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A B C D E F G H 1 2 3 Chapter 5. Mini Case: Bonds & Interest Rates 4 5 Situation 6 Sam Strother and Shawna Tibbs are vice-presidents of Mutual of Seattle Insurance Company and co-directors of the 7 company's pension fund management division. A major new client, the Northwestern Municipal Alliance, has requested that 8 Mutual of Seattle present an investment seminar to the mayors of the represented cities, and Strother and Tibbs, who will make 9 the actual presentation, have asked you to help them by answering the following questions. Because the Boeing Company 10 operates in one of the league's cities, you are to work Boeing into the presentation. 11 12 a. What are the key features of a bond? Answer: See Chapter 5 Mini Case Ppt Show 13 14 b. What are call provisions and sinking fund provisions? Do these provisions make bonds more or less risky? 15 16 Call Provisions and Sinking Funds 17 A call provision that allows the issuer to redeem the bond at a specified time before the maturity date. If interest rates fall, the 18 issuer can refund the bonds and issue new bonds at a lower rate. Because of this, borrowers are willing to pay more and 19 lenders require more on callable bonds. 20 21 In a sinking fund provision, the issuer pays off the loan over its life rather than all at the maturity date. A sinking fund reduces 22 the risk to the investor and shortens the maturity. This is not good for investors if rates fall after issuance. 23 24 c. How is the value of any asset whose value is based on expected future cash flows determined? Answer: See Chapter 5 Mini 25 Case Ppt Show 26 27 d. How is the value of a bond determined? What is the value of a 10-year, $1,000 par value bond with a 10 percent annual 28 coupon if its required rate of return is 10 percent? 29 30 Finding the "Fair Value" of a Bond 31 32 First, we list the key features of the bond as "model inputs": 33 Years to Mat: 10 34 Coupon rate: 10% 35 Annual Pmt: $100 36 Par value = FV: $1,000 37 Going rate, rd: 10% 38 39 The easiest way to solve this problem is to use Excel's PV function. Click fx, then financial, then PV. Then fill in the menu 40 items as shown in our snapshot in the screen shown just below. 41 42 43 44 45 46 47 48 49 50 51 52 53 A B C D E F G H 54 55 56 57 58 59 60 Value of bond = $1,000.00 Thus, this bond sells at its par value. That situation always exists if the going rate is equal to the 61 coupon rate. 62 63 The PV function can only be used if the payments are constant, but that is normally the case for bonds. 64 65 e. (1.) What would be the value of the bond described in Part d if, just after it had been issued, the expected inflation rate rose 66 by 3 percentage points, causing investors to require a 13 percent return? Would we now have a discount or a premium bond? 67 68 69 We could simply go to the input data section shown above, change the value for r from 10% to 13%. You can set up a data table 70 to show the bond's value at a range of rates, i.e., to show the bond's sensitivity to changes in interest rates. This is done below. 71 To make the data table, first type the headings, then type the rates in cells in the 72 Bond Value left column. Since the input values are listed down a column, type the formula in 73 Going rate, r: $1,000 the row above the first value and one cell to the right of the column of values (this 74 0% $2,000.00 is B73; note that the formula in B73 actually just refers to the bond pricing 75 7% $1,210.71 formula above in B58). Select the range of cells that contains the formulas and 76 10% $1,000.00 values you want to substitute (A73:B78). Then click Data, What-If-Analysis, and 77 13% $837.21 then Data Table to get the menu. The input data are in a column, so put the cursor 78 20% $580.75 on "column input cell" and enter the cell with the value for r (B37), then Click OK 79 to complete the operation and get the table. 80 We can use the data table to construct a graph that shows 81 the bond's sensitivity to changing rates. 