Chapter 5 notes

# Chapter 5 notes - In Chapter 5 we use present value of \$1...

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In Chapter 5 we use present value of \$1 and present value of an annuity formulas to determine the present value of a fixed income security – bond. Bonds: Interest Rates and Bond Prices The value of a pure discount bond (also called a zero coupon bond, or simply a zero) is: PV = F/(I+R) T The bond promises a single payment at fixed future date. With level payment bonds , the coupon payments form an annuity, and the principal repayment is a lump sum. The value of this type of bond is simply the sum of the values of its two parts. The value of a bond then is PV = C x A T R + \$1,000 / (1+R) T Remember that when we solved bond prices in Excel we used the present value of an annuity for the interest payments, and the present value of a single sum for the face, as shown in the par and discount examples below: P B = PV (interest/coupons payments) + PV (principal/par repayment) Example A: \$1,000 face, 8% coupon, 30 Year, semi annual. (\$40 paid semi annually). Market Interest rate = 8%. We have a par bond = PV = \$1,000. Example B: \$1,000 face, 8% coupon, 30 Year, semi annual. (\$40 paid semi annually). Market Interest rate = 10%. PV of Coupons \$757.17 '=-PV(0.05,60,40,0) PV of Par \$53.54 '=-PV(0.05,60,0,1000,0) \$810.71 Sells at discount Another important concept is yield to maturity , which is the single rate that discounts the payments on the bond to its purchase price. The PRICE & YIELD functions in Excel may be helpful in solving bond problems. Click this link: Bond Example Using Excel Functions to see how these functions work. YTM is the rate implied by the bond’s price. Essentially, it is the rate required to discount the bond’s cash flows to the current market price. It is a useful habit to assess the relations between coupon rate and yield to maturity ( ytm ). If ytm > coupon rate = we have a discount bond; if ytm < coupon rate = we have a premium bond. Simply put, there is an inverse relation between

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## Chapter 5 notes - In Chapter 5 we use present value of \$1...

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