In: Economics
Delray Auto are currently selling at $1,050, with 8% annual coupon payment and 1000 par. These bonds have 16 years left until maturity.
Yield to maturity = ??
Price a year later = ??
Current yield = ??
Capital gain = ??
Total return = ??
Face value (F) = $1,000
Annual coupon payment (C) = $1,000 x 8% = $80
(1) Years to maturity (N) = 16 and Price (P) = $1,050
(a) YTM = [C + {(F - P)/N] / [(F + P)/2]
= [80 + (1,000 - 1,050)/16] / [(1,000 + 1,050)/2]
= [80 - (50/16)] / (2,050/2)
= (80 - 3.125) / 1,025
= 76.875 / 1,025
= 0.075
= 7.5%
(b) Current yield = C / P = $80 / $1,050 = 0.0762
= 7.62%
(2) after 1 year, Years to maturity (N) = 15 and let bond price be $P. Then
(a) YTM = [C + {(F - P)/N] / [(F + P)/2]
0.075 = [80 + (1,000 - P)/15] / [(1,000 + P)/2]
0.075 = [80 - (1,000 - P)/15] / (500 + 0.5P)
0.075 x (500 + 0.5P) = [80 - (1,000 - P)/15]
37.5 + 0.0375P = 80 - [(1,000 - P)/15]
562.5 + 0.5625P = 1,200 - 1,000 + P
562.5 + 0.5625P = 200 + P
0.4375P = 362.5
P = $828.57
(b) Current yield = C / P = $80 / $828.57 = 0.0966 = 9.66%
(c) Capital gain = Change in price = $(828.57 - 1,050) = -$221.43 (there is a capital loss)
(d) Total return = New price + Annual coupon - Initial price = $(828.57 + 80 - 1,050) = -$141.43 (negative return)