Answer to Question #17257 in Management for ang

Question

A bond with a 5 percent coupon ($50 a year) that matures after eight years is selling for $779. What
is the yield to maturity?

Answer 1

The yield to maturity formula is used to calculate the yield on a bond based on its current price on the market.
c(1 + r)^-1 + c(1 + r)^-2 + . . . + c(1 + r)^-Y +B(1 + r)^-Y = P
where
c = annual coupon payment (in dollars, not a percent)
Y = number of years to maturity
B = par value
P = purchase price

C = $50
Y = 8
B = $1,000
P = $779

YTM = 8.99%

A bond that pays 1 coupon(s) of 5% per year, that has a market value of$779.00, and that matures in 8 years will have a yield to maturity of 8.99%.

What does it mean? Well, bond investors don't just buy only newly issued bonds (on the primary market) but can also buy previously issued bonds from other investors (on the secondary market). Depending on whether a bond on the secondary market is bought at a discount or premium, the actual rate of return can be greater or lower than the quoted annual coupon rate. This is why bond investors need to look at YTM, which measures the bond's yield from the day the investor buys it to the day it expires, when the principal is paid to the bondholder.