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%
