Question

A bond with 10 years to maturity has a face value of $1,000. The bond can be called in four years for $1050. The bond pays an 6 percent semiannual coupon, and the bond has a 4.5 percent nominal yield to maturity.  What is the price of the bond today assuming that it will be called?

Answer 1

Bond Valuation: The value of bond is the present value of the expected cashflows from the bond,discounted at Yield to Maturity(YTM).

Year	Cash flow	PVAF/PVF@2.25%	Present Value (Cashflow*PVAF/PVF)
1-8	30	7.2472*	217.42
8	1050	0.8369**	878.79

Current Market Price of Bonds = $\sum$ Cashflow*PVAF/PVF

= 217.42+878.79

= $1096.20

Note : Since the bond makes semiannual interest payments, total no. of period is 8 (4*2), cashflow per period is 30(1000*6%/2) and cashflows are discounted at 2.25% (4.5/2).

*PVAF = (1-(1+r)^-n)/r

**PVF = 1 / (1+r)^n