Question

Delray Auto are currently selling at $1,050, with 8% annual coupon payment and 1000 par. These bonds have 16 years left until maturity.

1. What is the yield to maturity?
2. Assume yield to maturity remain the same, what is the price a year later (with 15 years left until maturity)?
3. From current year to next year, calculate the current yield, capital gain, and total return from the bond?

Yield to maturity = ??

Price a year later = ??

Current yield = ??

Capital gain = ??

Total return = ??

Answer 1

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)