82 83 84 Interest Rate Sensitivity of a 10-Year Bond 85 Value at 7% Value at 13% 86 $2,500 87 $2,000 88 $1,500 89 $1,000 90 $500 91 $0 Put B37 here. 92 0% 5% 10% 15% 20% 93 94 95 96 (2.) What would happen to the value of the 10-year bond over time if the required rate of return remained at 13 percent, or 97 if it remained at 7 percent? Would we now have a premium or a discount bond in either situation? You pick a rate. 98 A B C D E F G H 99 Value of Bond in Given Year: 100 N 7% 10% 13% 101 0 $1,211 $1,000 $837 102 1 $1,195 $1,000 $846 103 2 $1,179 $1,000 $856 104 3 $1,162 $1,000 $867 105 4 $1,143 $1,000 $880 106 5 $1,123 $1,000 $894 107 6 $1,102 $1,000 $911 108 7 $1,079 $1,000 $929 109 8 $1,054 $1,000 $950 110 9 $1,028 $1,000 $973 111 10 $1,000 $1,000 $1,000 112 You pick the rate for a bond: 113 Rates fall to 7% Your choice: Value of the bond over time 114 Rates stay the same 20% Rates increase to 13% 115 116 Your choice $1,400 117 Resulting bond prices 118 $1,200 $581 119 $597 120 $1,000 $616 121 $640 $800 Price 122 $667 123 $600 $701 124 $741 125 $400 $789 126 $847 127 $200 $917 128 $1,000 $0 129 1 3 5 7 9 11 130 Years to maturity 131 132 133 134 If rates fall, the bond goes to a premium, but it moves towards par as maturity approaches. The reverse hold if rates rise and 135 the bond sells at a discount. If the going rate remains equal to the coupon rate, the bond will continue to sell at par. Note that 136 the above graph assumes that interest rates stay constant after the initial change. That is most unlikely--interest rates fluctuate, 137 and so do the prices of outstanding bonds. 138 139 Yield to Maturity (YTM) 140 141 f. (1.) What is the yield to maturity on a 10-year, 9 percent annual coupon, $1,000 par value bond that sells for $887.00? That 142 sells for $1,134.20? What does the fact that a bond sells at a discount or at a premium tell you about the relationship between r d 143 and the bond's coupon rate? What is the yield-to-maturity of the bond? 144 145 Use the Rate function to solve the problem. 146 147 Years to Mat: 10 148 Coupon rate: 9% 149 Annual Pmt: $90.00 Going rate, r =YTM: 10.91% See RATE function at right. 150 Current price: $887.00 151 Par value = FV: $1,000.00 A B C D E F G H 152 153 (2.) What are the total return, the current yield, and the capital gains yield for the discount bond? (Assume the bond is held 154 to maturity and the company does not default on the bond.) 155 156 Current and Capital Gains Yields 157 The current yield is the annual interest payment divided by the bond's current price. The current yield provides information 158 regarding the amount of cash income that a bond will generate in a given year. However, it does not account for any capital 159 gains or losses that will be realized if the bond is held to maturity or call. 160 161 Simply divide the annual interest payment by the price of the bond. Even if the bond made semiannual payments, we would 162 still use the annual interest. 163 164 Par value $1,000.00 165 Coupon rate: 9% Current Yield = 10.15% 166 Annual Pmt: $90.00 167 Current price: $887.00 168 YTM: 10.91% 169 170 The current yield provides information on a bond's cash return, but it gives no indication of the bond's total return. To see this, 171 consider a zero coupon bond. Since zeros pay no coupon, the current yield is zero because there is no interest income. 172 However, the zero appreciates through time, and its total return clearly exceeds zero. 173 174 YTM = Current Yield + Capital Gains Yield 175 176 177 Capital Gains Yield = YTM - Current Yield 178 179 Capital Gains Yield = 10.91% - 10.15% 180 181 Capital Gains Yield = 0.76% 182 183 184 g. How does the equation for valuing a bond change if semiannual payments are made? Find the value of a 10-year, semiannual 185 payment, 10 percent coupon bond if nominal rd = 13%. 186 187 Bonds with Semiannual Coupons 188 Since most bonds pay interest semiannually, we now look at the valuation of semiannual bonds. We must make three 189 modifications to our original valuation model: (1) divide the coupon payment by 2, (2) multiply the years to maturity by 2, and 190 (3) divide the nominal interest rate by 2. 191 192 Use the Rate function with adjusted data to solve the problem. 193 194 Periods to maturity = 10*2 = 20 195 Coupon rate: 10% 196 Semiannual pmt = $100/2 = $50.00 PV = $834.72 197 Future Value: $1,000.00 198 Periodic rate = 13%/2 = 6.5% 199 200 Note that the bond is now more valuable, because interest payments come in faster. 