The process of bond valuation is based on the fundamental concept that the current price of a security can be determined

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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 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:
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:
Complete the following table by identifying the appropriate
corresponding variables used in the equation.
Unknown
Variable Name
Variable Value
Based on this equation and the data, it is 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 (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 Olivia’s required return,
the bond’s intrinsic value will be less than its par value.
When the coupon rate is greater than Olivia’s required return,
the bond should trade at a premium.
A bond should trade at a par when the coupon rate is greater
than Olivia’s required return.
When the coupon rate is greater than Olivia’s required return,
the bond should trade at a discount.