Bond and Their Valuation

A.) Indicate whether bond is trading at a premium, at a discount, or at par.Bond A is selling at discount because its coupon rate (7%) is lesser than the yield to maturity rate (9%). Bond B is selling at par because its coupon rate (9%) is equal to the yield to maturity rate (9%). Bond C is selling at premium because its coupon rate (11%) is greater than the yield to maturity rate (9%).

B.) Calculate the price of each bondsVb= (Par Value * Coupon Rate) +Bond AVb= (1 000 0.07) + = $856.79Bond BVb= (1 000 0.09) + = $1 000.00Bond CVb= (1 000 0.11) + = $1 143.21

C.) Calculate the current yieldCoupon Pmt= Coupon Rate Par ValuePmt a= 7% 1000= $ 70Pmt b= 9% 1000= $ 90Pmt c= 11% 1000= $ 110

Current Yield= Coupon Payment / PriceCY a= 70 / 856.79= 8.17%CY b= 90 / 1 000= 9.00%CY c= 110 / 1 143.21= 9.62%D.) Current PriceBond AVb= (1 000 0.07) + = $863.90Bond BVb= (1 000 0.09) + = $1000.00Bond CVb= (1 000 0.011) + = $1136.10

Beginning PriceBond AVb= (1 000 0.07) + = $856.79Bond BVb= (1 000 0.09) + = $1 000.00Bond CVb= (1 000 0.011) + = $1 143.21

Expected Capital Gains YieldCapital Gains Yield = Bond ACapital Gains Yield = = .83%Bond BCapital Gains Yield = = 0%Bond CCapital Gains Yield = =.62%

Current Yield= Coupon Payment / PriceCY a= 70 / 863.9= 8.17%CY b= 90 / 1000= 9.00%CY c= 110 / 1136.1= 9.62%

Expected Total ReturnExpected Total Return = YTM or Current Yield + Capital Gains YieldBond AExpected Total Return = 8.17% + .83% = 9%Bond BExpected Total Return = 9% + 0% = 9%Bond CExpected Total Return = 9.62% + (-.62%) = 9%

E.1)Annual Interest payment = 80Par Value = $1000Market price = $1150Number of years = 9

= 5.89 %

E.2)Annual Interest payment = 80Call Price = 1040Market price = 1150Number of years = 5

= 5.30 %

E.3)Assuming the rates will not increase drastically in the next 5 years, the bond will be called, so he would likely receive the YTC than the YTM. This is because the YTM has a lower rate than the coupon rate and that the market price exceeds the call price.

F.)Price risk is the risk of a decline in a bonds price due to an increase in interest rates. Reinvestment risk is when the decline in interest will lead to a decline in income from a bond portfolio.The bond with the most price risk is the 10-year bond with zero coupon, because, according to the definition, price risk is higher on bonds that have long maturities, because interest rates will most likely change during the years, and long-term maturity bonds are more sensitive to changes in rates The bond with the most reinvestment risk is the 1-year bond with a 9% annual coupon, because it is short term, and because of fluctuating interest rates, it is subject to being called, therefore it will have to be reinvested again, most likely at bonds with lower coupons.

