1. Principles of Investing FIN 330 CHAPTER 12 Bond Valuation Dr. David P. EchevarriaAll Rights ReservedSlide 1

2. Dr. David P. EchevarriaAll Rights ReservedSlide 2 BOND VALUATION Special Section on BA II Plus Purchasing PowerRisk Management

3. Dr. David P. EchevarriaAll Rights ReservedSlide 3 FIVE BOND PRICING THEOREMS 1.Bond prices move inversely to changes in interest rates 2.The longer the maturity of a bond, the more price sensitive the bond 3.The price sensitivity of bonds to changes in interest rates increases as maturity increases, but at a decreasing rate 4.Bonds with lower coupon rates are more price sensitive 5.Yield decreases have a greater impact on bond prices than similar yield increases

4. TYPES OF YIELD Coupon Yield –The rate the bond promises to pay Current Yield –The [annual] coupon divided by the current price Yield to Maturity –The rate returned if held to maturity Yield To First Call –The adjusted YTM if bonds are called early Dr. David P. EchevarriaAll Rights ReservedSlide 4

5. Dr. David P. EchevarriaAll Rights ReservedSlide 5 FINANCIAL CALCULATORS & BOND PRICES The value of a bond (V B ) is a combination of a present value of an annuity (the present value of the coupons to be received) and the present value of the face value of the bond. V B = $Coupon * PVIFA + $Face * PVIF start here 3/20

6. Dr. David P. EchevarriaAll Rights ReservedSlide 6 [BA II Plus] FINANCIAL CALCULATORS & BOND PRICES [BA II Plus] For example, suppose we have a bond paying a 12% coupon rate ($120), paid semi-annually. The bond matures in 20 years and has a face value of $1,000. If the current market rate (YTM) is 9%, how much should this bond sell for (value)? In this type of problem we will use all five TVM keys; [ N ] [ I/Y ] [ PV ] [ PMT ] [ FV ]

7. Dr. David P. EchevarriaAll Rights ReservedSlide 7 [BA II Plus] FINANCIAL CALCULATORS & BOND PRICES [BA II Plus] The bond pays coupons (interest) twice a year (semi-annual): We set the periods per year (P/Y) and (C/Y) to 2. coupon rateThe 12% coupon rate ( $120 per year) is paid in two [PMT=] $60 installments. maturity valueThe bond will have a maturity value [FV] of $1000.00. current market rate YTMThe current market rate is [I/Y] 9% (the required YTM for bonds in this risk class).

8. Dr. David P. EchevarriaAll Rights ReservedSlide 8 [BA II Plus] FINANCIAL CALCULATORS & BOND PRICES [BA II Plus] A. BA II PLUS Solution 1. ENTER 20 [2nd] [N], [N] N = 40.00 2. ENTER 9 [I/Y] I/Y = 9.00 3. ENTER 60 [PMT] PMT = 60.00 4. ENTER 1000 [FV] FV = 1,000.00 5. PRESS [CPT] [PV] PV = -1,276.02 We would have to pay $1,276.02 to buy this bond today.

9. Dr. David P. EchevarriaAll Rights ReservedSlide 9 [BA II Plus] FINANCIAL CALCULATORS & BOND PRICES [BA II Plus] B. Playing "what if" with Several Different YTM Values. –For example, suppose the YTM is 11 percent; "I/Y" = 11. Enter 11, press [I/Y], then [CPT], then [PV]; -1,080.23 –If the YTM is 12%; enter 12, press [I/Y], then [CPT], [PV]; 1,000.00 or $1,000.00 * * If YTM = Coupon Rate, then PV = - FV –If the YTM is 15%, the price is $811.08

10. Yield to First Call Callable Bonds Pay Premiums –The premium results in a Yield-to-First-Call different from the Coupon Rate. –Calling a 30-year bond 5% coupon bond four years after issuance @ 107.50. –N = 4 –PV = -1000 –PMT = 50 –FV = 1075.00 –CPT I/Y = 6.70% Dr. David P. EchevarriaAll Rights ReservedSlide 10

11. Dr. David P. EchevarriaAll Rights ReservedSlide 11 Final Observations on Bonds When bonds sell at prices greater than their maturity or Face values, the are said to be selling at a premium. When bonds sell at prices less than their maturity or Face values, the are said to be selling at a discount. When bonds sell at prices equal to their maturity or Face values, the are said to be selling at a par.

12. HOMEWORK Questions: 1, 3, 6, 7 Problems:10, 11, 12 Dr. David P. EchevarriaAll Rights ReservedSlide 12