Question

A bond has a yield to maturity of 9.38 percent, a coupon of 7.5 percent paid semiannually, a $1,000 face value, and a maturity date 21 years from today. What is the current yield?

Answer 1

Answer:

Current yield = 9.05%

Explanation:

$CurrentYield=\frac{Annual Coupons}{Current Bond Price}$

Annual Coupons  = $1,000*0.075=75$

The price of a bond is equivalent to the present value of all the cash flows that are likely to accrue to an investor once the bond is bought. These cash-flows are the periodic coupon payments that are to be paid semi-annually and the par value of the bond that will be paid at the end of the 21 years.  

During the 21 years, there are 42 equal periodic coupon payments that will be made. In each  year, the total coupon of $75 will be split into two equal payments equal to $\frac{75}{2}=37.5$. This stream of cash-flows is an ordinary annuity.

The yield to maturity is equal to 9.38% per annum  which equates to 4.69% per semi annual period.

The  PV of the cash-flows = PV of the coupon payments + PV of the par value of the bond

=$37.5*PV Annuity Factor for 42 periods at 4.69%+ $1,000* PV Interest factor with i=4.69% and n =42

$= 37.5*\frac{[1-(1+0.0469)^-^4^2]}{0.0469}+ \frac{1,000}{(1+0.0469)^4^2} = 828.81$

given annual dividends of $75 and a current bond price of $828.81

$Current Yield=\frac{75}{828.81}=0.09049$