0 Tutorial 2 : Time Value of Money Conducted by : Mr. Chong Lock Kuah, CFA
1 Key Points • The first step in time value analysis is to set up a time line, which will help you to visualize what is happening in a particular problem CF 2 CF 1 CF 3 I/YR 0 1 2 3 Year Cash flows 1. Time 0 is today; Time 1 is the end of period 1; or the beginning of period 2 2. Negative CF (-CF) are cash outflows
2 Key Points • FV is the amount to which a cash flow or series of cash flows will grow over a given period of time when compounded at a given interest rate • PV is the value today of a future cash flow or series of cash flows • Annual Percentage Rate (APR) is the contracted, quoted or stated interest rate. It is equal to periodic interest rate times the number of period per year • Effective Annual Rate (EAR or EFF) is the annual interest rate actually being earned (or paid), as opposed to the quoted rate. An EAR is the interest rate expressed as if it were compounded once per year
3 Key Points square4 Solving time value of money problems using financial calculator TI II Plus is a preferred method square4 Before using a financial calculator, make sure that the calculator is set up as follows: square4 P/Y is set equal to 1, hit square4 Make sure that the calculator is in “End Mode” (default setting) square4 Set the calculator to display 8 decimal places, hit square4 Clear all memory hit and hit square4 Always make sure that the interest rate and the time period match. For example, when there are more than one periods in a year, use periodic interest rate (APR/m where m is the compounding frequency per year) and input N= number of periods per year x number of yrs square4 For example, APR =10% and the compounding frequency is twice per year and you enter in the financial calculator as I/Y =5 and then enter N= 2x number of years 2ND . FORMAT 1 2ND 8 2ND FV CLR TVM I/Y P/Y 2ND CE/C CLR WORK ENTER SET
4 Key Points • When calculating the PV of an ordinary annuity, 100 100 100 10% 0 1 2 3 Year Ordinary Annuity Using a financial calculator input: N = 3, I/Y = 10, PMT =100, FV = 0, and then solve for PV = -$248.69
5 Key Points • When calculating the PV of an annuity due, 100 100 10% 0 1 2 3 Year Annuity Due Using a financial calculator Hit and then enter : N = 3, I/Y = 10, PMT =100, FV = 0, and then solve for PV = - $273.55 100 2ND PMT BGN 2ND ENTER SET
6 Key Points • When calculating the PV of series of uneven cash flows, We have to enter individual cash flows using key 10% 0 1 2 3 Year 0 100 300 4 300 -50 NPV = 530.09 NPV = -CF 0 + PV(CF) Since CF 0 = 0, NPV=PV(CF) CF CF 0 ENTER SET 100 300 ENTER SET ENTER SET ENTER SET ENTER SET 2 50 ENTER SET NPV calculator will display I=0.000000, hit And then hit 10 ENTER SET CPT QUIT ↓ INS ↓ INS ↓ INS ↓ INS +/- RESET ↓ INS ↓ INS
7 Key Points • When calculating the FV of series of cash flows when payments occur annually, but compounding occurs each 6 months, I/YR = 10% 0 1 2 3 100 4 5 100 100 6 period Here we can’t use normal annuity valuation techniques. You can use the EAR and treat the cash flows as an ordinary annuity or use the periodic rate and compound the cash flows individually.)
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