Question

Basic bond valuation: Complex Systems has an outstanding issue of ​$1,000​-par-value bonds with a 14​% coupon interest rate. The issue pays interest annually and has 13 years remaining to its maturity date.

a.  If bonds of similar risk are currently earning a rate of return of 11​%,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 14​% instead of 11​%, what would the current value of Complex​ Systems' bond​ be? Contrast this finding with your findings in part a and discuss.

EXCEL

Answer 1

Given

Par value of a bond = $ 1000

Coupon interest rate = 14%

Years to Maturity = 13 Years

Interest amount= Par value * Coupon rate

= $ 1000*14%

= $ 140

a) Given Rate of interest = 11%

We know that Current price of a Bond = Present value of future cash flows discounted at required rate of return.

Current share price = PV of interest accruing from Year 1-10+ PV of Maturity amount.

Computation of Present value of interest.

Present value of interest = C [{1- ( 1+i)^-n} /i]

Here C = Cash flow per period

I = Interest rate per period

n = No.of payments

Present value of interest = $ 140[ { 1-( 1+0.11)^-13 } /0.11]

= $ 140[ { 1-( 1.11)^-13} /0.11]

= $ 140 [ { 1-0.257514} /0.11]

= $ 140*6.74987

= $ 944.98

Hence Present value of interest is $ 944.98

Computation of Present value of Maturity amount.

We know that Present vale = Future Value / ( 1+i)^n

Here I = Rate of interest

n = No.of Years

Present value = $ 1000/ ( 1.11)^13

= $ 1000/3.88328

= $257.51

Hence the Present value of Maturity amount is $ 257.51

Current Bond price = PV of interest accruing from Year 1-10+ PV of Maturity amount.

= $ 944.98+$ 257.51

= $ 1202.49

Complex system bond sell for $ 1202.49

b) The Market may be in Recession stage due to which investor expectation are low.

Bank might be giving lower interest rate.

The Risk profile of the Complex system bond is higher so that they are giving a higher coupon rate to compensate the risk than the general rate of intersest.

c) If the Required rate of return ie 14% is equal to the Coupon rate i.e 14% , then the Bond will be trading at par. So the Current bond price is $ 1000.

If you are having doubts,please post a comment.

Thank you.please rate it.