G.)Years Until MaturityBond ABond BBond C

12$ 856.79$ 1 000.00$ 1 143.21

11$ 863.90$ 1 000.00$ 1 136.10

10$ 871.65$ 1 000.00$ 1 128.35

9$ 880.10$ 1 000.00$ 1 119.90

8$ 889.30$ 1 000.00$ 1 110.70

7$ 899.34$ 1 000.00$ 1 100.66

6$ 910.28$ 1 000.00$ 1 089.72

5$ 922.21$ 1 000.00$ 1 077.79

4$ 935.21$ 1 000.00$ 1 064.79

3$ 949.37$ 1 000.00$ 1 050.63

2$ 964.82$ 1 000.00$ 1 035.18

1$ 981.65$ 1 000.00$ 1 018.35

0$ 1 000.00$ 1 000.00$ 1 000.00

G.1.)Years Until MaturityBond ABond BBond C

128.17%9.00%9.62%

118.10%9.00%9.68%

108.03%9.00%9.75%

97.95%9.00%9.82%

87.87%9.00%9.90%

77.78%9.00%9.99%

67.69%9.00%10.09%

57.59%9.00%10.21%

47.48%9.00%10.33%

37.37%9.00%10.47%

27.26%9.00%10.63%

17.13%9.00%10.90%

07.00%9.00%11.00%

G.2.)Years Until MaturityBond ABond BBond C

120.83%0.00%-0.62%

110.90%0.00%-0.68%

100.97%0.00%-0.75%

91.05%0.00%-0.82%

81.13%0.00%-0.90%

71.22%0.00%-0.99%

61.31%0.00%-1.09%

51.41%0.00%-1.21%

41.52%0.00%-1.33%

31.63%0.00%-1.47%

21.74%0.00%-1.63%

11.87%0.00%-1.90%

G.3.)Years Until MaturityBond ABond BBond C

129.00%9.00%9.00%

119.00%9.00%9.00%

109.00%9.00%9.00%

99.00%9.00%9.00%

89.00%9.00%9.00%

79.00%9.00%9.00%

69.00%9.00%9.00%

59.00%9.00%9.00%

49.00%9.00%9.00%

39.00%9.00%9.00%

29.00%9.00%9.00%

19.00%9.00%9.00%

SOLUTIONS FOR G

Price of Each BondVb= (Par Value * Coupon Rate) +

Bond AVb12= (1 000 0.07) + = $856.79Vb11= (1 000 0.07) + = $863.90Vb10= (1 000 0.07) + = $871.65Vb09= (1 000 0.07) + = $880.10Vb08= (1 000 0.07) + = $889.30Vb07= (1 000 0.07) + = $899.34Vb06= (1 000 0.07) + = $910.28Vb05= (1 000 0.07) + = $922.21Vb04= (1 000 0.07) + = $935.21Vb03= (1 000 0.07) + = $949.37Vb02= (1 000 0.07) + = $964.82Vb01= (1 000 0.07) + = $981.65Vb00= (1 000 0.07) + = $1000.00

Bond BVb12= (1 000 0.09) + = $1000.00Vb11= (1 000 0.09) + = $1000.00Vb10= (1 000 0.09) + = $1000.00Vb09= (1 000 0.09) + = $1000.00Vb08= (1 000 0.09) + = $1000.00Vb07= (1 000 0.09) + = $1000.00Vb06= (1 000 0.09) + = $1000.00Vb05= (1 000 0.09) + = $1000.00Vb04= (1 000 0.09) + = $1000.00Vb03= (1 000 0.09) + = $1000.00Vb02= (1 000 0.09) + = $1000.00Vb01= (1 000 0.09) + = $1000.00Vb00= (1 000 0.09) + = $1000.00

Bond CVb12= (1 000 0.11) + = $1143.21Vb11= (1 000 0.11) + = $1136.10Vb10= (1 000 0.11) + = $1128.35Vb09= (1 000 0.11) + = $1119.90

Vb08= (1 000 0.11) + = $1110.70Vb07= (1 000 0.11) + = $1100.66Vb06= (1 000 0.11) + = $1089.72Vb05= (1 000 0.11) + = $1077.79Vb04= (1 000 0.11) + = $1064.79Vb03= (1 000 0.11) + = $1050.63Vb02= (1 000 0.11) + = $1035.18Vb01= (1 000 0.11) + = $1018.35Vb00= (1 000 0.11) + = $1000.00

Capital Gains YieldCurrent Yield= Coupon Payment / Price

Bond ACY 12= 70 / 856.79= 8.17%CY 11= 70 / 863.90= 8.10%CY 10= 70 / 871.65= 8.03%CY 09= 70 / 880.10= 7.95%CY 08= 70 / 889.30= 7.87%CY 07= 70 / 899.34= 7.78%CY 06= 70 / 910.28= 7.69%CY 05= 70 / 922.21= 7.59%CY 04= 70 / 935.21= 7.48%CY 03= 70 / 949.37= 7.37%CY 02= 70 / 964.82= 7.26%CY 01= 70 / 981.65= 7.13%CY 00= 70 / 1000.00= 7.00%

Bond BCY 00= 90 / 1000.00= 9.00%

Bond CCY 12= 110 / 856.79= 9.62%CY 11= 110 / 863.90= 9.68%CY 10= 110 / 871.65= 9.75%CY 09= 110 / 880.10= 9.82%CY 08= 110 / 889.30= 9.90%CY 07= 110 / 899.34= 9.99%CY 06= 110 / 910.28= 10.09%CY 05= 110 / 922.21= 10.21%CY 04= 110 / 935.21= 10.33%CY 03= 110 / 949.37= 10.47%CY 02= 70 / 964.82= 10.63%CY 01= 70 / 981.65= 10.90%CY 00= 70 / 1000.00= 11.00%

