IRD Determination G3: Yield to Maturity Method for Bonds (worked example)

[Snoopy]

F = [P(2+nY) - 2nC]/(2-n)

Stick in the numbers you know of the RHS of the equation and you get 'F', the 'capital value' of the bond.

I think it is worth going through this equation again, this time using a six month investment period for reference.

C is the Coupon = $70k.
F is the Face Value of the bond (to be determined)
P is the current market price of the bond: $1,012.5k
n is the 'investment periods' to maturity. = 3,3507 sets of six months (post 21)
Y, the yield to maturity we are told is 16.2308% for the year, implying a multiplication factor of 1.162308. For six months the multiplication factor must be the square root of that figure.: 1.078104. This is equivalent to a yield to maturity of 7.8104% compounding for every six months.

F = [P(2+nY) - 2nC]/(2-nY)
= [ $1,012.5k(2 + 3.3507x0.078104) - 2 x 3.3507 x $70k ] / (2-3.3507 x 0.078104)
= [ $2,290.0k - $469.1k ] / 1.7383
= $1,047.52k

This is slightly different result to the annual figure calculation that I did before (post 24), because in this calculation the coupon is generated more frequently (every six months, not summed over a year). That in turn means you need slightly less discount on your bond purchase price to create the same coupon income stream per unit of investment time.

SNOOPY