Question

2. Bond valuation The process of bond valuation is based on the fundamental concept that the current price of a security can be determined by calculating the present value of the cash flows that the security will generate in the future There is a consistent and predictable relationship between a bond's coupon rate, its par value, a bondholder's required return, and the bond's resulting intrinsic value. Trading at a discount, trading at a premium, and trading at par refer to particular relationships between a bond's intrinsic value and its par value. These result from the relationship between a bond's coupon rate and a bondholder's required rate of return Remember, a bond's coupon rate partially determines the interest-based return that a bond wil pay, and a bondholder's required return reflects the return that a bondholder would like to receive from a given investment. The mathematics of bond valuation imply a predictable relationship between the bond's coupon rate, the bondholder's required return, the bond's par value, and its intrinsic value. These relationships can be summarized as follows: When the bond's coupon rate is equal to the bondholder's required return, the bond's intrinsic value will equal its par value, and the bond will trade at par .When the bond's coupon rate is greater than the bondholder's required return, the bond's intrinsic value will exceed its par value, and the bond will trade at a premium . When the bond's coupon rate is less than the bondholder's required return, the bond's intrinsic value will be less than its par value, and the bond will trade at a discount . For example, assume Ethan wants to earn a return of 14.00% and is offered the opportunity to purchase a $1,000 par value bond that pays a 12.00% coupon rate (distributed semiannually) with three years remaining to maturity. The following formula can be used to compute the bond's intrinsic value: Intrinsic Value (1+C)2

Answer 1

A = Semiannual coupon payment = 12% *1000/2 = $60

B = Par value or Face value = $1000

C = Semiannual required return = 14%/2 = 7%

Based on this equation it is incorrect to expect that Ethan's potential bond investment is currently exhibiting an intrinsic value of greater than 1000. (Because since the coupon rate is less than required rate, the intrinsic value is lower than the par value)

Now, consider Ethan wants to earn 10%..... If you round the bonds intrinsic value to the nearest dollar, then its intrinsic value of $1,051 is greater than its par value, so that the bond is trading at a premium

Which statement is TRUE

When the coupon rate is greater than Ethan's required return, the bond should trade at a premium