the present value is the unknown amount that we are looking for, then let us imagine the following equation: PV× (1+%6) = $300 Solving equation For PV gives PV= $300/(1+%6)= $283.02 Dr Abdeldjelil Ferhat BOUDAH

The present value of $ investment today at the 6% opportunity cost would result in $300 at the end of one year. Dr Abdeldjelil Ferhat BOUDAH

The calculation of present value The present value of future value can be found mathematically by solving the following equation: Dr Abdeldjelil Ferhat BOUDAH

Where, PV= Present Value C= Future value that can be received within n periods from now; that is FVn. k=Discounting rate n= Number of years Dr Abdeldjelil Ferhat BOUDAH

Example: An investor wishes to find the present value of $1700 that will be received 8 years fro now. The opportunity cost (discounting rate) is 8%. So, the present value would be calculated as follows: Note: Important to use Financial tables Dr Abdeldjelil Ferhat BOUDAH

Dr Abdeldjelil Ferhat BOUDAH

Time-line use: Illustration End of year FV= $1700 PV= $918.42 Dr Abdeldjelil Ferhat BOUDAH

Simplifying Present Value Calculations The present value calculations can be simplified by using a present value interest factor (PVIF). Dr Abdeldjelil Ferhat BOUDAH

Since and Dr Abdeldjelil Ferhat BOUDAH

Then Note: In this case it would definitely be better to use the financial tables. Dr Abdeldjelil Ferhat BOUDAH

3-2 Present Value of Cash Flow Streams Quite often in finance there is a need to find the present value of a stream of cash flows to be received in various future periods. Two basic types of cash flow streams are possible: the mixed stream and the annuity. Dr Abdeldjelil Ferhat BOUDAH

Present Value of a Mixed Stream The present value of a mixed stream of cash flows means a determination of the present value of each future amount. An example can be used to illustrate the procedure of calculation. Dr Abdeldjelil Ferhat BOUDAH

Example The Frey Company, a shoe manufacturer, has been offered an opportunity to receive the following mixed stream of cash flows over the next five (5) years. If the firm must earn 9%, at minimum, on its investment, what is the most it should pay for this opportunity. See data below Dr Abdeldjelil Ferhat BOUDAH

Cash flow year $ 400 1 800 2 500 3 400 4 300 5 Dr Abdeldjelil Ferhat BOUDAH

The present value of a mixed stream of cash flows Present value 3)])=(2)×[(1) PVIF9%,n (2) Cash flow (1) Year (n) $ 0.917 $400 1 673.60 0.842 800 2 386.00 0.772 500 3 Dr Abdeldjelil Ferhat BOUDAH

The present value of a mixed stream of cash flows Present value 3)])=(2)×[(1) PVIF9%,n(2) Cash flow (1) Year (n) 283.20 0.708 400 4 195.00 0.650 300 5 $ 1,904.60 Present value of mixed stream Dr Abdeldjelil Ferhat BOUDAH

Time-line use: Illustration End of year FV= $300 Dr Abdeldjelil Ferhat BOUDAH

Present Value of an Annuity The present value of can be found in a manner similar to that used for a mixed stream, but a short cut is possible. Dr Abdeldjelil Ferhat BOUDAH

Example: The Braden company, a small producer of plastic toys, is attempting to determine the most it should pay to purchase a particular annuity. The firm requires a minimum return of 8% on all investments, and the annuity consists of cash flows of $700 per year for 5 years. Note: Important to use Financial tables Dr Abdeldjelil Ferhat BOUDAH

Calculation Of Present Value of Annuity Cash flow year $ 700 1 700 2 3 4 5 Dr Abdeldjelil Ferhat BOUDAH

The present value of an annuity Present value 3)])=(2)×[(1) PVIF8%,n (2) Cash flow (1) Year (n) $ 0.926 $700 1 599.90 0.857 700 2 555.80 0.794 3 Dr Abdeldjelil Ferhat BOUDAH

The present value of an annuity Present value 3)])=(2)×[(1) PVIF8%,5(2) Cash flow (1) Year (n) 514.50 0.735 700 4 476.7 0.681 5 $ 2,795.10 Present value of Annuity Dr Abdeldjelil Ferhat BOUDAH

Conclusion It can be concluded that the time value of money helps managers make sound corporate finance, and investment decisions and also helps with personnel financial planning. Dr Abdeldjelil Ferhat BOUDAH

To properly use the tools presented in later chapters, time value concepts and techniques must be well understood. As well as other concepts such as risk, return, and valuation, which all fit together. Dr Abdeldjelil Ferhat BOUDAH

بحمد الله

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