Question

A bond outstanding with 10 years to maturity, an 9.25% nominal coupon, semiannual payments, and a $1,000 par value. The bond has a 6.50% nominal yield to maturity, but it can be called in 4.5 years at a price of $1,100. What is the bond's nominal yield to call?

Answer 1

Yield to call is the yield we can generate till the call date. This can be calculated as the compound interest rate at which the present value of bonds coupon payments and call price is equal to the market price of the bond.

9.25% nominal coupon paid semi-annually means we get coupons of (0.0925*1000/2 = 46.25) every 6 months

We can use excel function =pv to get the current market price of the bond.

The nominal yield of 6.5% becomes 3.25% per 6 months.

=pv(0.0325,20,46.25,1000) = 1199.92

Now, we have to use irr function to get yield to call for 6 months

In excel, write the cashflows side by side for every 6 months. Year 0 cashflow is -1199.92. The next 8 cashflows will be coupon payments i.e. 46.25.

The last cashflow at the end of 4.5 years will be call price plus coupon = 1100+46.25 = 1146.25

=irr(the above cashflows in consecutive columns) = 3.036% (for 6 months)

Nominal Yield to call will be 2*3.036 = 6.07%