1. All Rights Reserved Ch. 8: 1 Financial Management © Oxford Fajar Sdn. Bhd. (008974-T) 2010

2. All Rights Reserved Ch. 8: 2 Financial Management © Oxford Fajar Sdn. Bhd. (008974-T) 2010 Chapter 8 Time Value of Money

3. All Rights Reserved Ch. 8: 3 Financial Management © Oxford Fajar Sdn. Bhd. (008974-T) 2010 Learning Objectives At the end of this chapter, you should be able to:  Discuss the role of time value in finance and the use of various calculation techniques  Understand the concept of future value and present value and the components involved in the calculations  Understand ordinary annuity and an annuity due, in both present value and future value calculations, as well as the concept of perpetuity

4. All Rights Reserved Ch. 8: 4 Financial Management © Oxford Fajar Sdn. Bhd. (008974-T) 2010  Understand the calculation of effective annual rate (EAR), annual percentage rate (APR) and annual percentage yield (APY)  Calculate other components in time value of money such as periods, interest rate and loan amortization Learning Objectives (cont.)

5. All Rights Reserved Ch. 8: 5 Financial Management © Oxford Fajar Sdn. Bhd. (008974-T) 2010 Introduction  Finance and financial planning deal with the value of money over time.  Managing funds, be it in the form of investment or borrowing over a specified period of time, is referred as time value of money.  In finance, the focus is on economic gains and not accounting gains.

6. All Rights Reserved Ch. 8: 6 Financial Management © Oxford Fajar Sdn. Bhd. (008974-T) 2010 Time Value of Money  Time value of money relates to the concept that a sum of money today is worth more than the same sum in the future. –Lenders’ perspectives –Borrowers’ perspectives

7. All Rights Reserved Ch. 8: 7 Financial Management © Oxford Fajar Sdn. Bhd. (008974-T) 2010 Future Value of a Single Amount  Future value utilizes the concept of compounding.  FV 1 = PV 0 + Interest payment where: FV 1 is the future value at the end of the first period (year 1) PV 0 is the present value of the amount being saved or invested today  Example: Using the above formula, suppose you deposit RM1,000.00 today and the bank offers a 7% interest rate per annum. If you plan to save your money for 3 years, the calculation is as follows:

8. All Rights Reserved Ch. 8: 8 Financial Management © Oxford Fajar Sdn. Bhd. (008974-T) 2010 Future Value – Mathematical Expression

9. All Rights Reserved Ch. 8: 9 Financial Management © Oxford Fajar Sdn. Bhd. (008974-T) 2010 Future Value – Financial Table

10. All Rights Reserved Ch. 8: 10 Financial Management © Oxford Fajar Sdn. Bhd. (008974-T) 2010 Future Value – Financial Calculator

11. All Rights Reserved Ch. 8: 11 Financial Management © Oxford Fajar Sdn. Bhd. (008974-T) 2010 Compounding  Frequency of calculating interest  Compounding (frequency of interest calculation) can be done: –annually (once a year) –semi-annually (twice a year) –quarterly (four times a year) –monthly (twelve times a year) –daily (365 times a year) –continuously

12. All Rights Reserved Ch. 8: 12 Financial Management © Oxford Fajar Sdn. Bhd. (008974-T) 2010 Compounding (cont.)

13. All Rights Reserved Ch. 8: 13 Financial Management © Oxford Fajar Sdn. Bhd. (008974-T) 2010 Present Value of a Single Amount  Present value is the current value of a given future cash flow.  The present value tells us the amount of money needed today in order to obtain a desired amount after a period of time.  Example is given below:

14. All Rights Reserved Ch. 8: 14 Financial Management © Oxford Fajar Sdn. Bhd. (008974-T) 2010 Present Value – Formula

15. All Rights Reserved Ch. 8: 15 Financial Management © Oxford Fajar Sdn. Bhd. (008974-T) 2010 Present Value – Financial Table  The present value of RM10,000 in the above example can also be found by multiplying the amount by the present value interest factor which can be referred to in the financial tables.  Example: The present value interest factor (PVIF) is interest factor for 3 years (period 3) and 6% (interest rate) it is 1.910. Thus, the formula using Table 3 is as follows: PV 0 =FV × (PVIF r, n) [r = 6%, n = 3] =10000 × 0.8396 =8,396.00

16. All Rights Reserved Ch. 8: 16 Financial Management © Oxford Fajar Sdn. Bhd. (008974-T) 2010 Present Value – Financial Calculator (cont.)

