How to figure out bond yields

Question

What would the yield be on a 1.75 percent, $1,000, 10-year Treasury bond if the market price of the bond was $950?

Answer 1

We are given the following:

Face Value of bond $1000

Coupon rate 1.75%

Frequency Semi-annual (Most bonds pay a semi-annual coupon)

Coupon /Payment $8.75 [(1.75% x 1000)/2]

No of periods 20 (10-year term x 2 coupon periods per year)

Price / PV $950

Using a BA II Plus calculator, we have

20 N

? I/Y

-950 PV

8.75 PMT

1000 FV

Solving for I/Y, gives us 1.16%. we multiply this by 2 to give us 2.32%, the Yield to Maturity

You can also solve this in Excel using the rate function as follows:

=RATE(20,8.75,-950,1000) which also gives you 1.16%, which you also multiply by 2, to give you 2.32%, the Yield to Maturity.

How do we know this is right? Well, since the price of the bond is lower than the face value we know that this is a discount bond. For all discount bonds. YTM > Coupon Rate, as long as the bond's rate does not re-adjust.