Question

Consider a $1,000.00 face value bond with a $55 annual coupon and 10 years until maturity. Calculate the current yield; the coupon rate and the yield to maturity under each of the following:

a) The bond is purchased for $940.00

b) The bond is purchased for $1,130.00

c) The bond is purchased for $1,000.00

Answer 1

Face value (F) = $1,000

Annual coupon (C) = $55

Current price = P

Number of years to maturity (N) = 10

Then

(1) By approximation formula,

YTM = [C + {(F - P)/N] / [(F + P)/2] = [55 + (1,000 - P)/10] / [(1,000 + P)/2]

(2) Current yield = C / P

(3) Coupon rate = C / F

(a)

(i) Coupon rate = $55 / $1,000 = 0.055 = 5.5%

(ii) Current yield = $55 / $940 = 0.0585 = 5.85%

(iii) YTM = [55 + (1,000 - 940)/10] / [(1,000 + 940)/2]

= [55 + (60/10)] / (1940/2)

= (55 + 6) / 970

= 61 / 970

= 0.0629

= 6.29%

(b)

(i) Coupon rate = $55 / $1,000 = 0.055 = 5.5%

(ii) Current yield = $55 / $1,130 = 0.0487 = 4.87%

(iii) YTM = [55 + (1,000 - 1,130)/10] / [(1,000 + 1,130)/2]

= [55 - (130/10)] / (2,130/2)

= (55 - 13) / 1,065

= 42 / 1,065

= 0.0394

= 3.94%

(c)

(i) Coupon rate = $55 / $1,000 = 0.055 = 5.5%

(ii) Current yield = $55 / $1,000 = 0.055 = 5.55%

(iii) YTM = [55 + (1,000 - 1,000)/10] / [(1,000 + 1,000)/2]

= [55 + 0] / (2,000/2)

= 55 / 1,000

= 0.055

= 5.5%