Question

A $10,000 face value coupon bond is purchased on 2/10/2020 and matures on 5/31/2031. It pays a total of $300 annual coupon payments and is currently selling for $10,381.80.

a) What is the annual Coupon Rate?
b) What is the price per $100 face value?
c) What is the Face Value per $100?
d) What is the YTM?

Answer 1

(a)

Annual coupon rate = Annual coupon / Face value (FV) = $300 / $10,000 = 0.03 = 3%

(b)

Price per $100 face value = [Price / (FV / 100)] = [$10,381.8 / ($10,000 / 100)] = [$10,381.8 / $100] = 103.818

(c)

Face value per $100 = FV / 100 = $10,000 / 100 = $100

(d)

Quarterly coupon payment = Annual coupon payment / 4 = $300/4 = $75

Number of quarters between 2/10/2020 and 5/31/2031 = 45

Quarterly YTM is computed using Excel RATE function as follows.

Face value (FV) ($) =	10,000
Current price (PV) ($) =	-10,381.8
Quarterly coupon payment ($) =	75
Number of quarters (NPER) =	45
Quarterly YTM =	0.65%

Annual YTM = 4 x Quarterly YTM = 0.65% x 4 = 2.60%