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. 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 nredictable$\_$relationship between the bond's coupon rate, the bondholder's required return, the bond's par

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value, and its intrinsic value. These relationsmips 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

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

For example, assume Ella wants to earn a return of $8\mathrm{.}00\%$ and is offered the opportunity to purchase a $$1,000$ par value bond that pays a $14\mathrm{.}00\%$

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 $=\frac{A}{(1+C{)}^1}+\frac{A}{(1+C{)}^2}+\frac{A}{(1+C{)}^3}+\frac{A}{(1+C{)}^4}+\frac{A}{(1+C{)}^5}+\frac{A}{(1+C{)}^6}+\frac{B}{(1+C{)}^6}$

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

Based on this equation and the data, it is

greater than $$1,000.$

$\text{'}$ to expect that Ella's potential bond investment is currently exhibiting an intrinsic value

Now, consider the situation in which Ella wants to earn a return of $12\mathrm{.}00\%,$ but the bond being considered for purchase offers a coupon rate of

$14\mathrm{.}00\%.$ 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

$($rounded to the nearest whole dollar$)$ 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 Ella's required return, the bond should trade at a premium.

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

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

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