Question

he process of bond valuation is based on the fundamental concept that the current pice 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 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 relaionship 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 xeed 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 Grace wants to earn a return of 13.50% and is offered the opportunity to purchase a $1,000 par value bond that pays a 11.25% 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)1+C1+ C)s1+C6+1+C)6 Complete the following table by identifying the appropriate corresponding variables used in the equation Variable Name Bond's semiannual coupon payment Bond's par value Semiannual required return Unknown Variable Value $1,000 Based on this equation and the data, it is less than $1,000 to expect that Grace's potential bond investment is currently exhibiting an intrinsic value Now, consider the situation in which Grace wants to earn a return of 14%, but the bond being considered for purchase offers a coupon rate of 11.25%. Again, assume that the bond pays semiannual interest payments and has three years to maturity. If you round the bond's intrinsic value to the nearest whole dollar, then its intrinsic value of bond is (rounded to the nearest whole dollar) is its par value, so that the Given your computation and conclusions, which of the following statements is true? when the coupon rate is greater than Grace's required return, the bond should trade at a discount. O A bond should trade at a par when the coupon rate is greater than Grace's required return O When the coupon rate is greater than Grace's required return, the bond should trade at a premium when the coupon rate is greater than Grace's required return, the bond's intrinsic value will be less than its par value

Answer 1

Before we start answering this question, let us understand bond math in relation to coupon rate and required rate of return.

When coupon rate > required rate of return (or YTM), price of a bond is greater than par value. So, it is a premium bond.

When coupon rate < required rate of return (or YTM), price of a bond is less than par value. So, it is a discount bond.

When coupon rate = required rate of return (or YTM), price of a bond is equal to par value. So, it is a par value bond.

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Based on these, the two fill in the blanks statements are:

Remember, a bond’s coupon rate partially determines the interest-based return that a bond will pay, and a bondholder’s required rate of return reflects the return that a bondholder would like to receive from a given investment.

When the bond's coupon rate is greater than the bondholder's required rate of return, the bond's intrinsic value will exceed its par value, and the bond will trade at 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 bond will trade at a discount.

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Based on the numerical question,

Bond's semi-annual coupon payment = $1,000 * 11.25%/2 = $56.25 {Remember, I have divided by 2 because it says 'semi-annual'}

$1000 is bond's par value

Semi-annual required rate of return = 13.50%/2 = 6.75% {I hope you guessed it, why I divided by 2 again here!}

Coupon payment rate < Required Rate of Return ---> Bond will trade at discount

Based on this equation and the data, it is correct to expect that Grace’s potential bond investment is currently exhibiting an intrinsic value less than $1000.

Now, we need to calculate the price of bond given required rate = 14%, 11.25% coupon rate and 3 years to maturity. We need to calculate the price of bond, for which I will show you how to do it in Excel:

Now, consider the situation in which Grace wants...................................... If you round the bond's instrinsic value to the nearest whole dollar, then its intrinsic value of $934.5 is less than its par value, so that the bond is trading at discount.

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Correct statement is statement 3.

Only this statement and not the other three are in line with the explanation that I made at the beginning of the question.

Hope this helps... !!