Remember, a bond’s coupon rate partially determines the interest-based return that a bond (will / might) pay, and a bondholder’s required return reflects the return that a bondholder (is obligated / 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 (be less than / exceed / equal) 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 (par / a premium / a discount) .

For example, assume Olivia wants to earn a return of 9.00% and is offered the opportunity to purchase a $1,000 par value bond that pays a 15.75% coupon rate (distributed semiannually) with three years remaining to maturity. The following formula can be used to compute the bond’s intrinsic value:

Variable Name options for A - Bond's annual coupon payment, bondholder's required return, bond's semi-annual coupon payment

Variable Value options for A - $118.13, $315.00, $157.50, $78.75

Variable Name options for B - Bond's annual coupon payment, bond's market price, bond's par value.

Variable Value options for B - $1,000

Variable Name options for C - Semi-annual required return

Variable Value options for C - 7.125%, 4.5%, 5.7525%, 6.5%

Based on this equation and the data, it is (reasonable / unreasonable) to expect that Olivia’s potential bond investment is currently exhibiting an intrinsic value greater than $1,000.

Now, consider the situation in which Olivia wants to earn a return of 13.75%, but the bond being considered for purchase offers a coupon rate of 15.75%. 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 ($838 / 1048 / 1258 / 1362) (rounded to the nearest whole dollar) is (greater than / less than / equal to) its par value, so that the bond is trading at (a discount / a premium / par).

Given your computation and conclusions, which of the following statements is true?

When the coupon rate is greater than Olivia’s required return, the bond should trade at a premium.

When the coupon rate is greater than Olivia’s required return, the bond should trade at a discount.

When the coupon rate is greater than Olivia’s required return, the bond’s intrinsic value will be less than its par value.

A bond should trade at a par when the coupon rate is greater than Olivia’s required return.
 

Intrinsic Value = A A A A + (1+0) (1+0) + (1+0) + (1+C)* + ABC Unknown Variable Name Complete the following table by identifying the appropriate corresponding variables used in the equation. A A (1+0) + (1+06+ (1+C)5 Semiannual required return B (1+0)6 Variable Value $1,000