|
Yield to Maturity
The yield to maturity (YTM)
is a measure of a average rate of
return that will be earned on a bond if it is bought now
and held until maturity.
The
yield to maturity is the standard measure of the
total rate of return of the bond over its life. We have
noted that the current yield of a bond measures only the
cash income provided by the bond as a percentage of bond
price and ignores any prospective capital gains or
losses. We would like a measure of rate of return
that accounts for both current income as well as the
price increase or decrease over the bond's life.
In
practice, an investor considering the purchase of a bond
is not quoted a promised rate of return. To calculate
the yield to maturity, we solve the bond price equation
for the interest rate given the bond's price.
For
example, suppose an 8% coupon, 30-year bond is selling
at $1,276.76. What average rate of return would be
earned by an investor purchasing the bond at this price?
To answer this question, we find the interest rate at
which the present value of the remaining bond payments
equals the bond price. This is the rate that is
consistent with the observed price of the bond.
Therefore, we solve for r in the following equation,
$1,276.76 = 40 x PA(r,60) + 1000 x PF(r,60)
These
equations have only one unknown variable, the interest
rate, r. You can use a financial calculator to confirm
that the solution to the equation is r = 0.03 or 3% per
half year. This is considered the bond's yield to
maturity as the bond would be fairly priced at $1,276.76
if the fair market rate of return on the bond over its
entire life were 3% per half year.
The
bond's yield to maturity is the internal rate of return
on an investment in the bond. The yield to
maturity can be interpreted as the compound rate of
return over the life of the bond under the assumption
that all bond coupons can be reinvested at an interest
rate equal to the bond's yield to maturity. Yield to
maturity is widely accepted as a proxy for average
return.
Yield
to maturity is different from the current yield of a
bond, which is the bond's annual coupon payment divided
by the bond price. For example, for the 8%, 30-year bond
currently selling at $1,276.76, the current yield would
be $80/$1,276.76 = 0.0627, or 6.27% per year. In
contrast, recall that the effective annual yield to
maturity is 6.09%. For this bond, which is selling at a
premium over par value ($1,276.76 rather than
$1,000.00), the coupon rate (8%) exceeds the
current yield (6.27%), which exceeds the yield to
maturity (6.09%). The coupon rate exceeds current yield
because the coupon rate divides the coupon payments by
par value ($1,000.00) rather than by the bond price
($1,276.76). In turn, the current yield exceeds yield to
maturity because the yield to maturity accounts for the
built-in capital loss on the bond; the bond bought today
for $1,276.76 will eventually fall in value to $1,000.00
at maturity.
|
