Question

Bond P is a premium bond with a coupon rate of 10 percent. Bond D has a coupon rate of 5 percent and is currently selling at a discount. Both bonds make annual payments, have a YTM of 7 percent, and have ten years to maturity. What is the current yield for bond P and bond D? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) Current yield Bond P % Bond D % If interest rates remain unchanged, what is the expected capital gains yield over the next year for bond P and bond D? (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) Capital gains yield Bond P % Bond D %

Answer 1

Answer:

Stock P's current yield = 8.18%

Stock D's current yield = 5.87%

Stock P's capital gains yield = -1.31%

Stock D's capital gains yield = 1.4%

Explanation:

price of bond P:

0.07 = {100 + [(1,000 - MP) / 10]} / [(1,000 + MP) / 2]

0.07 x [(1,000 + MP) / 2] = 100 + [(1,000 - MP) / 10]

0.07 x (500 + 0.5MP) = 100 + 100 - 0.1MP

35 + 0.035MP = 200 - 0.1MP

0.135MP = 165

MP = 165 / 0.135 = $1,222.22

price of bond D:

0.07 = {50 + [(1,000 - MP) / 10]} / [(1,000 + MP) / 2]

0.07 x [(1,000 + MP) / 2] = 50 + [(1,000 - MP) / 10]

0.07 x (500 + 0.5MP) = 50 + 100 - 0.1MP

35 + 0.035MP = 150 - 0.1MP

0.135MP = 115

MP = 115 / 0.135 = $851.85

current yield = dividend / stock price

Stock P's current yield = 100 / 1,222.22 = 8.18%

Stock D's current yield = 50 / 851.85 = 5.87%

price of bond P in one year:

0.07 = {100 + [(1,000 - MP) / 9]} / [(1,000 + MP) / 2]

0.07 x [(1,000 + MP) / 2] = 100 + [(1,000 - MP) / 9]

0.07 x (500 + 0.5MP) = 100 + 111.11 - 0.111MP

35 + 0.035MP = 211.11 - 0.111MP

0.146MP = 176.11

MP = 176.11 / 0.146 = $1,206.23

price of bond D in one year:

0.07 = {50 + [(1,000 - MP) / 9]} / [(1,000 + MP) / 2]

0.07 x [(1,000 + MP) / 2] = 50 + [(1,000 - MP) / 9]

0.07 x (500 + 0.5MP) = 50 + 111.11 - 0.111MP

35 + 0.035MP = 161.11 - 0.111MP

0.146MP = 126.11

MP = 126.11 / 0.146 = $863.77

capital gains yield = (P₁ - P₀) / P₀

Stock P's capital gains yield = (1,206.23 - 1,222.22) / 1,222.22 = -1.31%

Stock D's capital gains yield = (863.77 - 851.85) / 851.85 = 1.4%