201 202 203 Excel Bond Functions 204 Supose today's date is January 1, 2010, and the bond matures on December 31, 2019 A B C D E F G H 205 206 Settlement (today) 1/1/2010 207 Maturity 12/31/2019 208 Coupon rate 10.00% 209 Going rate, r 13.00% 210 Redemption (par value) 100 211 Frequency (for semiannual) 2 212 Basis (360 or 365 day year) 0 213 214 215 Value of bond = $83.4737 or $834.74 216 217 Notice that you could choose a current date that is between coupon payments, and the PRICE function will calculate the correct 218 price. See the example below. 219 220 221 Settlement (today) 3/25/2010 222 Maturity 12/31/2019 223 Coupon rate 10.00% 224 Going rate, r 13.00% 225 Redemption (par value) 100 226 Frequency (for semiannual) 2 227 Basis (360 or 365 day year) 0 228 229 Value of bond = $83.6307 or $836.31 230 231 This is the value of the bond, but it does not include the accrued interest you would pay. The ACCRINT function will calculate 232 accrued interest, as shown below. 233 234 Issue date 1/1/2010 235 First interest date 6/30/2010 236 Settlement (today) 3/25/2010 237 Maturity 12/31/2019 238 Coupon rate 10.00% 239 Going rate, r 13.00% 240 Redemption (par value) 100 241 Frequency (for semiannual) 2 242 Basis (360 or 365 day year) 0 243 244 Accrued interest = $2.3333 or $23.33 245 246 247 Suppose the bond's price is $1,150. You can also calculate the yield using the YIELD function, as shown below. 248 249 Curent price $ 1,150.00 250 Settlement (today) 1/1/2010 251 Maturity 12/31/2019 252 Coupon rate 10.00% 253 Redemption (par value) 100 254 Frequency (for semiannual) 2 255 Basis (360 or 365 day year) 0 256 A B C D E F G H 257 Yield 7.81% 258 259 260 h. Suppose a 10-year, 10 percent, semiannual coupon bond with a par value of $1,000 is currently selling for $1,135.90, 261 producing a nominal yield to maturity of 8 percent. However, the bond can be called after 5 years for a price of $1,050. 262 (1.) What is the bond's nominal yield to call (YTC)? 263 (2.) If you bought this bond, do you think you would be more likely to earn the YTM or the YTC? Why? 264 265 Yield to Call 266 The yield to call is the rate of return investors will receive if their bonds are called. If the issuer has the right to call the bonds, 267 and if interest rates fall, then it would be logical for the issuer to call the bonds and replace them with new bonds that carry a 268 lower coupon. The yield to call (YTC) is found similarly to the YTM. The same formula is used, but years to maturity is 269 replaced with years to call, and the maturity value is replaced with the call price. 270 271 Use the Rate function to solve the problem. 272 273 Number of semiannual periods to call: 10 274 Seminannual coupon rate: 5% Semiannual Rate = I = YTC = 3.77% 275 Seminannual Pmt: $50.00 Annual nominal rate = 7.53% 276 Current price: $1,135.90 277 Call price = FV $1,050.00 278 Par value $1,000.00 279 280 281 i. Write a general expression for the yield on any debt security (rd) and define these terms: real risk-free rate of interest (r*), 282 inflation premium (IP), default risk premium (DRP), liquidity premium (LP), and maturity risk premium (MRP). Answer: See 283 Chapter 5 Mini CasePpt Show. 284 285 286 j. Define the nominal risk-free rate (r RF). What security can be used as an estimate of rRF? Answer: See Chapter 5 Mini Case 287 Ppt Show. 288 289 290 k. Describe a way to estimate the inflation premium (IP) for a T-Year bond. Answer: See Chapter 5 Mini Case Ppt Show. 291 292 293 l. What is a bond spread and how is it related to the default risk premium? How are bond ratings related to default risk? What 294 factors affect a company’s bond rating? Answer: See Chapter 5 Mini CasePpt Show. 295 296 297 m. What is interest rate (or price) risk? Which bond has more interest rate risk, an annual payment 1-year bond or a 30-year 298 bond? Why? 299 300 301 Interest Rate Risk is the risk of a decline in a bond's price due to an increase in interest rates. Price sensitivity to interest rates 302 is greater (1) the longer the maturity and (2) the smaller the coupon payment. Thus, if two bonds have the same coupon, the 303 bond with the longer maturity will have more interest rate sensitivity, and if two bonds have the same maturity, the one with 304 the smaller coupon payment will have more interest rate sensitivity. 