Zumwalt Corporation's Class S bonds have a 12-year maturity, $1,000 par value, and a 5.75% coupon paid semiannually (2.875% each 6 months), and those bonds sell at their par value. Zumwalt's Class A bonds have the same risk, maturity, and par value, but the A bonds pay a 5.75% annual coupon. Neither bond is callable. At what price should the annual payment bond sell? (hint: Bonds with same risk should have same effective rate of return, or YTM).

$993.23  

Explanation:

Note that the yield to maturity for the Class S bond is 5.75% because when a bond sells at par its coupon rate and yield should be the same.

However, Class A, pays annual coupons and the fact they both have the same level of risk means that yields are the same, however, S's yield is 5.75% compounded semiannually, in the case of A we need  an equivalent yield but compounded once a year since annual coupons are to be made, as a result, for A we would convert the yield to an equivalent effective annual yield

EAR=(1+yield/2)^2-1

there are 2 semiannual periods in a year, that is the reason for 2 in the formula above

EAR=(1+5.75%/2)^2-1

EAR=5.83%

The price of bond A is the present value of 12 annual coupons and face value discounted at 5.83% effective annual yield

annual coupon= 5.75%*$1,000

annual coupon=$57.50

bond price=$57.50/(1+5.83%)^1+$57.50/(1+5.83%)^2+$57.50/(1+5.83%)^3+$57.50/(1+5.83%)^4+$57.50/(1+5.83%)^5+$57.50/(1+5.83%)^6+$57.50/(1+5.83%)^7+$57.50/(1+5.83%)^8+$57.50/(1+5.83%)^9+$57.50/(1+5.83%)^10+$57.50/(1+5.83%)^11+($1000+$57.50)/(1+5.83%)^12

bond price=$993.23  

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