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FIN 365 Business Finance

FIN 365 Business Finance. Topic 7: Time Value of Money III: Non-Annual Cash Flows, Rates of Change; Amortization Larry Schrenk, Instructor. Today’s Outline. Non-Annual Cash Flows Percentages Rates of Change Amortization. 1. Non-Annual Cash Flows. Non-Annual Periods.

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FIN 365 Business Finance

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  1. FIN 365 Business Finance Topic 7: Time Value of Money III: Non-Annual Cash Flows, Rates of Change; Amortization Larry Schrenk, Instructor

  2. Today’s Outline • Non-Annual Cash Flows • Percentages • Rates of Change • Amortization

  3. 1. Non-Annual Cash Flows

  4. Non-Annual Periods • m = Periods per Year • Examples • 2 = Semi-Annual • 4 = Quarterly • 12 = Monthly • 52 = Weekly • 364 or 360 = Daily

  5. Calculator Adjustments • 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 = 60

  6. Changing P/Y • TI • [2nd ] [I/Y] • m [Enter] • HP • m • [Orange] • PMT

  7. FV and Compounding Period

  8. PV and Compounding Period

  9. Single Dollar • How much do we have after 2 years if we deposit $500 and the interest rate is 10% (compounded quarterly)? • Set P/Y = 4 • Input 8, Press N (2 x 4 = 8) • Input 10, Press I/Y (annual rate) • Input 500, press +/-, press PV (you get -500) • Press CPT, FV to get $609.20

  10. Non-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. Annuity 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%? • Set P/Y = 12 • Input 0, Press PV • Input 36, Press N (3 x 12 = 36) • Input 12, Press I/Y • Input 200, press +/-, press PMT(you get -200) • Press CPT, FV to get $8,615.38

  12. Annuity 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? • Set P/Y = 12 • Input 0, Press FV • Input 60, Press N (5 x 12 = 60) • Input 15, Press I/Y • Input 10,000, press +/-, press PV (you get -10,000) • Press CPT, PMT to get $237.90

  13. Non-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. Non-Annual Perpetuities • Formula: • Remember that C is the period cash flow.

  15. T-S-P • If you increase the number of periods per year, the present value will: • Increase • Remain the same • Decrease • Cannot determine

  16. 2. Percentages

  17. Percentages • 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. Percentages • 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

  19. 3. Rates of Change

  20. Types 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 Time

  21. Simple 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. Compound 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!

  23. Holding Period Return • Most basic rate calculation • Change from one point of time (t = 0) to another (t = 1):

  24. Holding 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!

  25. Holding 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. Non-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 m

  27. Rate Conversions

  28. Rate Conversions • Most often we will be converting a non-annual rate to an annual rate. • Unfortunately, there are several ‘versions’ of annual rates.

  29. Annual Percentage Rate (APR) • Annual percentage rate (APR) • This is an application of simple (not compound) interest. • AKA: Nominal, Stated, Quoted Rate

  30. APR 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 my return by 2.82%!

  31. Effective Annual Return (EAR) • The correct annual rate to use is the Effective Annual Return (EAR). • This form of the annual rate recognizes compound interest. • AKA: • Equivalent Annual Return (EAR)

  32. Effective Annual Return (EAR) • If you have an APR and want to convert it to EAR: • In our example, we had an APR of 24%.

  33. Effective Annual Return (EAR) • If you have a non-annual rate and want to convert it to EAR: • In our example, we had a monthly rate of 2%.

  34. IMPORTANT DISTINCTION Formula: APR  EAR Formula: Non-Annual Rate  EAR

  35. Effective Annual Return (EAR) • We can also start with the EAR and find any equivalent non-annual rate. • If my EAR is 31%, then the equivalent weekly return is:

  36. Calculator Functions • Nom = Nominal Rate (APR) • Eff = Effective Rate (EAR)

  37. Rate Practice HPRweekly = 0.2%. Find EAR and APR. APRweekly = 20%. Find EAR EAR = 10%. Find rquarterly. ▪

  38. Amortization

  39. Amortization • Installment Loan • Compound Interest • Equal Payments • Distinguish • Repayment of Principle • Repayment of Interest

  40. Amortization Graph

  41. Amortization Example • Loan: $1,000 • Maturity: 3 years • Interest Rate: 8% • Period: Annual • Calculate Equal Payments • N =3; I/Y = 8; PV = -1,000; PMT = $388.03; FV = 0

  42. Amortization Calculation • Find Interest due on Balance. • Subtract Interest from Payment to get Principle. • Subtract Principle from Balance to get New Balance.

  43. Amortization Calculation End Bal. 691.97 359.29 0 Year 1 2 3 Interest 80.00 55.36 28.74 Principal 308.03 332.68 359.29 End Bal. 691.97 359.29 0 Begin Bal. 1,000 691.97 • 359.29 Payment 388.03 • 388.03 • 388.03 Interest 80.00 55.36 28.74 Principal 308.03 332.68 359.29 Interest = Rate x Balance 359.29(0.08) = 28.74 691.97(0.08) = 55.36 1,000(0.08) = 80 Principal = Payment – Interest 388.03 – 55.36 = 332.68 388.03 – 28.74 = 359.29 388.03 – 80 = 308.03 Balance = Balance – Principal 691.97 – 332.68 = 359.29 359.29 – 359.29 = 0 1,000 – 308.03 = 691.97

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