Copyright © 2008 Pearson Education Canada 15-1 Contemporary Business Mathematics With Canadian Applications Eighth Edition S. A. Hummelbrunner/K. Suzanne Coombs PowerPoint: D. Johnston Chapter 15 Bond Valuation and Sinking Funds

Copyright © 2008 Pearson Education Canada 15-2 Objectives After completing chapter 15, the student will be able to: Determine the purchase price of bonds. Calculate the premium or discount on the purchase of a bond. Construct bond schedules for amortization of premiums or accumulation of discounts. Calculate yield using method of averages. Make sinking fund computations.

Copyright © 2008 Pearson Education Canada 15-3 Bond Promises

Copyright © 2008 Pearson Education Canada 15-4 Bond Terminology Face value (or par value or denomination) - amount owed to holder of bond bond rate (or coupon rate or nominal rate) - rate of interest paid, usually semi-annually, based on face value of bond redemption date (or maturity date or due date) - date on which the principal of the bond is to be repaid (continued)

Copyright © 2008 Pearson Education Canada 15-5 Bond Terminology (Continued) Redemption price - money paid by the issuer to the bondholder at date of surrender of bonds Debenture -bond for which no security is offered Callable bond - can be redeemed before maturity at a price greater than face value

Copyright © 2008 Pearson Education Canada 15-6 Premium and Discount

Copyright © 2008 Pearson Education Canada 15-7 Purchase Price of Bond (bought on interest date)

Copyright © 2008 Pearson Education Canada 15-8 Calculating the Purchase Price

Copyright © 2008 Pearson Education Canada 15-9 Discount

Copyright © 2008 Pearson Education Canada Formula for Calculating Purchase Price

Copyright © 2008 Pearson Education Canada Interest Rates Used in Calculating Purchase Price

Copyright © 2008 Pearson Education Canada Determining Purchase Price of Bonds between Interest Dates

Copyright © 2008 Pearson Education Canada Finding Purchase Price between Interest Payment Dates

Copyright © 2008 Pearson Education Canada Finding the Purchase Price (continued)

Copyright © 2008 Pearson Education Canada Accrued Interest Accrued interest is interest earned but not yet paid. If a bond is sold between interest payment dates, the accrued interest is the property of the seller. Price = Flat Quoted Price + Accrued Interest Quoted Price = Flat Price - Accrued Interest

Copyright © 2008 Pearson Education Canada Determining the Purchase Price (General annuities)

Copyright © 2008 Pearson Education Canada Bond Rates and Market Rates

Copyright © 2008 Pearson Education Canada Finding Yield Rate i

Copyright © 2008 Pearson Education Canada Finding Yield Rate i

Copyright © 2008 Pearson Education Canada Finding Yield Rate (Average Investment Method)

Copyright © 2008 Pearson Education Canada Finding Yield Rate (Average Investment Method)

Copyright © 2008 Pearson Education Canada Finding the Yield (Average Investment Method)

Copyright © 2008 Pearson Education Canada Canada Savings Bonds Canada savings bonds differ from other bonds because they cannot be freely traded after purchase. Regular interest bonds (R-Bonds) pay simple interest every year. Compound interest bonds (C-Bonds) pay compound interest every year which is reinvested by the government. (continued)

Copyright © 2008 Pearson Education Canada Canada Savings Bonds Government of Canada fully guarantees the principal and interest of CSBs. When CSBs are issued, interest rates are set and guaranteed for each year of CSB’s life. If market interest rates rise, CSB interest rates usually rise, but they never fall below the guaranteed rates.

Copyright © 2008 Pearson Education Canada Sinking Fund Interest-bearing account. Payments made at periodic intervals to provide for an accumulated value at a specific date in the future. Used by corporations to save for future projects.

Copyright © 2008 Pearson Education Canada Finding the Payment for a Sinking Fund

Copyright © 2008 Pearson Education Canada Sinking Fund

Copyright © 2008 Pearson Education Canada Sinking Fund

Copyright © 2008 Pearson Education Canada Summary The purchase price of a bond equals the sum of the present value of the two cash flows represented by the future redemption price and the periodic interest payments. A sinking fund can be set up to accumulate funds for a large future capital expenditure and involves calculations dealing with the future value of an annuity.