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4. Single-Period Investment Multi-Period Investment The Discount Rate Number of Periods Calculating Present Value Present Value, Single Amount The Time Value of Money > Present Value, Single Amount Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/finance?campaign_content=book_192_section_56&campaign_term=Finance&utm_campaign=powerpoint&utm_medium=dir ect&utm_source=boundless

5. A single period investment has the number of periods (n or t) equal to one. For both simple and compound interest, the PV is FV divided by 1+i. The time value of money framework says that money in the future is not worth as much as money in the present. Single-Period Investment Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/finance/textbooks/boundless-finance-textbook/the-time-value-of-money-5/present-value-single-amount-56/single-period- investment-260- 7560?campaign_content=book_192_section_56&campaign_term=Finance&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess FV of a single payment View on Boundless.com The Time Value of Money > Present Value, Single Amount

6. Finding the PV for a multi-period investment is the same as for a single-period investment: plug FV, the interest rate, and the number of periods into the correct formula. PV varies jointly with FV, and inversely with i and n. When n>1, simple and compound interest cease to provide the same answer (unless the interest rate is 0). Multi-Period Investment Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/finance/textbooks/boundless-finance-textbook/the-time-value-of-money-5/present-value-single-amount-56/multi-period- investment-261- 7561?campaign_content=book_192_section_56&campaign_term=Finance&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess View on Boundless.com The Time Value of Money > Present Value, Single Amount

7. The discount rate represents some cost (or group of costs) to the investor or creditor. Some costs to the investor or creditor are opportunity cost, liquidity cost, risk, and inflation. The discount rate is used by both the creditor and debtor to find the present value of an amount of money. The Discount Rate Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/finance/textbooks/boundless-finance-textbook/the-time-value-of-money-5/present-value-single-amount-56/the-discount-rate- 262- 709?campaign_content=book_192_section_56&campaign_term=Finance&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundle ss Borrowing and lending View on Boundless.com The Time Value of Money > Present Value, Single Amount

8. A period is just a general term for a length of time. It can be anything- one month, one year, one decade- but it must be clearly defined and fixed. For both simple and compound interest, the number of periods varies jointly with FV and inversely with PV. The number of periods is also part of the units of the discount rate: if one period is one year, the discount rate must be defined as X% per year. If one period is one month, the discount rate must be X% per month. Number of Periods Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/finance/textbooks/boundless-finance-textbook/the-time-value-of-money-5/present-value-single-amount-56/number-of- periods-263- 3905?campaign_content=book_192_section_56&campaign_term=Finance&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess FV of a single payment View on Boundless.com The Time Value of Money > Present Value, Single Amount

9. The first step is to identify if the interest is simple or compound. Most of the time, it is compound. The interest rate and number of periods must have consistent units. The PV is what a future sum is worth today given a specific interest rate (often called a "discount rate"). Calculating Present Value Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/finance/textbooks/boundless-finance-textbook/the-time-value-of-money-5/present-value-single-amount-56/calculating- present-value-264- 1422?campaign_content=book_192_section_56&campaign_term=Finance&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess Simple Interest Formula View on Boundless.com The Time Value of Money > Present Value, Single Amount

10. Free to share, print, make copies and changes. Get yours at www.boundless.com Appendix

11. Key terms compound interest Interest, as on a loan or a bank account, that is calculated on the total on the principal plus accumulated unpaid interest. discount to account for the time value of money discount rate The interest rate used to discount future cash flows of a financial instrument; the annual interest rate used to decrease the amounts of future cash flow to yield their present value. discounting The process of finding the present value using the discount rate. interest rate The percentage of an amount of money charged for its use per some period of time. It can also be thought of as the cost of not having money for one period, or the amount paid on an investment per year. multi-period More than one unit of time. period The length of time during which interest accrues. simple interest interest paid only on the principal. Free to share, print, make copies and changes. Get yours at www.boundless.com The Time Value of Money

12. Simple Interest Formula Simple interest is when interest is only paid on the amount you originally invested (the principal). You don't earn interest on interest you previously earned. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia. "Future value." GNU FDL http://en.wikipedia.org/wiki/Future_value View on Boundless.comGNU FDLhttp://en.wikipedia.org/wiki/Future_valueView on Boundless.com The Time Value of Money

