Question

A Treasury bond with a face(or promised) value of $1000 sold in the market for $1287.19 yesterday. at this price, the yield to maturity (ytm) was 2.43%. the bond's coupon rate is 6.75% and matures in 2026. Why would anyone in his/her sound mind buy this bond for $1287 only to be paid $1000 at maturity but many people did? explain why?

Answer 1

What we need to understand here is a bond gives two types of inflows to the investor

1) Annual return in the form of cupons

2) Redemption/Maturity value of the bond

Assuming Bond is sold at $ 1287 in 2019

The investor gets annual return of 6.75% i.e. $ 67.5 for 7 years and redemption value of 1000 at the end of 7 year

total inflow - (67.5*7)+1000 = 1472.5 (this is higher than current market price because cashflows are not discounted)

to get the current price of the bond we need to discount annual cashflows and redemption/Maturity value

= 67.5 (∑1/(1.0243)^7) + (1000* 1/(1.0243)^7 = $ 1287

= 67.5 ( PVAF (2.43, 7)) + 1000 (PVF (2.43, 7)

conclusion : current price of the bond also includes cupon payments annual hence the current price is higher that the maturity