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FIN 200: Personal Finance

FIN 200: Personal Finance. Topic 3-The Time Value of Money Larry Schrenk, Instructor. Learning Objectives. Explain the reasons for a time value of money . ▪ Explain compounding and discounting. Define a lump sum payment. Calculate the present and future value . ▪.

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FIN 200: Personal Finance

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  1. FIN 200: Personal Finance Topic 3-The Time Value of Money Larry Schrenk, Instructor

  2. Learning Objectives • Explain the reasons for a time value of money. ▪ • Explain compounding and discounting. • Define a lump sum payment. • Calculate the present and future value . ▪

  3. The Time Value of Money

  4. Time Value of Money • Why a Time Value of Money? • Components▪ • Opportunity Cost • Inflation • Risk NOTE: I will use ‘cash flow’ (CF) as a general term to designate any flow of money positive or negative.▪

  5. Compounding

  6. Compounding (Saving) • Compounding is calculating the amount you will have in the future: if, for example, you put money in a savings account. • If you make a deposit, called the present value (PV), how much will you have after N years if you get I/Y interest rate per year?▫ • The answer is the future value (FV).

  7. Future Value (FV) • Compounding • This is the equivalent to a one-time deposit in a savings account. • If I put in $100.00 today, how much will I have in... • One year? • Ten years? • One hundred years?

  8. Note on Percentages • Percentages can be expressed in • Integer form 8%, or • Decimal form 0.08. • These are mathematically the same. • But calculators normally have a ‘percentage convention’ when you do financial calculations: • If the interest rate is 12%, you should type 12 (the calculator assumes the ‘%’).▫

  9. Future Value (FV) • Calculating the Future Value • How much do I have after one year? • If the interest rate (I/Y) is 10%, then $100.00 × (1 + 10%) = $100.00 × 1.1 = $110.00▫ • I multiply the original sum by 1, because I still have my original deposit ($100.00) and I also multiply by 0.10 to calculate the additional interest ($10.00). • NOTE: In calculations the red font will indicate the solution or emphasize a certain part of a calculation

  10. Future Value (FV) • Calculating the Future Value • How much do I have after two years?▪ • At the beginning of the second year I have $110.00. • If the interest rate is 10%, then in two years: $110.00 × (1 + 10%) = $110.00 × 1.1 = $121.00▪

  11. Compound Interest • Compound Interest: Interest is ‘compound’ because we get interest on previous interest. • How do we get $121.00 after two years? Original amount: $100.00▪ Interest in first year: $10.00 Interest in second year: $10.00 Interest in the second year on the interest from the first year $10.00 × (1 + 10%): $1.00 TOTAL $121.00▪

  12. Simple Interest • Simple interest is when you do not receive interest on the previous interest. • Deposit $100 at a simple interest rate of 10%. • Deposit $100 • Year 1 $110 • Year 2 $120 • Year 3 $130... • Simple interest is rarely used in modern financial calculations because it underestimates the true value of an investment over several periods.

  13. Future Value (FV) • Calculating the Future Value • How much do I have after more years? • We can generalize the technique, so that each year the value increases by 1 + I/Y (here 1 + 10%).

  14. Timelines • If the timing of cash flows is ever confusing, use a timeline: I/Y I/Y I/Y I/Y 1 0 2 3 4 FV PV 10% 10% 10% 10% 1 0 2 3 4 ??? $100.00

  15. Future Value Formula • We could construct a formula: • FV is the value of our money in year N. • PV is how much we invest now. • I/Y is the interest rate each year. • N is the number of years we let it grow.

  16. Calculations • Possible Methods of Calculation • Formulae–Complicated • Tables (Textbook)–Confusing • Calculator!

  17. Calculator Help • In examples I use one particular calculator, but fortunately most financial calculators work is almost the same way. • If you get into trouble, first try reading the manual, though these can be very confusing. If you can’t figure it out, didn't get frustrated, instead... • Come to office hours. Bring your calculator and the manual.

