Question

Current yield and yield to maturity An annual coupon bond has a $1,000 face value, coupon rate of 5%, will mature in 10 years, and currently sells for $810.34.

a. What is the yield to maturity of the bond?
b. What is the current yield of the bond?
c. Why does the current yield differ from the yield to maturity?
d. One year later, the market rates have increased to 8%. Assume that you have just received a coupon payment and you sold the bond. If you sold your bond at its intrinsic value, what would be the rate of return on your investment?

Answer 1

Solution

i.) FV= 1000

PMT = 50

N = 10

PV= -810.34

Putting all these values in a financial calculator

we get I/Y or YTM as 7.80%

ii.) Current yield = Annual coupon/ Market price of the bond

= 50/810.34 = 6.17%

iii.) YTM is the yield when we keep the bond until maturity. It is being discounted while the current yield is the yield at the present moment. The YTM is an anticipated rate of return associated with the bonds while the current yield is used to make an assessment on the relationship between the current price of the bond and the annual interest generated by the bonds.

iv) Now I/Y = 8%

N = 9( because he is selling after 1 year at intrinsic value)

FV= 1000

PMT = 50

Calculating PV= -812.59

One year interest = 50(1.08) = $54

and now to calculate compound interest

[(54+812.59)/810.34 ]- 1 = 6.941%

or we can solve it like

we are now selling it at 812.59

We bought it at 810.34

Profit is = 2.25 + one year interest = 54

So 56.25/810.34 = 6.94%