4. 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 ows 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 band's resulting intrinsic value. Trading ata 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 V pay, and a bondholder's required return reflects the return that a bondholder V to receive from a given investment. The mathematics of bond valuation imply a predictable relationship between the band's coupon rate, the bondholder's required return, the band'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 band's intrinsic value will v its par value, and the bond will trade at par. 0 When the band's coupon rate is greater to the bondholder's required return, the band's intrinsic value will V its par value, and the bond will trade at a premium. - When the band's coupon rate is less than the bondholder's required return, the band's intrinsic value will be less than its par value, and the bond will trade at V . For example, assume Ethan wants to earn a return of 15.75% and is offered the opportunity to purchase a $1,000 par value bond that pays a 18.00% coupon rate (distributed semiannually) with three years remaining to maturity. The following formula can be used to compute the bond's intrinsic value: For example, assume Ethan wants to earn a return of 15.75% and is offered the opportunity to purchase a $1,000 par value bond that pays a 18.00% coupon rate (distributed semiannually) with three years remaining to maturity. The following formula can be used to compute the band's intrinsic value: A A A A A A B (1+C)l + (1+C)1 + (1+C)3 + (1+C)' + (1+C)s + (1+C)'S + (1+C)6 Intrinsic Value = Complete the following table by identifying the appropriate corresponding variables used in the equation. Unknown Variable Name Variable Value A v v B V $1,000 C Semiannual required return v Based on this equation and the data, it is V to expect that Ethan's potential bond investment is currently exhibiting an intrinsic value less than $1,000. Now, consider the situation in which Ethan wants to earn a return of 16.00%, but the bond being considered for purchase offers a coupon rate of 18.00%. Again, assume that the bond pays semiannual interest payments and has three years to maturity. If you round the band's intrinsic value to the nearest whole dollar, then its intrinsic value of V (rounded to the nearest whole dollar) is V its par value, so that the bond is V . Given your computation and conclusions, which of the following statements is true? O When the coupon rate is greater than Ethan's required return, the bond should trade at a premium. 0 When the coupon rate is greater than Ethan's required return, the bond should trade at a discount. O When the coupon rate is greater than Ethan's required return, the bond's intrinsic value will be less than its par value. 0 A bond should trade at a par when the coupon rate is greater than Ethan's required return