305 306 307 308 Your Choice of Maturity 10-Yr Maturity 1-Yr Maturity 309 Years to Mat: 10 Rate Price Rate Price Rate A B C D E F G H 310 Coupon rate: 9% $929.60 $887.63 311 Annual Pmt: $90.00 5.0% 1173.179067 5.0% $1,308.87 5.0% 312 Current price: $887.63 7.0% 1082.003949 7.0% $1,140.47 7.0% 313 Par value = FV: $1,000.00 9.0% 1000 9.0% $1,000.00 9.0% 314 YTM = 10.9% 11.0% 926.0820596 11.0% $882.22 11.0% 315 13.0% 859.3107495 13.0% $782.95 13.0% 316 Years to Mat: 1 317 Coupon rate: 9% 318 Annual Pmt: $90.00 10 Yr. versus 1 Yr. 319 Current price: $982.87 $1,400.00 Your Choice 320 Par value = FV: $1,000.00 $1,300.00 321 YTM = 10.9% 322 $1,200.00 323 $1,100.00 324 Enter your $1,000.00 325 choice for years $900.00 326 to maturity: 5 327 $800.00 328 $700.00 329 330 5.0% 7.0% 9.0% 11.0% 13.0% YTM 331 332 333 334 335 n. What is reinvestment rate risk? Which has more reinvestment rate risk, a 1-year bond or a 10-year bond? Answer: See 336 Chapter 5 Mini Case Ppt Show. 337 338 339 o. How are interest rate risk and reinvestment rate risk related to the maturity risk premium? Answer: See Chapter 5 Mini 340 Case Ppt Show. 341 342 343 p. What is the term structure of interest rates? What is a yield curve? 344 345 The term structure describes the relationship between long-term and short-term interest rates. Graphically, this relationship 346 can be shown in what is known as the yield curve. See the hypothetical curve below. 347 348 349 Hypothetical Inputs See to right for actual date used in graph. 350 Real risk free rate 3.00% 351 Expected inflation of 5% for the next 1 years. 352 Expected inflation of 6% for the next 1 years. 353 Expected inflation of 8% thereafter. 354 355 Hypothetical Treasury Yield Curve 356 357 358 14.00% 359 360 12.00% MRP 361 10.00% Interest Rate A B C D E F G H 362 10.00% Interest Rate Inflation 363 Premium 364 8.00% 365 366 6.00% 367 Real Risk 368 4.00% Free Rate 369 370 2.00% 371 372 0.00% 373 1 3 5 7 9 11 13 15 17 19 374 Maturity 375 376 377 378 The yield is upward sloping due to increasing expected inflation and an increasing maturity risk premium 379 380 381 q. Briefly describe bankruptcy law. If a firm were to default on the bonds, would the company be immediately liquidated? 382 Would the bondholders be assured of receiving all of their promised payments? Answer: See Chapter 5 Mini Case Ppt Show. 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 I J K L M N O P 1 1/1/2012 2 3 4 5 -directors of the 6 ance, has requested that 7 r and Tibbs, who will make 8 9 the Boeing Company 10 11 12 13 ess risky? 14 15 16 e. If interest rates fall, the 17 18 ng to pay more and 19 20 21 te. A sinking fund reduces uance. 22 23 24 wer: See Chapter 5 Mini 25 26 27 th a 10 percent annual 28 29 30 31 32 33 34 35 36 37 38 39 Then fill in the menu 40 41 42 43 44 45 46 47 48 49 50 51 52 53 I J K L M N O P 54 55 56 57 58 59 e going rate is equal to the 60 61 62 ds. 63 64 65 xpected inflation rate rose 66 ount or a premium bond? 67 68 69 You can set up a data table rates. This70 done below. is 71 e the rates in cells in the 72 umn, type the formula in 73 the column of values (this 74 to the bond pricing 75 tains the formulas and 76 a, What-If-Analysis, and 77 a column, so put the cursor 78 for r (B37), then Click OK 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 emained at 13 percent, or You pick a 97 rate. 98 I J K L M N O P 99 100 101 102 103 104 105 106 107 108 109 110 111 k the rate112 a bond: for 113 114 115 116 117 ulting bond prices 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 erse hold if rates rise and 134 par. e to sell at135 Note that 136 ely--interest rates fluctuate, 137 138 139 140 $887.00? That at sells for141 the relationship between r d 142 143 144 145 146 147 148 See RATE149 function at right. 150 151 I J K L M N O P 152 (Assume 153bond is held the 154 155 156 eld provides information 157 158 account for any capital 159 160 161 ual payments, we would 162 163 164 165 166 167 168 169 d's total return. To see this, 170 171 o interest income. 172 173 174 175 176 177 178 179 180 181 182 183 184 ue of a 10-year, semiannual 185 186 187 must make three 188 189 ears to maturity by 2, and 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 I J K L M N O P 205 206 207 208 209 210 211 212 213 214 215 216 217 on will calculate the correct 218 219 220 221 222 223 224 225 226 227 228 229 230 231 INT function will calculate 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 I J K L M N O P 257 258 259 260 ling for $1,135.90, 261 r a price of $1,050. 