# 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

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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%

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

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

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

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

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

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

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

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

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?

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?

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?

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

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

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

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

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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