Discussion Question
4A
| Problem 1 | |
| For a bond selling for $921, with a par value of $1,000 and a coupon rate of 7.45 percent, the current yield is _____. | |
| Step 1: Calculate annual coupon payments = $1000 *7.45% = $74.50 | 74.50 |
| Step 2: Calculate current yield = $74.50 / $921 = 8.09% | 8.09% |
| Problem 2 | |
| You paid $1,189 for a corporate bond that has a 8.76 percent coupon rate. What is the bond’s current yield? | |
| Step 1: Calculate annual coupon payments = $1000 *8.76% = $87.60 | 87.60 |
| Step 2: Calculate current yield = $87.60 / $1189 = 7.37% | 7.37% |
| Problem 3 | |
| A $1,000 par value bond with a 9.12 percent coupon rate, currently selling for $977, has a current yield of _____. | |
| Step 1: Calculate annual coupon payments = $1000 *9.12% = $91.20 | 91.20 |
| Step 2: Calculate current yield = $91.20 / $977 = 9.33% | 9.33% |
4B
| Problem 1 | |||||
| What is the value of a bond that has a par value of $1,000, a coupon rate of 9.82 percent (paid annually), and that matures in 14 years? Assume a required rate of return on this bond is 12.76 percent. | |||||
| Market i | Coupon i | Nper | PMT | FV | Type |
| 0.1276 | 0.0982 | 14 | 98.20 | 1,000.00 | 0 |
| =PV(12.76%,14,98.2,1000,0) = $812.48 | ($812.48) | ||||
| Problem 2 | |||||
| Fresh Water, Inc. sold an issue of 23-year $1,000 par value bonds to the public. The bonds have a 9.56 percent coupon rate and pay interest annually. The current market rate of interest on the Fresh Water, Inc. bonds is 8.13 percent. What is the current market price of the bonds? | |||||
| Market i | Coupon i | Nper | PMT | FV | Type |
| 0.0813 | 0.0956 | 23 | 95.60 | 1,000.00 | 0 |
| Coupon Pmt | 95.60 | ||||
| ($1,146.75) | |||||
4C
| Problem 1 | |||||
| General Mills has a $1,000 par value, 25-year to maturity bond outstanding with an annual coupon rate of 8.56 percent per year, paid semiannually. Market interest rates on similar bonds are 12.16 percent. Calculate the bond’s price today. | |||||
| Market i | Coupon i | Nper | PMT | FV | Type |
| 0.1216 | 0.0856 | 25 | 42.80 | 1,000.00 | 0 |
| =PV(12.16%/2,25*2,85.6/2,1000,0) = 719.42 | ($719.42) | ||||
| Problem 2 | |||||
| Pet Food Company bonds pay an annual coupon rate of 12.77 percent. Coupon payments are paid semiannually. Bonds have 5 years to maturity and par value of $1,000. Compute the value of Pet Food Company bonds if the market interest rate on this type of bond is 9.44 percent. | |||||
| Market i | Coupon i | Nper | PMT | FV | Type |
| 0.0944 | 0.1277 | 5 | 127.70 | 1,000.00 | 0 |
| =PV(9.44%/2,5*2,127.7/2,1000,0) = 1,130.33 | ($1,130.33) | ||||
| Problem 3 | |||||
| Flower Valley Company bonds have a 14.29 percent coupon rate. Interest is paid semiannually. The bonds have a par value of $1,000 and will mature 29 years from now. Compute the value of Flower Valley Company bonds if investors’ required rate of return is 9.03 percent. | |||||
| Market i | Coupon i | Nper | PMT | FV | Type |
| 0.0903 | 0.1429 | 29 | 142.90 | 1,000.00 | 0 |
| =PV(9.03%/2,29*2,142.9/2,1000,0) = 1,537.53 | ($1,537.53) | ||||
4D
| Problem 1 | ||||||
| What is the yield to maturity of a 22-year bond that pays a coupon rate of 11.65 percent per year, has a $1,000 par value, and is currently priced at $1,214? Assume annual coupon payments. | ||||||
| Market i | Coupon i | Nper | PMT | FV | Type | PV |
| 0.1165 | 22 | 116.50 | 1,000.00 | 0 | 1,214.00 | |
| =RATE(22,116.5,-1214,1000,0) = 9.33% | 9.33% | |||||
| Problem 2 | ||||||
| Blue Crab, Inc. plans to issue new bonds, but is uncertain how the market would set the yield to maturity. The bonds would be 27-year to maturity, carry a 13.94 percent annual coupon, and have a $1,000 par value. Blue Crab, Inc. has determined that these bonds would sell for $1,190 each. What is the yield to maturity for these bonds? | ||||||