13. Borrowing and lending Banks like HSBC take such costs into account when determining the terms of a loan for borrowers. Free to share, print, make copies and changes. Get yours at www.boundless.com Geograph. "HSBC Bank Acocks Green 40-11-01 (C) Roy Hughes :: Geograph Britain and Ireland." CC BY-SA http://www.geograph.org.uk/photo/1107226 View on Boundless.comCC BY-SAhttp://www.geograph.org.uk/photo/1107226View on Boundless.com The Time Value of Money

14. Present Value Single Payment Finding the PV is a matter of plugging in for the three other variables. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia. "Time value of money." GNU FDL http://en.wikipedia.org/wiki/Time_value_of_money View on Boundless.comGNU FDLhttp://en.wikipedia.org/wiki/Time_value_of_moneyView on Boundless.com The Time Value of Money

15. FV of a single payment The PV and FV are directly related. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia. "Time value of money." GNU FDL http://en.wikipedia.org/wiki/Time_value_of_money View on Boundless.comGNU FDLhttp://en.wikipedia.org/wiki/Time_value_of_moneyView on Boundless.com The Time Value of Money

16. Car Car loans, mortgages, and student loans all generally have compound interest. Free to share, print, make copies and changes. Get yours at www.boundless.com Open ClipArt. "Clipart - American Sport Car." Public domain http://openclipart.org/detail/16372/american-sport-car-by-bobocal-16372 View on Boundless.comPublic domainhttp://openclipart.org/detail/16372/american-sport-car-by-bobocal-16372View on Boundless.com The Time Value of Money

17. FV of a single payment The FV is related to the PV by being i% more each period. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia. "Time value of money." GNU FDL http://en.wikipedia.org/wiki/Time_value_of_money View on Boundless.comGNU FDLhttp://en.wikipedia.org/wiki/Time_value_of_moneyView on Boundless.com The Time Value of Money

18. Free to share, print, make copies and changes. Get yours at www.boundless.com The Time Value of Money In a year, you expect to receive a payment of $1 million in a year. That annual interest rate is 5%. What is the present value of the future payment? A) $666,667 B) $952,381 C) $995,025 D) $1,050,000

19. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ The Time Value of Money In a year, you expect to receive a payment of $1 million in a year. That annual interest rate is 5%. What is the present value of the future payment? A) $666,667 B) $952,381 C) $995,025 D) $1,050,000

20. Free to share, print, make copies and changes. Get yours at www.boundless.com The Time Value of Money What is the present value of $100,000 that will be received 5 years from today if you face a 10% compound interest rate every year (rounded up to the nearest dollar)? A) 62092 B) 52092 C) 72092 D) 82092

21. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Saylor OER. "Business Administration « Saylor.org – Free Online Courses Built by Professors." CC BY 3.0 http://www.saylor.org/majors/Business/CC BY 3.0 http://www.saylor.org/majors/Business/ The Time Value of Money What is the present value of $100,000 that will be received 5 years from today if you face a 10% compound interest rate every year (rounded up to the nearest dollar)? A) 62092 B) 52092 C) 72092 D) 82092

22. Free to share, print, make copies and changes. Get yours at www.boundless.com The Time Value of Money Assume you invest money in a bond that will pay you $250,000 in four years. The bond has an annual interest rate of 5%. You do not receive interest payments while you own the bond; it is zero- coupon. What is the bond's present value? A) $205,482 B) $205,676 C) $238,095 D) $240,385

23. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ The Time Value of Money Assume you invest money in a bond that will pay you $250,000 in four years. The bond has an annual interest rate of 5%. You do not receive interest payments while you own the bond; it is zero- coupon. What is the bond's present value? A) $205,482 B) $205,676 C) $238,095 D) $240,385

24. Free to share, print, make copies and changes. Get yours at www.boundless.com The Time Value of Money Which of the following is a cost to the investor that is included in the calculation of an investment's interest rate? A) Opportunity Cost. B) Inflation. C) Risk of a bad investment. D) All of these answers.

25. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ The Time Value of Money Which of the following is a cost to the investor that is included in the calculation of an investment's interest rate? A) Opportunity Cost. B) Inflation. C) Risk of a bad investment. D) All of these answers.

26. Free to share, print, make copies and changes. Get yours at www.boundless.com The Time Value of Money Which of the following could be an appropriate period used in a present value calculation? A) A year. B) A month. C) Three months. D) All of these answers.

27. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ The Time Value of Money Which of the following could be an appropriate period used in a present value calculation? A) A year. B) A month. C) Three months. D) All of these answers.

28. Free to share, print, make copies and changes. Get yours at www.boundless.com The Time Value of Money Which of the following the correct formula for calculating present value using compound interest? A) PV = FV/(1+(i*t)) B) PV = FV / (1+i)n C) PV = FV/(i) D) All of these answers.

29. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ The Time Value of Money Which of the following the correct formula for calculating present value using compound interest? A) PV = FV/(1+(i*t)) B) PV = FV / (1+i)n C) PV = FV/(i) D) All of these answers.

30. Attribution Boundless Learning. "Boundless." CC BY-SA 3.0 http://www.boundless.com//finance/definition/discountCC BY-SA 3.0http://www.boundless.com//finance/definition/discount Boundless Learning. "Boundless." CC BY-SA 3.0 http://www.boundless.com//finance/definition/discounting--2CC BY-SA 3.0http://www.boundless.com//finance/definition/discounting--2 Wiktionary. "discount rate." CC BY-SA 3.0 http://en.wiktionary.org/wiki/discount+rateCC BY-SA 3.0http://en.wiktionary.org/wiki/discount+rate Wikipedia. "Cost of capital." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Cost_of_capitalCC BY-SA 3.0http://en.wikipedia.org/wiki/Cost_of_capital Wikipedia. "Discounting." CC BY-SA 3.0 http://en.wikipedia.org/wiki/DiscountingCC BY-SA 3.0http://en.wikipedia.org/wiki/Discounting Wikipedia. "Present value." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Present_valueCC BY-SA 3.0http://en.wikipedia.org/wiki/Present_value Wiktionary. "simple interest." CC BY-SA 3.0 http://en.wiktionary.org/wiki/simple+interestCC BY-SA 3.0http://en.wiktionary.org/wiki/simple+interest Wiktionary. "compound interest." CC BY-SA 3.0 http://en.wiktionary.org/wiki/compound+interestCC BY-SA 3.0http://en.wiktionary.org/wiki/compound+interest Wikipedia. "Present value." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Present_valueCC BY-SA 3.0http://en.wikipedia.org/wiki/Present_value Wikipedia. "period." CC BY-SA 3.0 http://en.wikipedia.org/wiki/periodCC BY-SA 3.0http://en.wikipedia.org/wiki/period Wikipedia. "Present value." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Present_valueCC BY-SA 3.0http://en.wikipedia.org/wiki/Present_value Wiktionary. "interest rate." CC BY-SA 3.0 http://en.wiktionary.org/wiki/interest+rateCC BY-SA 3.0http://en.wiktionary.org/wiki/interest+rate Wikipedia. "period." CC BY-SA 3.0 http://en.wikipedia.org/wiki/periodCC BY-SA 3.0http://en.wikipedia.org/wiki/period Wiktionary. "compound interest." CC BY-SA 3.0 http://en.wiktionary.org/wiki/compound+interestCC BY-SA 3.0http://en.wiktionary.org/wiki/compound+interest Boundless Learning. "Boundless." CC BY-SA 3.0 http://www.boundless.com//finance/definition/multi-periodCC BY-SA 3.0http://www.boundless.com//finance/definition/multi-period http://fonetika3.appspot.com/wiki/Time_value_of_money#Present_value_of_a_future_sum. CC BY-SA http://fonetika3.appspot.com/wiki/Time_value_of_money#Present_value_of_a_future_sumCC BY-SA http://fonetika3.appspot.com/wiki/Time_value_of_money#Present_value_of_a_future_sum Free to share, print, make copies and changes. Get yours at www.boundless.com The Time Value of Money