Answer:
a. Complex Systems' bond price today = $1,476.36
Explanation:
a. If bonds of similar risk are currently earning a rate of return of 9%, how much should the Complex Systems bond sell for today?
This can be calculated by adding the Present Value of Coupons and the Present Value of Par Value as follows:
<u>Calculation of Present Value of Coupons</u>
The present of coupons is calculated using the formula for calculating the present value of an ordinary annuity as follows:
Present value of coupons = C × [{1 - [1 ÷ (1 + r)]^n} ÷ r] …………………………………. (1)
Where;
C = Annual coupon amount = Par value * Coupon rate = $1,000 * 16% = $160
r = required rate of return or return of similar risk = 9%, or 0.09
n = number of years = 11
Substitute the values into equation (1) to have:
Present value of coupons = $160 × [{1 - [1 ÷ (1 + 0.09)]^11} ÷ 0.09] = $1,088.83
<u>Calculation of Present Par of Value</u>
To calculate this, we use the present value formula as follows:
Present Value of Par Value = Par value / (1 + r)^n
Since Par Value is $1000 and r and n are as already given above, we have:
Present value of Par Value = $1,000 / (1 + 0.09)^11 = $387.53
Therefore, we have:
Complex Systems' bond price today = Present value of coupons + Present value of Par Value = $1,088.83 + $387.53 = $1,476.36
b. Describe the two possible reasons why the rate on similar-risk bonds is below the coupon interest rate on the Complex Systems bond.
The following are the possible two reasons:
1. Interest may vary bust the coupon is fixed. What can cause the interest rate to vary is the bond rating by rating agency. But his will not affect the coupon rate which is fixed. When the rating is high, the interest will be low. But when the rating is low, the interest will be high. This indicates a negative relationship between the rating and the interest rate.
2. The level of demand may also influence the interest rate to change. When the demand is high, the interest will be low. But when the demand is low, the interest will be high. This also indicates a negative relationship between the demand and the interest rate.
c. If the required return were at 16% instead of 9%, what would the current value of Complex Systems' bond be? Contrast this finding with your findings in part a and discuss.
To do this, we simply change he required return to 16% (or 0.16) in part a and proceed as follows:
Present value of coupons at 16% = $160 × [{1 - [1 ÷ (1 + 0.16)]^11} ÷ 0.016] = $804.58
Present value of Par Value at 16% = $1,000 / (1 + 0.16)^11 = $195.42
Complex Systems' bond price today at 16% = $804.58 + $195.42 = $1,000.00
Comparing part c result with part a result shows that if the coupon rate is greater than the required rate of return, the bond is sold at a premium. That is, price of bond will be more than par. As it can be seen in part a, the price of bond is $1,476.36 when the coupon rate of 16% is greater than the required return of 9%.
Also, the bond will be sold at par when the coupon rate and require return are equal. This is shown in part c where the bond is sold at $1,000 when both coupon rate and required return rate are equal to 16%.
By implication, we can also infer without doing any calculation that the bond will be sold at a discount if the coupon rate is less than the required rate of return.