17. All Rights Reserved Ch. 8: 17 Financial Management © Oxford Fajar Sdn. Bhd. (008974-T) 2010 Annuities  Each payment of an ordinary annuity belongs to the payment at the end of the period.  The payment of an annuity-due refers to a payment period starting beginning of the period.

18. All Rights Reserved Ch. 8: 18 Financial Management © Oxford Fajar Sdn. Bhd. (008974-T) 2010 Annuities (cont.)  Figure 8.1 below illustrates the two types of annuity:

19. All Rights Reserved Ch. 8: 19 Financial Management © Oxford Fajar Sdn. Bhd. (008974-T) 2010 Present Value of an Ordinary Annuity  The present value of each payment must be calculated by dividing each by 1 plus the discount rate raised to the power of the number of periods involved.  Suppose we want to find the present value of RM50 received every year for three years at a discount rate of 7%.  The calculation is shown in Figure 8.2 below:

20. All Rights Reserved Ch. 8: 20 Financial Management © Oxford Fajar Sdn. Bhd. (008974-T) 2010 Present Value – Ordinary Annuities

21. All Rights Reserved Ch. 8: 21 Financial Management © Oxford Fajar Sdn. Bhd. (008974-T) 2010 Present Value – Annuity Due  The annuities are often paid with the first payment starting at the beginning of the year- starting immediately at year 0 is called an annuity due.  A sum of RM50 is paid every year for three years but the first payment starts immediately.  The details are shown below:

22. All Rights Reserved Ch. 8: 22 Financial Management © Oxford Fajar Sdn. Bhd. (008974-T) 2010 Present Value – Annuity Due (cont.)

23. All Rights Reserved Ch. 8: 23 Financial Management © Oxford Fajar Sdn. Bhd. (008974-T) 2010 Perpetuity  Payments of equal periodic cash flows are to be made till infinity or forever is called a perpetuity.  Roslan has invested in a special government bond that provides income on investment of RM100 per annum in perpetuity. Determine the present value of this perpetual annuity if you are told that the time value of money is 8% per annum. Solution: PV = PMT r = 100 0.08 = 1250 i.e. RM1,250

24. All Rights Reserved Ch. 8: 24 Financial Management © Oxford Fajar Sdn. Bhd. (008974-T) 2010 Future Value – Annuity  The future value of an annuity refers to the amount that we will accumulate by making regular payments at a given interest rate over a specified period of time.  Figure 8.4, below shows how the future value is determined using an interest rate of 9% and the yearly payment is RM25:

25. All Rights Reserved Ch. 8: 25 Financial Management © Oxford Fajar Sdn. Bhd. (008974-T) 2010 Future Value – Annuity (cont. )

26. All Rights Reserved Ch. 8: 26 Financial Management © Oxford Fajar Sdn. Bhd. (008974-T) 2010 Future Value – Annuity Due  Payments are to begin immediately, NOT at the end of the first period, we must therefore calculate the future value of an annuity due.  As the last payment is made at the beginning of the last period, the entire future value of the annuity earns an extra year’s interest by the end of the last period.  Similar to the present value of an annuity calculation, to calculate the future value – multiply the future value of the annuity by 1 plus the interest rate.

27. All Rights Reserved Ch. 8: 27 Financial Management © Oxford Fajar Sdn. Bhd. (008974-T) 2010 FV – Annuity Due (Figure 8.5)  Refer to Figure 8.5 below:

28. All Rights Reserved Ch. 8: 28 Financial Management © Oxford Fajar Sdn. Bhd. (008974-T) 2010 Effective Annual Rate  Effective annual rate (EAR)—the rate has a very significant impact on TVM  Contractual annual interest rate—in FV and PV calculations is called the nominal rate.  The formula to calculate EAR:

29. All Rights Reserved Ch. 8: 29 Financial Management © Oxford Fajar Sdn. Bhd. (008974-T) 2010 Annual Percentage Rate  Annual percentage rate (APR) refers to the rate obtained by multiplying the periodic short term rate (e.g. semi-annually, quarterly, monthly, etc.) by the number of periods in a year.  A rate that is stated in annual terms  Example: Suppose a bank is charging its credit card holders 1.2% on a monthly basis, thus, in a year the calculation will be: 1.2 × 12 = 14.4%. This 14.4% is the APR.