| Market i | Coupon i | Nper | PMT | FV | Type | PV |
| 0.1394 | 27 | 139.40 | 1,000.00 | 0 | 1,190.00 | |
| =RATE(27,139.4,-1190,1000,0) = 11.61% | 11.61% | |||||
| Problem 3 | ||||||
| Fresh Fruit, Inc. has a $1,000 par value bond that is currently selling for $1,031. It has an annual coupon rate of 6.44 percent, paid semiannually, and has 22-years remaining until maturity. What would the annual yield to maturity be on the bond if you purchased the bond today and held it until maturity? | ||||||
| Market i | Coupon i | Nper | PMT | FV | Type | PV |
| 0.0644 | 22 | 64.40 | 1,000.00 | 0 | 1,031.00 | |
| =RATE(22*2,64.4/2,-1031,1000,0)*2 = 6.18% | 6.18% | |||||
| Problem 4 | ||||||
| A few years ago, Spider Web, Inc. issued bonds with a 7.79 percent annual coupon rate, paid semiannually. The bonds have a par value of $1,000, a current price of $864, and will mature in 16 years. What would the annual yield to maturity be on the bond if you purchased the bond today? | ||||||
| Market i | Coupon i | Nper | PMT | FV | Type | PV |
| 0.0779 | 16 | 77.90 | 1,000.00 | 0 | 864.00 | |
| =RATE(16*2,77.9/2,-864,1000,0)*2 = 9.46% | 9.46% | |||||
4E
| Problem 1 | |||||||
| Marco Chip, Inc. just issued zero-coupon bonds with a par value of $1,000. The bond has a maturity of 19 years and a yield to maturity of 11.63 percent, compounded semi-annually. What is the current price of the bond? | |||||||
| Market i | Coupon i | Nper | PMT | FV | Type | PV | YTM |
| 19 | 1,000.00 | 0.1163 | |||||
| =PV(11.63%/2,19*2,0,1000,0) = 116.74 | ($116.74) | ||||||
| Problem 2 | |||||||
| Black Water Corp. just issued zero-coupon bonds with a par value of $1,000. The bond has a maturity of 30 years and a yield to maturity of 6.49 percent, compounded annually. What is the current price of the bond? | |||||||
| Market i | Coupon i | Nper | PMT | FV | Type | PV | YTM |
| 30 | 1,000.00 | 0.0649 | |||||
| =PV(6.49%,30,0,1000,0) = 151.61 | ($151.61) | ||||||
| Problem 3 | |||||||
| 10 years ago, Mini Max Inc. issued 30 year to maturity zero-coupon bonds with a par value of $1,000. Now the bond has a yield to maturity of 8.63 percent, compounded semi-annually. What is the current price of the bond? | |||||||
| Market i | Coupon i | Nper | PMT | FV | Type | PV | YTM |
| 20 | - 0 | 1,000.00 | 0.0863 | ||||
| =PV(8.63%/2,20*2,0,1000,0) = 184.56 | ($184.56) | ||||||
| Problem 4 | |||||||
| 15 years ago, Blue Lake Corp. issued 30 year to maturity zero-coupon bonds with a par value of $5,000. The bond has current yield to maturity of 5.83 percent, compounded annually. What is the current price of the bond? | |||||||
| Market i | Coupon i | Nper | PMT | FV | Type | PV | YTM |
| 15 | - 0 | 5,000.00 | 0.0583 | ||||
| =PV(5.83%,15,0,5000,0) = 2,137.17 | ($2,137.17) | ||||||
4F
| Problem 1 | |||||||
| What is the yield to call of a 30-year to maturity bond that pays a coupon rate of 6.47 percent per year, has a $1,000 par value, and is currently priced at $1,031? The bond can be called back in 8 years at a call price $1,081. Assume annual coupon payments. | |||||||
| Market i | Coupon i | Nper | PMT | FV | Type | PV | YTM |
| 0.0647 | 8 | 64.70 | 1,081.00 | 1,031.00 | |||
| =RATE(8,64.7,-1031,1081,0) = 6.75% | 6.75% | ||||||
| Problem 2 | |||||||
| Bright Sun, Inc. sold an issue of 30-year $1,000 par value bonds to the public. The bonds had a 14.14 percent coupon rate and paid interest annually. It is now 5 years later. | |||||||
| The current market rate of interest on the Bright Sun bonds is 8.71 percent. What is the current market price (intrinsic value) of the bonds? | |||||||
| Market i | Coupon i | Nper | PMT | FV | Type | PV | YTM |
| 0.0871 | 0.1414 | 25 | 141.40 | 1,000.00 | 0 | ??? | |
| =PV(8.71%,25,141.4,1000,0)= $1,546.15 | ($1,546.15) | ||||||
| Problem 3 | |||||||
