Question

A four-year coupon bond has face value $1000, coupons of 80, and a YTM of 8%

a- what is the bond's current price?

b- what is the bond's future value if coupons can be reinvested each year at YTM= 8% ?

c- what is the bond's annual return?

suppose that next year the interest rate falls to 4%

a- what is the bond's future value?

b- what is the bond's annual return?

Answer 1

a.

current price = Coupon1 / (1+r) + Coupon2 / (1+r)² + Coupon3 / (1+r)³ + (Coupon4 + Face value)/(1+r)⁴

= 80/ (1+0.08) + 80/ (1+0.08)² + 80/ (1+0.08)³ + (80 + 1000)/ (1+0.08)⁴

= (80 /1.08) + (80 /1.1664) + (80 /1.2597) + (1080 /1.36)

= 74.07 + 68.587 + 63.51 + 794.12

= $1000

where r = YTM

b.

each coupon reinvest at 8 %

first coupon will reinvest for 3 year so future value after 3 year = 80 * (1+0.08)³ = 80*1.2597 = 100.776

second coupon will reinvest for 2 year so future value after 2 year = 80 * (1+0.08)² = 80*1.1664= 93.312

third coupon will reinvest for 1 year so future value after 1 year = 80 * (1+0.08) = 80*1.08 = 86.4

foth year coupon =80

Bond future value = total fv of coupon + Face value = (100.776 + 93.312 + 86 + 80) + 1000 = 360.488 +1000 = $1360.488

c

Annual return = (Bond future value / Bond current value)^1/n - 1 = (1360.488 / 1000)^1/4-1 = 1.3604^0.25-1 = 1.08-1 = 0.08 = 8%

hence annual return will be the same as YTM 8%