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8,900 x1.06 9,434 x1.06 10,000 CHAPTER 6 Accounting and the Time Value of Money ……..…………………………………………………………... 2007 2006 2005 $10,000 8,900 Discounted @ 6%

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Using Present Value in Accounting notes receivable and payable amortization of bond premiums and discounts valuation of long-term assets Interest rates Sometimes effective interest rates need to be estimated purchase a 5-year, 3%, $1000 bond for $874 Sometimes an appropriate interest rate must be chosen capitalizing interest costs

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Future Value of a Single Sum PV = $1,000 Rate = 9% Periods = 4 FV = ? Rate = number Nper = number Pmt = number Pv = number Type = number FV

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Present Value of a Single Sum PV = ? Rate = 5% Periods = 4 FV = $5,000 Rate = number Nper = number Pmt = number Fv = number Type = number PV

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Future Value of an Annuity PV = $5,000 Rate = 8% Periods = 4 FV = ? ($1300) Rate = number Nper = number Pmt = number Pv = number Type = number FV

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Date Cash Withdrawal Interest (8%) Inc (decr) in balance Bank Balance 1/1/03 5,000 12/31/03(1,300) 400 (900)4,100 12/31/04 12/31/05 12/31/06

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Second Example PV = $0 Rate = 8% Periods = 4 FV = ? $1000 Rate = number Nper = number Pmt = number Pv = number Type = number FV

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Future Value of an Annuity Due PV = $5,000 Rate = 8% Periods = 4 FV = ? ($1300) Payments at beg. of period Rate = number Nper = number Pmt = number Pv = number Type = number FV

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Date Cash Withdrawal Interest (8%) Inc (decr) in balance Bank Balance 1/1/03 5,000 1/1/03(1,300) 1/1/04(1,300) 1/1/05(1,300) 1/1/06(1,300) 12/31/06

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PeriodsRatePVAnnuityFVAD? Sample Problems What is the present value of $7,000, due 8 periods hence, discounted at 11%? PeriodsRatePVAnnuityFVAD? Jane Pauley has $20,000 to invest today at 9% to pay a debt of $56,253. How many years to accumulate enough?

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PeriodsRatePVAnnuityFVAD? How much deposited every 6 months for next 5 years to accumulate $14,000. Interest rate = 8%, compounded semiannually? PeriodsRatePVAnnuityFVAD? You deposit $15,000 on 8/31 in a bank account paying 3% interest compounded monthly. How much can you withdrawal on the first day of each of the next 9 months?

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PeriodsRatePVAnnuityFVAD? What would you pay for a $50,000 bond that matures in 15 years and pays $5,000 a year in interest if you wanted to earn a 12% return?

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Issuing Long-Term Bonds Firm issues bonds and receives cash premium: cash exceeds face value discount: cash is less than face value Firm makes annual interest payments based on face value and stated rate Firm pays face value to bondholders at maturity $43,189 $5,000 $50,000

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Amortizing Bond Discount or Premium Issuing bonds at a discount: Cash43,189 Discount on Bonds Payable6,811 Bonds Payable50,000 Date Cash Payment Interest (12%) Inc (decr) in balance Carrying Amount 10/1/04 43,189 10/1/05(5,000) 5,18318343,372 10/1/06(5,000) 5,20520543,577 10/1/19(5,000)5,89389350,000

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Making the first interest payment: Interest Expense5,183 Discount - Bonds Pay183 Cash5,000 Making the second interest payment: Interest Expense5,205 Discount - Bonds Pay205 Cash5,000 Date Cash Payment Interest (12%) Inc (decr) in balance Carrying Amount 10/1/04 43,189 10/1/05(5,000) 5,18318343,372 10/1/06(5,000) 5,20520543,577

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Future Value of a Deferred Annuity PV = $0FV = ? $1500 An ordinary 8%, 4-year annuity deferred 2 years. PeriodsRatePVAnnuityFVAD?

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Present Value of a Deferred Annuity An ordinary 8%, 4-year annuity deferred 2 years. PeriodsRatePV1AnnuityFVAD? PV2 = ?FV = 0 ($1500) PV1 = ? PeriodsRatePV2AnnuityFVAD?

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Chapter 6: Time Value of Money

Chapter 6: Time Value of Money

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