| 23 years ago, Delicious Mills, Inc. issued 30-year to maturity bonds that had a 10.23 percent annual coupon rate, paid semiannually. The bonds had a $1,000 face value. Since then, interest rates in general have changed and the yield to maturity on the Delicious Mills bonds is now 10.38 percent. | |||||||
| Given this information, what is the price today for a Delicious Mills bond? | |||||||
| Market i | Coupon i | Nper | PMT | FV | Type | PV | YTM |
| 0.1038 | 0.1023 | 7 | 102.30 | 1,000.00 | 0 | ??? | |
| =PV(10.38%/2,7*2,102.3/2,1000,0) = 992.67 | ($992.67) | ||||||
| Problem 4 | |||||||
| Dan is considering the purchase of Super Technology, Inc. bonds that were issued 9 years ago. When the bonds were originally sold they had a 26-year maturity and a 9.01 percent coupon interest rate, paid annually. | |||||||
| The bond is currently selling for $809. What is the yield to maturity on the bonds if you purchased the bond today? | |||||||
| Market i | Coupon i | Nper | PMT | FV | Type | PV | YTM |
| 0.0901 | 17 | 90.10 | 1,000.00 | 0 | 809.00 | ||
| =RATE(17,90.1,-809,1000,0) = 11.64% | 11.64% | ||||||
4G
| Problem 1 | ||||||
| Assume that today's date is February 15, 2015. Robin Hood Inc. bond is an annual-coupon bond. Par value of the bond is $1,000. How much you will pay for the bond if you purchased the bond today? | ||||||
| Company | Maturity Date | Current Yield | ||||
| Price | Coupon Rate | YTM | Rating | |||
| Robin Hood | 112.599 | 6.056 | 2-15- 2037 | - | - | D |
| The number in the second column (112.599) is the price per each $100 of par value. Par value of the bond is $1000, so the price of the bond in dollars is | ||||||
| ($1000/100) * 112.599 = 10* 112.599 = $1,125.99 | 1125.99 | |||||
| Problem 2 | ||||||
| Assume that today's date is February 15, 2015. Robin Hood Inc. bond is an annual-coupon bond. Par value of the bond is $1,000. Calculate annual coupon interest payments. | ||||||
| Company | Maturity Date | Current Yield | ||||
| Price | Coupon Rate | YTM | Rating | |||
| Robin Hood | 127.495 | 10.123 | 2-15- 2026 | - | - | D |
| Coupon rate is 10.123% | ||||||
| Par value of the bond is $1000 | ||||||
| Coupon payment = $1000*10.123% = $101.23 | 10,123.00 | |||||
| Problem 3 | ||||||
| Assume that today's date is February 15, 2015. Robin Hood Inc. bond is an annual-coupon bond. Par value of the bond is $1,000. Calculate the bond's current yield. | ||||||
| Company | Maturity Date | Current Yield | ||||
| Price | Coupon Rate | YTM | Rating | |||
| Robin Hood | 121.819 | 8.175 | 2-15- 2039 | - | ? | D |
| 0.0671 | ||||||
| Problem 4 | ||||||
| Assume that today's date is April 15, 2015. Fresh Bakery Inc. bond is an annual-coupon bond. Par value of the bond is $5,000. | ||||||
| How much you will pay for the bond if you purchased the bond today? | ||||||
| Company | Maturity Date | Current Yield | ||||
| Price | Coupon Rate | YTM | Rating | |||
| Fresh Bakery | 92.148 | 8.433 | 04-15- 2027 | - | - | AA |
| 4,607.40 | ||||||
| ($5000/100) * 92.148 = 50* 92.148 = $4,607.40 | ||||||
| Problem 5 | ||||||
| Assume that today's date is April 15, 2015. Fresh Bakery Inc. bond is an annual-coupon bond. Par value of the bond is $5,000. | ||||||
| Calculate annual coupon interest payments. | ||||||
| Company | Maturity Date | Current Yield | ||||
| Price | Coupon Rate | YTM | Rating | |||
| Fresh Bakery | 94.262 | 9.399 | 04-15- 2028 | - | - | AA |
| 469.95 | ||||||
| Problem 6 | ||||||
| Assume that today's date is April 15, 2015. Fresh Bakery Inc. bond is an annual-coupon bond. Par value of the bond is $5,000. Calculate the bond's current yield. | ||||||
| Company | Maturity Date | Current Yield | ||||
| Price | Coupon Rate | YTM | Rating | |||
| Fresh Bakery | 101.189 | 11.424 | 04-15- 2021 | - | ? | AA |
| Coupon Pmt = | 571.2 | |||||
| Yield = | 0.11290 | |||||