  18. Calculator Buttons • For Now… • FV = Future Value • PV = Present Value • N = Number of Payments • I/Y, I = Interest Rate • CPT = Compute (only on the TI) • Later… • PMT = Payment • P/Y = Payments per Year

  19. Future Value with a Calculator • How much do we have after 4 years if we begin with $200 and the interest rate is 12%?▪ • Input 4, Press N • Input 12, Press I/Y • Input 200, press +/-, press PV (you get -200) (Why negative? In a minute) • Press CPT, FV to get 314.70, i.e., $314.70 NOTES: 1) Calculators assume the % when you press the I/Y key (do not input 12% as 0.12), 2) some calculators do not require the CPT key, and 3) the order of the inputs does not matter.▪

  20. Future Value with a Calculator I/Y I/Y I/Y I/Y 1 0 2 3 N FV PV Number of Periods Annual Interest Present Value Future Value

  21. Future Value with a Calculator 12% 12% 12% 12% 1 0 2 3 4 $314.70 $200.00 Remember to press CPT, before FV (TI Only).

  22. Essential Note: Clearing/Resetting • When you start a new problem, remove any values the calculator may hold from the last calculation. • You can ‘clear’ selected values. This is the process of returning them to the default (usually 0 for numeric values). • The more thorough solution is to ‘reset’ your calculator which clears all values, e.g., you will lose any numbers held in memory. • Do not assume that turning your calculator off and on clears all the values.

  23. TI and HP Calculators • Reset/Clear the TI • [2nd ] • [RESET] • [ENTER] • “RST 0.00” • Reset/Clear the HP • [Orange] • [C ALL]

  24. Why the Negative? • We calculate: • The calculator calculates: • For the latter calculation, one and only one of the cash flows we input must be negative, but it does not matter which one.

  25. Compounding Practice Problems • How much is $350.00 worth in 5 years if the interest rate is 9%?▪ $538.52 • How much is $400.00 worth in 15 years if the interest rate is 11%? $1,913.84 • How much is $1.00 worth in 100 years if the interest rate is 15%? $1,174,313.45▪

  26. Discounting

  27. Discounting • Discounting is calculating the current value (PV) of money coming in the future. • What is the current value (PV) of money (FV) I expect to receive in N years given I/Y interest? • The answer is the present value (PV). • If someone promises me $100.00 next year, how much is that worth today? • Or how much would I need to save today to have $100.00 next year?

  28. Discounting • Discounting is the exact opposite of compounding. • More technically, discounting is the inverse of compounding. • If I start with $100.00, compound it and then discount it (using the same values, e.g., N), I get the original $100.00.

  29. Discounting • What is the value today of $100.00 I receive it in... • One year? • Ten years? • One hundred years?

  30. Discounting • Calculating the Present Value • How much is money worth if I receive it in one year? • If the interest rate (I/Y) is 10%, then $100.00/(1 + 10%) = $100.00/1.1 = $90.91 • All I did was change the ‘×’ to ‘/’ in the formula. • I divide the original future value by 1 + 10%, because 10% is the growth of money over time.

  31. Discounting • We can generalize this for money coming at different times:

  32. Timelines • Again, if the timing of cash flows is ever confusing, use a time line: I/Y I/Y I/Y I/Y 1 0 2 3 4 FV PV 10% 10% 10% 10% 1 0 2 3 4 $100.00 ???

  33. Present Value Formula • We could construct a formula: • FV is the value of our money in year N. • PV is how much we invest now. • I/Y is the interest rate each year. • N is the number of years we let it grow. • But again we will just use a calculator.

  34. Present Value with a Calculator • How much is $200 received in 4 years worth now, if we the interest rate is 12%?▪ • Input 4, press N • Input 12, press I/Y • Input 200, press +/-, press FV (you get -200) • Press CPT, PV to get 127.10, i.e., $127.10 NOTES: 1) Calculators assume the % when you press the I/Y key (do not input 12% as 0.12), 2) some calculators do not require the CPT key, and 3) the order of the inputs does not matter.▪

  35. Present Value with a Calculator 12% 12% 12% 12% 1 0 2 3 4 $200.00 $127.10 Remember to press CPT, before FV (if necessary).

  36. Discounting Practice Problems • How much is $350.00 received in 5 years worth if the interest rate is 9%?▪ $227.48 • How much is $400.00 received in 15 years worth if the interest rate is 11%? $83.60 • How much is $1,000,000 received in 100 years worth if the interest rate is 15%? 85 cents!▪

  37. Ethical Dilemma (Chap. 3, 76.16) • Cindy and Jack have budgeted $300 per month for car payments. A salesman, Herb, insists that they look at a more expensive car with payments of $500 per month. They can only afford the expensive car by discontinuing a $200 monthly retirement contribution. Since they plan to retire in 30 years, Herb explains that they would only need to stop the $200 monthly payments for the five years of the car loan and calculates that the $12,000 in lost contributions could be made up over the remaining 25 years by increasing their monthly contribution by only $40 per month. • a. Comment on the ethics of a salesperson who attempts to talk customers into spending more than they had originally planned and budgeted. • b. Is Herb correct in his calculation?

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