Chapter 3 1 Norazidah Shamsudin

Objectives Explain the time value of money concepts and its relevance in financial decision making. Explain the importance of timing of cash flows in financial decisions. Identify and solve application problems that deal with different types of cash flows in financial decisions. Use time value of money tables in solving applications problems. 2 Norazidah Shamsudin

Contents 3 PV Present Value / Discounted FV Future Value / Compounded a Ordinary Annuity Annuity Due i Interest Rate / Interest factor n 1 period Multiple periods Amortization Norazidah Shamsudin

Principle “A dollar today is worth more than a dollar tomorrow…” Components: 4 Interest Time Value Norazidah Shamsudin

Activity..Lets Share…. Your pocket money while you in Form 1 …. Nowadays Form 1 students’ pocket money…. 5 Toyota Vios price (new)…. 1 year old Toyota Vios car…. Norazidah Shamsudin

Value vs. Price 6 Value FurnitureCarMachinesLandGoldProperty Norazidah Shamsudin

7 Value vs. Price DemandSupply Price Norazidah Shamsudin

Methodology for Time Value of Money Time value of money problem can be solved in 3 ways i.e. 8 Numerically with a regular calculation (numbers) 1. Numerical Solution Numerically with interest tables 2. Tabular Solution Numerically with a financial calculator 3. Fin L Calculator Sol. Norazidah Shamsudin

Is the most important tools in time value of money analysis and is used to help visualize what is happening in a particular problem and help to set up the problem for solution. Time 0 i ? Cash Flow 9 Time Lines Norazidah Shamsudin

Time Lines..Cont…  Cash Flow – Below the tick mark are the value of the cash flows represent cash outflow (investment or payment) and a +ve sign means a cash inflow (receipt). Ringgit Malaysia (RM) are not required to be stated in the time line to reduce clutter.  Interest Rate Interest rates (i) are shown directly above the time line. If interest is constant in all periods, it will be shown once only in the 1 st period, but if it changes every period then all the relevant rates will be shown on the time line. 10 Norazidah Shamsudin

Time Lines.. Cont…  Periods – the value above the tick marks i.e. 0,1,2,3 & 4 represent time period. Time 0 represent today; time 1 one period from today, or the end of period 1 or the beginning of the period 2. Period can be years, semiannual, quarters, months and days. 11 Norazidah Shamsudin - Dungun

Present Value (Discounted) Is the amount that if we had it now and if we invest it at specified interest rate (i), would equal the future payment (FVn). 2 methods under PV: 12 Present Value of Lump Sum PV Present Value of Annuity PV A Norazidah Shamsudin - Dungun

Discounted value which will be paid out or received once only. The equations for discounting: 13 PV of Lump Sum PV = FVn(PVIFi,n) Tabular Solution PV = FVn (1+i) n Numerical Solution Norazidah Shamsudin - Dungun

PV.. Cont… Where, PV = Principal, present value or beginning amount at time 0 i = Interest rate FVn = Value at the end of the periods PVIF i,n = Present value interest factor at the rate of i percent and n periods 14 Norazidah Shamsudin - Dungun

Exercise..Let’s try… Solution: 0 10% PV = ?FV= 1, PV = FVn (PVIF i,n ) = RM1, (PVIF 10%,5 ) = RM1, (0.6209) = RM1, E.g: Calculate the present value of RM1, due in 5 years if the discount rate is 10%. Norazidah Shamsudin - Dungun

Future Value (Compounded) Refer to the amount at a later date with consideration of interest (i), time (n), and the discounted value (PVn). In compounding, money is moved forward in time. 16 Future Value of Lump Sum FV Future Value of Annuity FV A Norazidah Shamsudin - Dungun

Is defined as the sum to which a beginning amount of principal (PV) will grow over n years when interest is earned at the rate of i% of a year. The equations for compounding: 17 FV of Lump Sum FV = PVn(FVIFi,n) Tabular Solution FV = PV (1+i) n Numerical Solution Norazidah Shamsudin - Dungun

FV.. Cont… Where, FV = Value or the ending amount at the end of period (n). i = Interest rate PVn = Present Value or beginning value FVIF i,n = Future value interest factor at the rate of i percent and n periods 18 Norazidah Shamsudin - Dungun

E.g: If a person invests RM1,000 in a security that pays 10% interest compounded annually. How much will this person have at the end of 1 year? Solution: Time Line 0 10% 1 PV = -1,000FV = ? 19 Exercise Norazidah Shamsudin - Dungun

Solution 20 Numerical Solution FVn = PV (1+i) n = RM1,000 (1+0.10) 1 = RM1,000 (1.1) 1 = RM1,100 Numerical Solution FVn = PV (1+i) n = RM1,000 (1+0.10) 1 = RM1,000 (1.1) 1 = RM1,100 Tabular Solution FVn= PV (FVIF i,n ) = RM1,000 (FVIF 10%,1 ) = RM1,000 (1.1000) = RM1,100 Tabular Solution FVn= PV (FVIF i,n ) = RM1,000 (FVIF 10%,1 ) = RM1,000 (1.1000) = RM1,100 Norazidah Shamsudin - Dungun

Annuity It is a series of equal payments or receipts for a specified number of years. The payments or receipts must be of equal amount and for a certain number of years. 2 types of annuity : 21 Annuity due – where each receipt or payment occurs at the beginning of the year Ordinary or regular Annuity - where each receipt or payment occurs at the end of the year. Norazidah Shamsudin - Dungun

