Questions: Assignment: Chapter 06 Bonds (Debt) - Characteristics and Valuation Assume Grace wants to earn a return of 9.00% and is offered the opportunity to purchase a 1,000 par value bond that pays a 7.50% 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 = A/(1+C)^1 + A/(1+C)^2 + A/(1+C)^2 + A/(1+C)^4 + A/(1+C)^2 + A/(1+C)^6 + 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 to expect that Grace's potential bond investment will exhibit an intrinsic value less than 1,000.

Assignment: Chapter 06 Bonds (Debt) - Characteristics and Valuation

Assume Grace wants to earn a return of 9.00% and is offered the opportunity to purchase a 1,000 par value bond that pays a 7.50% 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 = A/(1+C)^1 + A/(1+C)^2 + A/(1+C)^2 + A/(1+C)^4 + A/(1+C)^2 + A/(1+C)^6 + 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 to expect that Grace's potential bond investment will exhibit an intrinsic value less than 1,000.

Transcript text: Assignment: Chapter 06 Bonds (Debt) - Characteristics and Valuation Assume Grace wants to earn a return of $9.00 \%$ and is offered the opportunity to purchase a $\$ 1,000$ par value bond that pays a $7.50 \%$ coupon rate (distributed semiannually) with three years remaining to maturity. The following formula can be used to compute the bond's intrinsic value: \[ \text { Intrinsic Value }=\frac{A}{(1+C)^{1}}+\frac{A}{(1+C)^{2}}+\frac{A}{(1+C)^{2}}+\frac{A}{(1+C)^{4}}+\frac{A}{(1+C)^{2}}+\frac{A}{(1+C)^{6}}+\frac{B}{(1+C)^{6}} \] Complete the following table by identifying the appropriate corresponding variables used in the equation. Based on this equation and the data, it is $\qquad$ to expect that Grace's potential bond investment will exhibit an intrinsic value less than $\$ 1,000$.

Solution

Solution Steps

To solve this problem, we need to calculate the intrinsic value of the bond using the given formula. The bond pays a semiannual coupon, so we need to adjust the coupon rate and the required return to a semiannual basis. The intrinsic value is the present value of the bond's future cash flows, which include the semiannual coupon payments and the par value at maturity. We will use the formula provided to compute the present value of these cash flows.

Step 1: Calculate Semiannual Rates

The bond has an annual coupon rate of $7.5\%$ and a required return of $9\%$ . To find the semiannual rates, we divide these values by $2$ : $\text{Semiannual Coupon Rate} = \frac{0.075}{2} = 0.0375$ $\text{Semiannual Required Return} = \frac{0.09}{2} = 0.045$

Step 2: Calculate Semiannual Coupon Payment

The semiannual coupon payment is calculated as follows: $\text{Semiannual Coupon Payment} = 1000 \times 0.0375 = 37.5$

Step 3: Calculate Intrinsic Value of the Bond

The intrinsic value of the bond is computed using the formula for the present value of future cash flows. The bond pays $37.5$ every six months for $3$ years (or $6$ periods), and the par value of $1000$ is paid at the end of the last period. The intrinsic value $IV$ is given by: $IV = \sum_{t=1}^{6} \frac{A}{(1+C)^{t}} + \frac{B}{(1+C)^{6}}$ Where:

$A = 37.5$ (semiannual coupon payment)
$B = 1000$ (par value)
$C = 0.045$ (semiannual required return)

Calculating each term: $IV = \frac{37.5}{(1+0.045)^{1}} + \frac{37.5}{(1+0.045)^{2}} + \frac{37.5}{(1+0.045)^{3}} + \frac{37.5}{(1+0.045)^{4}} + \frac{37.5}{(1+0.045)^{5}} + \frac{37.5}{(1+0.045)^{6}} + \frac{1000}{(1+0.045)^{6}}$ After performing the calculations, we find: $IV \approx 961.316$