You purchase today a callable annual coupon rate bond under

You purchase today a callable annual coupon rate bond under the following conditions: Bond characteristics:

Coupon rate: 7.5%

Maturity of bond: 20 years

Call Premium: 8% Time to call period: 4 years

Current YTM: 8.5%

Expected hold assumptions:

Expected hold time: 4 years

Reinvestment rate (average money market return): 2.1%

Expected YTM (non-callable bonds) at sale: 4.0%

Based upon the above items, find the Horizon Yield (HY) for this bond position.

Solution

Bond price before change in YTM Interest compounded annually

Par value of bond is 1000

Coupon rate on bond is 0.075

Initial YTM on bond is 0.085

Years till maturity are 20 Price = coupon rate x par value x PVIFA(ytm%, n) + par value x PVIF(ytm%, n) PVIFA(0.085, 20) =9.463 PVIF(0.085, 20) = 0.1956

Price = 0.075 x 1000 x 9.4633 + 1000 x 0.1956
Price = 905.347
Horizon rate of return Bond price 905.347
Bond price after change in YTM = 1080 (assume at premium given)

Change in YTM = 4.5%
Bond horizon = 4

horizon rate = (1080/905.347)^1/4 * (1+0.045) - 1
horizon rate = (1.1929)^(0.25) * (1.045) - 1
horizon rate = 1.0450835 * 1.045 - 1

horizon rate = 1.0921566261655 - 1

horizon rate = 9.21%

Annual horizon rate = 9.21%

The 9.21% is the nominal yield to horizon

Now if you have any query regarding it then ask through comments
Assumption ... Price after change in ytm is 1080 as all data regarding it is not given