262 Why? 263 264 265 the right to call the bonds, 266 h new bonds that carry a 267 268 years to maturity is 269 270 271 272 273 274 275 276 277 278 279 280 -free rate of interest (r*), 281 282 mium (MRP). Answer: See 283 284 285 See Chapter 5 Mini Case 286 287 288 289 290 5 Mini Case Ppt Show. 291 292 293 lated to default risk? What 294 295 296 297 1-year bond or a 30-year 298 299 300 to interest rates sensitivity 301 ve the same coupon, the 302 303 e maturity, the one with 304 305 306 307 308 1-Yr Maturity 309 Price I J K L M N O P 310 $982.87 311 $1,038.10 312 $1,018.69 313 $1,000.00 314 $981.98 315 $964.60 316 Scratch sheet for Your Choice 317 Years to Mat: 5 318 Coupon rate: 9% 319Your Choice Annual Pmt: $90.00 320 Current price: $929.60 321 Par value = FV: $1,000.00 322 YTM = 10.9% 323 324 325 326 327 328 329 13.0% 330 331 332 333 334 335 ar bond? Answer: See 336 337 338 339 wer: See Chapter 5 Mini 340 341 342 343 344 345 phically, this relationship 346 347 348 349 r actual date used in graph. 350 351 Suppose most investors expect the inflation rate to be 5 percent next year, 6 percent the following year 352 rate is 3 percent. The maturity risk premium is zero for securities that mature in 1 year or less, 0.1 pe 353 increases by 0.1 percent per year thereafter for 20 years, after which it is stable. What is the interest 354 securities? Draw a yield curve with these data. What factors can explain why this constructed yield c 355 356 Now, we want to set up a table that encompasses all of the information for our yield curve. 357 358 INPUT DATA 359 Real risk free rate 3.00% 360 Expected inflation of 5% for the next 1 361 Expected inflation of 6% for the next 1 I J K L M N O P 362 Expected inflation of 8% thereafter. 363 Years to Real risk-free Inflation Maturity Risk Treasury 364 Maturity rate (r*) Premium (IP) Premium (MRP) Yield 365 1 3.00% 5.00% 0.00% 8.00% 366 2 3.00% 5.50% 0.10% 8.60% 367 3 3.00% 6.33% 0.20% 9.53% 368 4 3.00% 6.75% 0.30% 10.05% 369 5 3.00% 7.00% 0.40% 10.40% 370 6 3.00% 7.17% 0.50% 10.67% 371 7 3.00% 7.29% 0.60% 10.89% 372 8 3.00% 7.38% 0.70% 11.08% 373 9 3.00% 7.44% 0.80% 11.24% 374 10 3.00% 7.50% 0.90% 11.40% 375 11 3.00% 7.55% 1.00% 11.55% 376 12 3.00% 7.58% 1.10% 11.68% 377 13 3.00% 7.62% 1.20% 11.82% 378 14 3.00% 7.64% 1.30% 11.94% 379 15 3.00% 7.67% 1.40% 12.07% 380 16 3.00% 7.69% 1.50% 12.19% 381 mmediately liquidated? 17 3.00% 7.71% 1.60% 12.31% er 5 Mini 382 Ppt Show. Case 18 3.00% 7.72% 1.70% 12.42% 383 19 3.00% 7.74% 1.80% 12.54% 384 20 3.00% 7.75% 1.90% 12.65% 385 21 3.00% 7.76% 2.00% 12.76% 386 22 3.00% 7.77% 2.10% 12.87% 387 23 3.00% 7.78% 2.20% 12.98% 388 24 3.00% 7.79% 2.30% 13.09% 389 25 3.00% 7.80% 2.40% 13.20% 390 26 3.00% 7.81% 2.50% 13.31% 391 27 3.00% 7.81% 2.60% 13.41% 392 28 3.00% 7.82% 2.70% 13.52% 393 29 3.00% 7.83% 2.80% 13.63% 394 30 3.00% 7.83% 2.90% 13.73% 395 396 The table above gives us all of the components for our Treasury yield curve. Recall, we have said that 397 of risk premiums, the inflation premium and the maturity risk premium. Just as we "built" Treasury 398 curve based upon these expectations. Q R S T 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 Q R S T 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 Q R S T 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 Q R S T 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 Q R S T 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 Q R S T 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 Q R S T 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 year, 6 percent the following year, and 8 percent thereafter. The real risk-free 351 hat mature in 1 year or less, 0.1 percent for 2-year securities, and then the MRP 352 353 h it is stable. What is the interest rate on 1-year, 10-year, and 20-year Treasury xplain why354 constructed yield curve is upward sloping? this 355 on for our356 curve. yield 357 358 359 360 years. 361 years. Q R S T 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 d curve. Recall, we have said that Treasury securities are subject to two kinds 396 ium. Just 397 "built" Treasury yields in the table, we can "build" a yield as we 398