Question

Amir Enterprises’ non-callable semiannual coupon bonds currently sell for $1,150.  They have a 20-yearmaturity, an annual coupon of $100, and a par value of $1,000. What is their yield to maturity (annual)?  Show work.

Answer 1

Yield to maturity is the total return earned for holding a bond until maturity. To calculate YTM, first we find out the approximate value of YTM using the formula as given below:

Approx. YTM = [Coupon rate + (F - P)/ N] / [ (F + P)/ 2]

where: F = Face value of the bond

P = Price paid by the investor for a bond

N = number of years to maturity

Coupon Payment = 100/2 = $50 (since it is given semiannual coupon bond)

Price of Bond (P) = $1,150

n = 20 x 2 = 40 (since semi-annual coupon payments)

Face Value = $1,000

Approx. YTM = [50 + (1000 - 1150)/ 40] / [( 1000 + 1150)]/2

= 46.25 / 1075 = 0.04302 or 4.3023%

Annual YTM = ( 1 + Semi-annual YTM)² - 1

= ( 1 + 0.04302)² - 1 = 0.0879 or 8.79% (approx. annual YTM)

This figure gives us a rough idea of the annual YTM that we shall arrive at using the trial and error method:

As per this method,

Price of bond = [C/ (1 + YTM)¹ ] +  [C/ (1 + YTM)² ] + ........+ [C/ (1 + YTM)^N ] + [F/ (1 + YTM)^N]

$1,150 = [$50/ (1+YTM)¹] + [$50/ (1+YTM)²] ........+ [$50/ (1+YTM)⁴⁰] + [1000/ (1+YTM)⁴⁰]

It is a pretty tedious task to calculate the above equation without excel so we use the IRR function in MS Excel.

Hence, we get YTM as 4.22% now this is a semi-annual YTM in order to calculate the annual YTM we use the formula as given below:

Annual YTM = ( 1 + Semi-annual YTM)² - 1

= ( 1 + 0.0422)² - 1 = 0.0862 or 8.62%

Answer: Annual YTM = 8.62%