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# Calculating the current yield and yield to maturity

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Throughout this question consider the following bond: face value of \$1,000, coupon rate is 8%, semi-annual coupon payments, 4 years of maturity, and a purchase price of \$1,055.69.

(a) Calculate the current yield and yield to maturity on the bond as of the date of purchase.

(b) Calculate the current yield and bond price on each anniversary date of the bond purchase until maturity. Suppose on each of these dates the yield to maturity on the bond is 7%, 6.6%, 6.2%, and 6.36%, respectively.

(c) Assume instead of holding the bond until maturity, you sell the bond on the second anniversary of its purchase (right after you receive the last coupon). Based on your results in part (b) above, what is your total rate of return over this 2-year holding period? What is your annual rate of return over the same period? Assume you can reinvest the previous coupons at an APR of 10% quarterly compounded.

#### Solution Preview

a) Current yield = Coupon payment / Purchase price of bond = (1000*8%/2)/1055.69
= 0.0379 semi annual
The nominal annual current yield = 0.0379*2=0.0758 or 7.58%
However, the effective annual current yield would be =(1+0.0379)^2-1 =0.0772 or 7.72%

For yield to maturity identify the cash flows attached with the bond and then calculate IRR. The IRR is the yield to maturity on the bond.
Period (half year) Cash Flow
0 -1055.69
1 40
2 40
3 40
4 40
5 40
6 40
7 40
8 40 + 1000

The irr is 3.20%, ...

#### Solution Summary

This solution provides calculations for current yield, yield to maturity, and bond price.

\$2.19