Question

Complex Systems has an outstanding issue of ​$1,000 par-value bonds with a  9​% coupon interest rate. The issue pays interest annually and has 16 years remaining to its maturity date.

a.  If bonds of similar risk are currently earning a rate of return of 8​%, how much should the Complex Systems bond sell for​ today?  

b.  Describe the two possible reasons why the rate on​ similar-risk bonds is below the coupon interest rate on the Complex Systems bond.

c.  If the required return were at 9​% instead of 8​%, what would the current value of Complex​ Systems' bond​ be? Contrast this finding with your findings in part a and discuss.

Answer 1

Complex Systems has an outstanding issue of $1,000 par-value bonds with a 9​% coupon interest rate. The issue pays interest annually and has 16 years remaining to its maturity date.

1. If bonds of similar risk are currently earning a rate of return of 8​%, how much should the Complex Systems bond sell for​today?  

Formula to calculate the bond price

Bond price P0 = C* [1- 1/ (1+i) ^n] /i + M / (1+i) ^n

Where,

P0 = current market price of the bond =?

M = value at maturity, or par value = $1000

C = coupon payment = 9% of $1000 = $90

n = number of remaining payments = 16

i = interest rate, or required yield = 8% (yield of a similar risk bond)

Therefore,

Bond Price = $90 * [1 – 1 / (1+8%) ^16] /8% + $1000 / (1+8%) ^16

= $796.62 + $291.89

= $1,088.51

Complex Systems bond will sell for $1,088.51 today

2. Describe the two possible reasons why the rate on similar-risk bonds is below the coupon interest rate on the Complex Systems bond.

The two possible reasons why the rate on similar-risk bonds is below the coupon interest rate on the Complex Systems bond are –

• May have been a shift in the supply-demand relationship for money
• May be a change in the risk towards the firm

3. If the required return were at 9​% instead of 8​%, what would the current value of Complex​ Systems' bond​ be? Contrast this finding with your findings in part a and discuss.

If the required return were at 9% instead of 8%, the current value of Complex Systems' bond will be equal to its par value of $1,000 because if the required return equals the coupon rate (both are 9%) then the price of the bond is equal to its par value.

The answer in part a) states that if the required return is less than the coupon rate in that case the price of bond will be more than its par value and it will sell at a premium.