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$1.$ 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$$s resulting value. Trading at a discount, trading at a premium, and trading at par$$refer to particular relationships between a bond$$s value and its par value. This also results from the relationship between a bond$$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$$s required return reflects the return that a bondholder$$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 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 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 value will $$its par value, and the bond will trade at a premium.$$When the bond$$s coupon rate is less than the bondholder$$s required return, the bond$$s value will be less than its par value, and the bond will trade at$.$

For example, assume Dina wants to earn a return of $5\mathrm{.}00\%$ and is offered the opportunity to purchase a $$1,000$ par value bond that pays a $5\mathrm{.}00\%$ coupon rate $($distributed semiannually$)$ with three years remaining to maturity. The following formula can be used to compute the bond$$s value:

Bond$$s$$ValueBond$$s$$Value$==$A$(1+$C$)1+$A$(1+$C$)2+$A$(1+$C$)3+$A$(1+$C$)4+$A$(1+$C$)5+$A$(1+$C$)6+$B$(1+$C$)6$A$(1+$C$)1+$A$(1+$C$)2+$A$(1+$C$)3+$A$(1+$C$)4+$A$(1+$C$)5+$A$(1+$C$)6+$B$(1+$C$)6$

Complete the following table by identifying the appropriate corresponding variables used in the equation.

Unknown

Variable Name

Variable Value

A$$B$$$$1,000$CSemiannual required return$$

Based on this equation and the data, it is$$to expect that Dina$$s potential bond investment is currently exhibiting a value of equal to $$1,000.$

Suppose Dina wants to earn a return of $2\mathrm{.}00\%,$ but the bond being considered for purchase offers a coupon rate of $5\mathrm{.}00\%.$ Again, assume that the bond pays semiannual interest payments and has three years to maturity. If you round the bond$$s value to the nearest whole dollar, then its value of$$is$$its par value, so that the bond is$.$

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

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

When the coupon rate is greater than Dina$$s required return, the bond$$s value will be less than its par value.

A bond should trade at par when the coupon rate is greater than Dina$$s required return.

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

What will happen to the price of a fixed$-$rate bond when expectations for inflation fall?

The bond price will fall.

The bond price will rise.