Annuity = Periodic payment PV of Annuity The concept of present value of annuity is mostly concerned with payment of loans, bonds, mutual funds and others. 22 Norazidah Shamsudin - Dungun

PV A..Cont… Formula: Where, a = annual receipt or payment or installment PVIFA i,n = Present Value Interest Factor Annuity at the rate of i% and n periods 23 Norazidah Shamsudin - Dungun

Exercise 24 Farah won ‘Who Want to be a Millionaire’ contest. She had two options that are: 1. To collect RM1,000,000 cash today. 2. To collect RM200,000 a year for 6 years. If the amount is discounted 5%, which option should she choose? Norazidah Shamsudin - Dungun

Solution PV A = a x PVIFA i,n = 200,000 (PVIFA 10%,6 ) = 200,000 (5.0757) = RM1,015, % PV A = ? 200k 200k 200k 200k 200k 200k Tabular Solution Hence, RM1,000,000 vs. RM1,015,140….choose? 25Norazidah Shamsudin - Dungun

26 FV of Annuity Is the total amount will have at the end of the annuity period if each payment is invested at a certain interest rate and is held to the end of the annuity period. Norazidah Shamsudin - Dungun

Activity When would be the companies pay day? Are all on the same date? No…Different company would have different date of salary, depends on the management of the company (unless for government staff who will received salary on the same date) So, banker would earn higher value than govt. servant since the pay day is earlier… 27 Norazidah Shamsudin - Dungun

Formula: Where, a =annual receipt FVIFA i,n = Future Value Interest Factor Annuity at the rate of i% and n periods 28 FV A..Cont… Future value of an annuity = a x FVIFAi,n (ordinary annuity) Future value of an annuity = a (FVIFAi,n) (1+i) (annuity due) Norazidah Shamsudin - Dungun

Exercise..FV A ( Ordinary Annuity) How much do we have at the end of 3 years if RM1,000 is invested at the end of every year for 3 years and the security pays 10% interest annually? Numerical Solution: Time Line 0 10% ,000 1,000 1,000 1,000 1,000 (1+0.1) 1 1,100 1,000 (1+0.1) 2 1,210 RM 3, Norazidah Shamsudin - Dungun

Tabular Solution Future value of annuity = a x FVIFA i,n = RM1,000 (FVIFA 10%,3 ) = RM1,000 (3.3100) = RM3, Solution Norazidah Shamsudin - Dungun

Refer to example above. Assume RM1,000 is invested at the beginning of every year for 3 years, instead of at the end of every year then the amount that we will have at the end of 3 years will be… 31 Exercise..FV A ( Annuity Due) Norazidah Shamsudin - Dungun

Time Line 0 10% ,000 1,0001,000FVA = ? 32 Solution Future value of annuity = a (FVIFA i,n ) (1+i) =1,000 (3.310) (1+0.1) = RM3,641 Norazidah Shamsudin - Dungun

Determining Interest Rate If other details given and we want to calculate for the interest rate, any formula can be used for this purpose. 33 Exercise: E.g.: Suppose a bank offers to lend you RM4,000 today if you sign a note agreeing to pay back the bank RM7,050 at the end of 5 years. What rate of interest would you be paying on the loan? Norazidah Shamsudin - Dungun

FV 5 = PV (FVIF i, n ) 7,050 = 4,000 (FVIF i, 5 ) FVIF i, 5 = 7,050 4,000 = Solution By referring to FVIF table, at period 5, interest rate is 12%. Norazidah Shamsudin - Dungun

Semi Annual and Other Compounding Period Compounding period is not always be annually, but it can also be semi-annually, quarterly, monthly and daily. To find the future value of an investment for which interest is compounded in non-annual periods: 35 Norazidah Shamsudin - Dungun

Where, m = number of times per year that compounding occurs semi annually,m=2 quarterly,m=4 monthly, m=12 daily,m= Norazidah Shamsudin - Dungun

Formula: Norazidah Shamsudin - Dungun37 Tabular SolutionNumerical Solution PV = FV (PVIF i,n ) PV = FV. (1+i) n FV = PV (FVIF i,n ) FV = PV (1+i) n PV A = a (PVIFA i,n ) PV A = a x [1-1/(1+i) n ] i FV A = a (FVIFA i,n ) FV A = a x (1+i) n -1 i

To find the amount to which RM1,000 will grow after 5 years if semi annual compounding is applied to a stated 10% interest rate. Solution: 38 Exercise FV n = PV (FVIF i/m, mn ) = RM1,000 (FVIF 10%/2,2x5 ) = RM1,000 (FVIF 5%,2x5 ) = RM1,000 (1.6289) = RM1, Norazidah Shamsudin - Dungun

Amortization Amortization of loan involves the procedure of paying off loan by making periodic equal payments at regular intervals. Payment = Principal + interest However final payment is necessary to be adjusted in order to get zero balance at the end of the period 39 Norazidah Shamsudin - Dungun

Exercise Mr. Aliff plan to borrow RM10,000 for a period of 5 10% p/annum. The yearly annuity payments would be: Present Value of annuity = a x PVIFA i,n RM10,000 = a (PVIFA 10%,5 ) = 10,000/3.791 a = RM2, Norazidah Shamsudin - Dungun

Adjustment on final payment: Final payment = Beginning balance (1 + i) = RM2, ( ) = RM2, Hence, every year will pay RM2, and the final payment would be RM2, Solution Norazidah Shamsudin - Dungun