Essays Solution

Workshop 3 invade Rates and shackle Valuation Terminology Face valuate/par value the original issue equipment casualty (the number borrowed). matureness date date on which loan has to be repaid. Coupon matter to stride original evoke respect on the link up. Coupon open the fixed take payment on the confiscate. YTM= unavoidable order of return. ? sequesters pay fixed verifier payments at fixed intervals and the count value at matureness. ?there is an inverse kinship amongst the charge of an investment and the rate of return on the investment if you pay a high set for an investment your rate of return must be lower (holding each other factors constant)) ?If the YTM = coupon rate the bond pass on sell for the face value (i. e. true expenditure = face value). ?If the YTM coupon rate the bond will sell for a discount ( getting even goes up, price goes down). If the YTM coupon rate the bond will sell for a bounteousness (yield goes down, price goes up). reciprocation 1. Identify the three most central de statusinants of the price of a bond. key the effect of each? Answer The three factors affecting the price of a bond argon coupon yield term to maturity. T The relationship between price and coupon is a direct 1 the higher the coupon, the higher the price. The relationship between price and yield is an inverse one the higher the yield the lower the price, all other factors held constant. The relationship between price and maturity is not so clearly evident. Price changes resulting from changes in yields will be more pronounced, the longer the term to maturity. 2. Given a change in the level of interest rates, discuss how cardinal major(ip) factors will influence the relative change in price of separate bonds. AnswerFor a given change in the level of interest rates, two factors that will influence the relative change in bond prices are the coupon and maturity of the issues. Bonds with longer maturity and/or lower coupons will maintain the greatest price changes in response to a given change in interest rates. Other factors likewise cause differences in price volatility, including the call features, but these factors are typically much little important. 3. What is the purpose of bond ratings? Answer Bond ratings provide a rattling important service in the market for fixed income securities because they provide the heavy analysis for thousands of issues.The rating agencies conduct extensive analyses of the intrinsic characteristics of the issue to experience the default assay for the investor and inform the market of the analyses through their ratings. 4. What are the important assumptions made when you calculate the promised YTM? Answer The most crucial assumption that the investor makes is that gold flows will be received in full (i. e. investors hold the bond to maturity) and reinvested at the promised yield. 5. You expect interest rates to decline everyplace the following(a) 6 months.Wha t kind of bonds do you want in your portfolios in term of duration and explain your reasoning for this choice. Answer Given that you expect interest rates to decline during the next six months, you should choose bonds that will contribute the largest price increase, that is, bonds with long durations. 6. Which of the following bonds will bear the greatest parcel increase in value if all interest rates strike by 1 portion? a. 20- course of instruction, zero coupon bond. b. 10-year, zero coupon bond. c. 20-year, 10 percent coupon bond. d. 20-year, 5 percent coupon bond. AnswerSince a zero coupon bonds price today is unconquerable on the nose by the NPV of its par value, all of its payment is discounted for the maximum come of time, whereas a coupon bond has many payments discounted for little than the maximum amount of time. Therefore, a zero coupon bond is most affected by interest rate changes. So, the longest zero coupon bond is the check answer, which is statement a. 7. Which of the following statements is most correct? a. All else equal, long-term bonds have more interest rate risk than short-term bonds. b. All else equal, high-coupon bonds have less reinvestment rate risk than low-coupon bonds. . All else equal, short-term bonds have less reinvestment rate risk than do long-term bonds. d. All of the statements above are correct. Answer Statement a since high-coupon bonds have more reinvestment rate risk than low-coupon bonds and short-term bonds have more reinvestment rate risk than do long-term bonds. Problems 1. Two years ago you bought a government bond for $1,000 because you want the 10% p. a. coupon interest payment that you would receive for 10 years. Interest on the bond is paid annually. Two years later, when the market interest rate has fallen to 8% p. a. what is the value of your bond? declarationSince coupon rate is 10% and YTM has fallen to 8%, it must be the case that the price of this bond has increased (remembering the inverse r elationship between bond price and yield). 2. The Morgan Corporation has two different bonds currently outstanding. Bond M has a face value of $20,000 and matures in 20 years. The bond makes no payments for the depression six years, consequently payS $800 every six months over the subsequently octonary years, and finally pays $1,000 every six months over the last 6 years. Bond N also has a face value of $20,000 and a maturity of 20 years it makes no coupon payments over the life of the bond.If the required return on both these bond is 8 percent deepen semiannually, what is the current price of bond M? and bond N? Solution The price of any bond (or financial instrument) is the PV of the future cash flows. even out though Bond M makes different coupons payments, to find the price of the bond, we just find the PV of the cash flows. The PV of the cash flows for Bond M is PM = $800(PVIFA4%,n=16)(PVIF4%,n=12) + $1,000(PVIFA4%,1n=2)(PVIF4%,n=28) + $20,000(PVIF4%,n=40) PM = $13,117. 88 Notice that for the coupon payments of $800, we found the PVA for the coupon payments, and then discounted the lump sum back to today.Bond N is a zero coupon bond with a $20,000 par value therefore, the price of the bond is the PV of the par, or PN = $20,000(PVIF4%,40) = $4,165. 78 3. Bond P is a premium bond with a 9 percent coupon. Bond D is a 5 percent coupon bond currently selling at a discount. both(prenominal) bonds make annual payments, have a YTM of 7 percent, and have pentad years to maturity. What is the current yield for bond P? for bond D? if interest rates remain unchanged, what is the expected capital gains yield over the next year for bond P? for bond D? condone your answers and the interrelationship among the various types of yields.Solution To find the capital gains yield and the current yield, we indispensableness to find the price of the bond. The current price of Bond P and the price of Bond P in one year is PP0 = $90(PVIFA7%,5) + $1,000(PVIF7%,5) = $1,082. 00 P1 = $90(PVIFA7%,4) + $1,000(PVIF7%,4) = $1,067. 74 Current yield = $90 / $1,082. 00 = . 0832 or 8. 32% The capital gains yield is bully gains yield = (New price Original price) / Original price Capital gains yield = ($1,067. 74 1,082. 00) / $1,082. 00 = 0. 0132 or 1. 32% The current price of Bond D and the price of Bond D in one year isDP0 = $50(PVIFA7%,5) + $1,000(PVIF7%,5) = $918. 00 P1 = $50(PVIFA7%,4) + $1,000(PVIF7%,4) = $932. 26 Current yield = $50 / $918. 00 = 0. 0545 or 5. 45% Capital gains yield = ($932. 26 918. 00) / $918. 00 = 0. 0155 or 1. 55% All else held constant, premium bonds pay a high current income while having price depreciation as maturity nears discount bonds pay a lower current income but have price appreciation as maturity nears. For either bond, the total return is still 7%, but this return is distributed differently between current income and capital gains.