Slide 1Today’s OutlineSlide 3Non-Annual PeriodsCalculator AdjustmentsChanging P/YFV and Compounding PeriodPV and Compounding PeriodSingle DollarNon-Annual AnnuitiesAnnuity FV with a CalculatorAnnuity PV with a CalculatorNon-Annual Practice ProblemsNon-Annual PerpetuitiesT-S-PSlide 16PercentagesPercentagesSlide 19Types of Rate of Change ProblemSimple Rates (Interest)Compound Rates (Interest)Holding Period ReturnHolding Period ReturnHolding Period ReturnNon-Annual RatesSlide 27Rate ConversionsAnnual Percentage Rate (APR)APR ExampleEffective Annual Return (EAR)Effective Annual Return (EAR)Effective Annual Return (EAR)IMPORTANT DISTINCTIONEffective Annual Return (EAR)Calculator FunctionsRate PracticeSlide 38AmortizationAmortization GraphAmortization ExampleAmortization CalculationAmortization Calculation1 of 4310:07 AMTopic 7: Time Value of Money III: Non-Annual Cash Flows, Rates of Change; AmortizationLarry Schrenk, InstructorFIN 365 Business Finance2 of 4310:07 AM1. Non-Annual Cash Flows2. Percentages3. Rates of Change4. AmortizationToday’s Outline3 of 4310:07 AM1. Non-Annual Cash Flows4 of 4310:07 AM•m = Periods per Year•Examples–2 = Semi-Annual–4 = Quarterly–12 = Monthly–52 = Weekly–364 or 360 = DailyNon-Annual Periods5 of 4310:07 AM•Two Changes:–Periods per Year (P/Y)•Adjust P/Y to m•Weekly P/Y = 52–Number of Periods (N)•Remember N is the Number of Periods•Monthly Discounting for 5 Years–N = 12 x 5 = 60Calculator Adjustments6 of 4310:07 AM•TI1. [2nd ] [I/Y]2. m [Enter]•HP1. m2. [Orange] 3. PMTChanging P/Y7 of 4310:07 AMFV and Compounding Period8 of 4310:07 AMPV and Compounding Period9 of 4310:07 AM•How much do we have after 2 years if we deposit $500 and the interest rate is 10% (compounded quarterly)?1. Set P/Y = 42. Input 8, Press N (2 x 4 = 8)3. Input 10, Press I/Y (annual rate)4. Input 500, press +/-, press PV (you get -500)5. Press CPT, FV to get $609.20Single Dollar10 of 4310:07 AMNon-Annual Annuities •Unfortunately, not all annuities have annual cash flows: –Bonds Semi-annual coupons, –Loans Monthly payments, –Dividends Quarterly, –We can put money in a bank quarterly, weekly, daily or even hourly.•Need a mechanism for adapting all of our annuity formulae for non-annual periods.11 of 4310:07 AMAnnuity FV with a Calculator•How much do we have after 3 years if we save $200 per month beginning next month and the interest rate is 12%?1. Set P/Y = 122. Input 0, Press PV3. Input 36, Press N (3 x 12 = 36)4. Input 12, Press I/Y5. Input 200, press +/-, press PMT (you get -200)6. Press CPT, FV to get $8,615.3812 of 4310:07 AMAnnuity PV with a Calculator•You have a loan of $10,000 to be repaid in monthly installments over 5 years with an interest rate of 15%? What is the monthly payment?1. Set P/Y = 122. Input 0, Press FV3. Input 60, Press N (5 x 12 = 60)4. Input 15, Press I/Y5. Input 10,000, press +/-, press PV (you get -10,000)6. Press CPT, PMT to get $237.9013 of 4310:07 AMNon-Annual Practice Problems•How much will you have if you save $100.00 per month for 25 years at 8%?–$95,102.64•How much can you borrow if you pay $50.00 per week for 5 years at 7%?–$10,962.57•How much do you need to save per month to have $10,000 in 5 years at 10%? ▪–$129.14 ▪14 of 4310:07 AMNon-Annual Perpetuities•Formula:–Remember that C is the period cash flow.PerpetuityCPVrm=PerpetuityPV = Present Value of a PerpetuityC = Period Cash Flowr = Discount Ratem = Periods per Year15 of 4310:07 AM•If you increase the number of periods per year, the present value will:1. Increase2. Remain the same3. Decrease4. Cannot determineT-S-P16 of 4310:07 AM2. Percentages17 of 4310:07 AMPercentages•Using Absolute (Dollar) Value versus Ratios (e.g., Percentages)•Numerical Representation of Percentages–Integer Form 5%–Decimal Form 0.05•If in doubt, use the decimal form!18 of 4310:07 AMPercentages•Calculating a Percentage–If you have 35 balls and 12 are red, what is the percentage of red balls?•Basis Points–A ‘basis point’ is 1/100 of a percentage•1% = 100 basis points•0.25% = 25 basis points= =120.3429 34.29%3519 of 4310:07 AM3. Rates of Change20 of 4310:07 AMTypes of Rate of Change Problem•Three types of change are central:–Returns: Change of Dollar Value over Time–Growth Rates: Change of Size over Time–Inflation: Change of Prices over Time21 of 4310:07 AMSimple Rates (Interest)•Returns–Return on your principal, but –No return on the accumulated interest•$100 in an account for three year at 12% simple interest–100 + 12 + 12 + 12 = $136.22 of 4310:07 AMCompound Rates (Interest) •Returns–Return on your principal, and –Return on the accumulated interest•$100 in an account for three year at 12% compound interest–A gain of $4.49 over simple interest!0 100.00 100.001 100.00*1.12 112.002 112.00*1.12 125.443 125.44*1.12 140.4923 of 4310:07 AMHolding Period Return •Most basic rate calculation–Change from one point of time (t = 0) to another (t = 1):-=1 00V VHPRV10HPR = Holding Period Return = Value at t = 1 = Value at t = 0VV24 of 4310:07 AMHolding Period Return •My portfolio was worth $123,000 5 years ago and it is now worth $131,000:–REMEMBER: The earlier value always goes in the denominator!131,000 123,0000.065 6.5%123,000HPR-= = =25 of 4310:07 AMHolding Period Return•Problem: Comparing assets with different holding periods.•Which is better?–7.8% over 7 years–10.5% over 10 year•Need a common time period–Convert all rates to an annual basis–‘Annualize’ them (as with ratios)26 of 4310:07 AMNon-Annual Rates•For example, monthly data for stock returns. •If a stock was at $110 at the end of last month and $108 at the end of this month:–Need to annualize the return.–NOTE: rm is rate for period m108 1100.018 1.8%110monthlyHPR-= =- =-27 of 4310:07 AMRate Conversions28 of 4310:07 AMRate Conversions•Most often we will be converting a non-annual rate to an annual rate.•Unfortunately, there are several ‘versions’ of annual rates.29 of 4310:07 AMAnnual Percentage Rate (APR)•Annual percentage rate (APR)–This is an application of simple (not compound) interest.–AKA: Nominal, Stated, Quoted RatemAPR r m= �APR = Annual Percentage Rate = Return for Period mm = Periods per Yearmr30 of 4310:07 AMAPR Example•If you have a monthly rate of 2%•But if I put $100 in an account at 2% per month and left it there for 12 months, I would have:•So the APR understates