8. 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. pay, and a bondholder's required return Remember, a bond's coupon rate partially determines the interest-based return that a bond will 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 to 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 be less than its par value, and the bond will trade at a discount For example, assume Sophia wants to earn a return of 12.25% and is offered the opportunity to purchase a $1,000 par value bond that pays a 14.00% coupon rate (distributed semiannually) with three years remaining to maturity. The following formula can be used to compute the bond's intrinsic value: B Intrinsic Value = + + (140* + + 0* + (+cja + (1 toj + (1+cq6 + + ( (1) +C) (24C Complete the following table by identifying the appropriate corresponding variables used in the equation. Unknown Variable Name Variable Value A Bond's semiannual coupon payment $70.00 B $1,000 Bond's par value Semiannual required return C 6.125% Based on this equation and the data, it is reasonable to expect that Sophia's potential bond investment will exhibit an intrinsic value less than $1,000 Now, consider the situation in which Sophia wants to earn a return of 5%, but the bond being considered for purchase offers a coupon rate of 7%. 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 is its par value, so that the bond is trading at Given your computation and conclusions, which of the following statements is true? O when the coupon rate is greater than Sophia's required return, the bond should trade at a premium. O When the coupon rate is greater than Sophia's required return, the bond's intrinsic value will be less than its par value. O A bond should trade at a par when the coupon rate is greater than Sophia's required return. O When the coupon rate is greater than Sophia's required return, the bond should trade at a discount
