1.Consider two bonds, Bond A and Bond B, both with a coupon rate of 10 percent a
ID: 2565796 • Letter: 1
Question
1.Consider two bonds, Bond A and Bond B, both with a coupon rate of 10 percent and a yield to maturity of 9 percent. These are standard bonds with semi-annual coupon payments. Bond A matures in 5 years while Bond B matures in 10 years. What is the price of each bond?
2. What is the fair value today of a common share with expected annual dividends of $1.29, $1.34, and $1.39 in each of the mext three years and an expected share price of $21.10 in three years, assuming a required return of 9.3 percent?
3. Consider two bonds, Bond C and Bond D, both with a yield to maturity of 7.3 percent and with 5 years to maturity. These are standard bonds with semi-annual coupon payments. Bond C has a coupon rate of 8.4 percent (with semi-annual coupon payments) while Bond D does not pay any coupons (i.e., it is a zero-coupon bond). What is the price of each bond?
4. Consider two bonds, Bond A and Bond B, both with a coupon rate of 11 percent and a yield to maturity of 9.7 percent. These are standard bonds with semi-annual coupon payments. Bond A matures in 5 years while Bond B matures in 10 years. What is the price of each bond?
Explanation / Answer
1. Price Of Bond A :
price (Present value) = face value / (1+ market interest)number of payments + interest [1-(1+ market interest)-number of payment / market interest]
= 1000 / (1+ 9%/2)5*2 + (1000 * 10%/2) [1-(1+ 9%/2)-5*2 / 9%/2]
= 1000 / (1+ 0.045)10 + (1000 * 0.05) [1-(1+ 0.045)-10 / 0.045]
= 1000 / (1.045)10 + 50 * [1-(1.045)-10 / 0.045]
= 1000 / 1.5530 + 50 * [(1- 1 / 1.5530) / 0.045]
= 643.92 + 50 * [0.3561 / 0.045]
= 643.92 + 395.67
= 1039.59
Price Of Bond B :
price (Present value) = face value / (1+ market interest)number of payments + interest [1-(1+ market interest)-number of payment / market interest]
= 1000 / (1+ 9%/2)10*2 + (1000 * 10%/2) [1-(1+ 9%/2)-10*2 / 9%/2]
= 1000 / (1+ 0.045)20 + 50 [1-(1+ 0.045)-20 / 0.045]
= 1000 / (1.045)20 + 50 [1-(1.045)-20 / 0.045]
= 1000 / (1.045)20 + 50 [1- 1/(1.045)20 / 0.045]
= 1000 / 2.4117 + 50 [1- 1/2.4117 / 0.045]
= 414.65 + 50 [0.5854 / 0.045]
= 414.65 + 650.44
=1065.09
2. fair value of a common share = D1 / (1+ required return) + D2 / (1+ required return)2 + D3 / (1+ required return)3 + price at 3 year end * (1+ required return)-3
= 1.29 / (1+ 0.093) + 1.34 / (1+ 0.093)2 + 1.39 / (1+ 0.093)3 + $21.10 * (1+0.093)-3
= 1.29 / (1.093) + 1.34 / (1.093)2 + 1.39 / (1.093)3 + $21.10 *(1.093)-3
= 1.29 / (1.093) + 1.34 / (1.093)2 + 1.39 / (1.093)3 + $21.10 *1 /(1.093)3
= 1.29 /1.093 + 1.34 /1.1946 + 1.39 /1.3058 + $21.10 *1 /1.3058
= 1.1802 + 1.1217 + 1.0645 + 16.1587
= $19.53
3. Price Of Bond C :
price (Present value) = face value / (1+ market interest)number of payments + interest [1-(1+ market interest)-number of payment / market interest]
= 1000 / (1+ 7.3%/2)5*2 + (1000 * 8.4%/2) [1-(1+ 7.3%/2)-5*2 / 7.3%/2]
= 1000 / (1+ 0.0365)10 + (1000 *0.042) [1-(1+0.0365)-10 / 0.0365]
= 1000 / (1.0365)10 + 42 [1-(1.0365)-10 / 0.0365]
= 1000 / (1.0365)10 + 42 [1- 1/(1.0365)10 / 0.0365]
= 1000 / 1.4312 + 42 [(1- 1/1.4312)/ 0.0365]
= 698.71 + 346.68
= $1045.39
Price Of Bond D :
Price ( zero-coupon bond ) = face value / (1 +yield to maturity )time
= 1000 / (1 + 7.3%/2 )5*2
= 1000 / (1 + 0.0365 )10
= 1000 / (1.0365 )10
= 1000 / 1.4312
= $698.71
4. Price Of Bond A :
price (Present value) = face value / (1+ market interest)number of payments + interest [1-(1+ market interest)-number of payment / market interest]
= 1000 / (1+ 9.7%/2)5*2 + (1000 * 11%/2) [1-(1+ 9.7%/2)-5*2 / 9.7%/2]
= 1000 / (1+ 0.0485)10 + 55 [1-(1+ 0.0485)-10 / 0.0485]
= 1000 / (1.0485)10 + 55 [1-(1.0485)-10 / 0.0485]
= 1000 / (1.0485)10 + 55 [1- 1 /(1.0485)10 / 0.0485]
= 1000 /1.6058 + 55 [(1- 1 /1.6058) / 0.0485]
= 1000 /1.6058 + 55 [0.3773 / 0.0485]
= 622.74 + 427.87
=1050.61
Price Of Bond B :
price (Present value) = face value / (1+ market interest)number of payments + interest [1-(1+ market interest)-number of payment / market interest]
= 1000 / (1+ 9.7%/2)10*2 + (1000 * 11%/2) [1-(1+ 9.7%/2)-10*2 / 9.7%/2]
= 1000 / (1+ 0.0485)20 + 55 [1-(1+ 0.0485)-20 / 0.0485]
= 1000 / (1.0485)20 + 55 [1-(1.0485)-20 / 0.0485]
= 1000 / (1.0485)20 + 55 [1- 1 /(1.0485)20 / 0.0485]
= 1000 / 2.5785 + 55 (1- 1/2.5785) / 0.0485]
= 387.82 + 55 * [0.6122 / 0.0485]
= 387.82 + 694.25
=1082.07
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.