Capital Gains YieldCapital Gains Yield =

Bond A12 years before maturity: (863.9-856.79)/856.79=0.83%11 years before maturity: (871.65-863.9)/ 863.9=0.90%10 years before maturity:(880.1-871.65)/ 871.65=0.97%9years before maturity: (889.3-880.1)/ 880.1 =1.05%8years before maturity: (899.34-889.3)/ 889.3=1.13%7years before maturity: (910.28-899.34)/ 899.34=1.22%6 years before maturity: (922.21-910.28)/ 910.28=1.31%5 years before maturity: (935.21-922.21)/ 922.21=1.41%4 years before maturity: (949.37-935.21)/ 935.21=1.52%3years before maturity: (964.82-949.37)/ 949.37=1.63%2years before maturity:(981.65-964.82)/ 964.82=1.74%1years before maturity:(1000-981.65)/ 981.65=1.87%

Bond B(1000-1000)/1000 = 0.00% (applies to all the years before maturity)

Bond C12 years before maturity: (1136.1-1143.21)/ 1143.21=-0.62%11 years before maturity: (1128.35-1136.1)/ 1136.1=-0.68%10 years before maturity: (1119.9-1128.35)/ 1128.35=-0.75%9 years before maturity: (1110.7-1119.9)/ 1119.9=-0.82%8 years before maturity: (1100.66-1110.7)/ 1110.7=-0.90%7 years before maturity: (1089.72-1100.66)/ 1100.66=-0.99%6 years before maturity: (1077.79-1089.72)/ 1089.72=-1.09%5 years before maturity: (1064.79-1077.79)/ 1077.79=-1.21%4 years before maturity: (1050.63-1064.79)/ 1064.79=-1.33%3 years before maturity:(1035.18-1050.63)/ 1050.63=-1.47%2 years before maturity: (1018.35-1035.18)/ 1035.18=-1.63%1 years before maturity: (1000-1018.35)/ 1018.35=-1.83%

Total Return for Each BondExpected Total ReturnExpected Total Return = Current Yield + Capital Gains Yield

Bond A12 Years to Maturity = 8.17% + .83% = 9%11 Years to Maturity = 8.1% + .9% = 9%10 Years to Maturity = 8.03% + .97% = 9%9 Years to Maturity= 7.95% + 1.05% = 9%8 Years to Maturity = 7.87% + 1.13% = 9%7 Years to Maturity= 7.78% + 1.22% = 9%6 Years to Maturity= 7.69% + 1.31% = 9%5 Years to Maturity= 7.59% + 1.41% = 9%4 Years to Maturity= 7.48% + 1.52% = 9%3 Years to Maturity= 7.37% + 1.63% = 9%2 Years to Maturity= 7.26% + 1.74% = 9%1 Year to Maturity= 7.13% + 1.87% = 9%

Bond B12 Years to Maturity= 9% + 0% = 9%11 Years to Maturity= 9% + 0% = 9%10 Years to Maturity= 9% + 0% = 9%9 Years to Maturity= 9% + 0% = 9%8 Years to Maturity= 9% + 0% = 9%7 Years to Maturity= 9% + 0% = 9%6 Years to Maturity= 9% + 0% = 9%5 Years to Maturity= 9% + 0% = 9%4 Years to Maturity= 9% + 0% = 9%3 Years to Maturity= 9% + 0% = 9%2 Years to Maturity= 9% + 0% = 9%1 Years to Maturity= 9% + 0% = 9%

Bond C12 Years to Maturity= 9.62% + (-.62%) =9%11 Years to Maturity= 9.68% + (-.68%) =9%10 Years to Maturity= 9.75% + (-.75%) = 9%9 Years to Maturity= 9.82% + (-.82%) = 9%8 Years to Maturity= 9.90% + (-.90%) = 9%7 Years to Maturity= 9.99% + (-.99%) = 9%6 Years to Maturity= 10.09% + (-1.09%) = 9%5 Years to Maturity= 10.21% + (-1.21%) = 9%4 Years to Maturity= 10.33% + (-1.33%) = 9%3 Years to Maturity= 10.47% + (-1.47%) = 9%2 Years to Maturity= 10.63% + (-1.63%) = 9%1 Year to Maturity= 10.90% + (-1.90%) = 9%