Introduction to Valuation: The Time Value of Money

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Presentation transcript:

Introduction to Valuation: The Time Value of Money 5 Introduction to Valuation: The Time Value of Money

Chapter 5 – Index of Sample Problems Slide # 02 - 03 Simple interest versus compound interest Slide # 04 - 06 Future value Slide # 07 - 09 Present value Slide # 10 - 12 Interest rate for a single period Slide # 13 - 15 Interest rate for multiple periods Slide # 16 - 18 Number of time periods Slide # 19 Present value and rate changes Slide # 20 Future value and rate changes Slide # 21 Present value and time changes Slide # 22 Future value and time changes

Interest rate Principle =1 (future rate) Interest rate: r (per period), periods: n Simple interest rate: 1+nr Compound interest rate: (1+r)^n Interest rate: r (annually), time: t years Continuous compound interest rate: e^(rt)

Discount rate Future rate is the value of now one dollar at end. Discount rate is the value of end one dollar at now. Discount rate = 1/future rate

2: Simple versus compound interest First United Bank pays 4% simple interest on their savings accounts. Second Federal Bank pays 4% interest compounded annually on their savings accounts. If you invest $1,000 in each bank, how much will you have in your accounts after twenty years? Why are the balances different?

3: Simple versus compound interest First United Bank Second Federal Bank Difference

4: Future value You invest $3,000 in the stock market today. How much will your account be worth forty years from now if you earn a 9% rate of return?

5: Future value

6: Future value Enter 40 9 3,000 N I/Y PV PMT FV Solve for 94,228.26

7: Present value You want to have $7,500 three years from now to buy a car. You can earn 6% on your savings. How much money must you deposit today to have the $7,500 in three years?

8: Present value

9: Present value Enter 3 6 7,500 N I/Y PV PMT FV Solve for -6,297.14

10: Interest rate for a single period Last year your investments were worth $369,289. Today they are worth $401,382. No deposits or withdrawals were made during the year. What rate of return did you earn on your investments this year?

11: Interest rate for a single period

12: Interest rate for a single period Enter 1 369,289 401,382 N I/Y PV PMT FV Solve for 8.6905

13: Interest rate for multiple periods The City Museum owns a rare painting currently valued at $1.2 million. The museum paid $240,000 to purchase the painting twelve years ago. What is the rate of appreciation on this painting?

14: Interest rate for multiple periods

15: Interest rate for multiple periods Enter 12 240,000 1,200,000 N I/Y PV PMT FV Solve for 14.35298

16: Number of time periods Tom originally started to work for Jackson Enterprises at an annual salary of $36,500. Today, Tom earns $68,200. Tom calculated that his average annual pay raise has been 3.4%. How long has Tom worked for Jackson Enterprises?

17: Number of time periods

18: Number of time periods Enter 3.4 36,500 68,200 N I/Y PV PMT FV Solve for 18.697

19: Present value and rate changes Enter 1 6 100 N I/Y PV PMT FV Solve for -94.34 Enter 1 7 100 Solve for -93.46

20: Future value and rate changes Enter 1 6 100 N I/Y PV PMT FV Solve for 106 Enter 1 100 N I/Y PV PMT FV Solve for 107

21: Present value and time changes Enter 1 5 100 N I/Y PV PMT FV Solve for -95.24 Enter 2 5 100 N I/Y PV PMT FV Solve for -90.70

22: Future value and time changes Enter 1 5 100 N I/Y PV PMT FV Solve for 105 Enter 2 5 100 N I/Y PV PMT FV Solve for 110.25

5 End of Chapter 5