Question

draw a timeline:

Complex Systems has an outstanding issue of $1,000-par-value bonds with a 12% 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 10% rate of return, 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 12% instead of 10%, what would the current value of Complex Systems

Answer 1

Price of the bond could be calculated using below formula.

P = C* [{1 - (1 + YTM) ^ -n}/ (YTM)] + [F/ (1 + YTM) ^ -n]

Where,

                Face value = $1000

                Coupon rate = 12%

                YTM or Required rate = 10%

                Time to maturity (n) = 16 years

                Annual coupon C = $120

Let's put all the values in the formula to find the bond current value

P = 120* [{1 - (1 + 0.1) ^ -16}/ (0.1)] + [1000/ (1 + 0.1) ^16]

P = 120* [{1 - (1.1) ^ -16}/ (0.1)] + [1000/ (1.1) ^16]

P = 120* [{1 - 0.21763}/ 0.1] + [1000/ 4.59497]

P = 120* [0.78237/ 0.1] + [217.62928]

P = 120* 7.8237 + 217.62928

P = 938.844 + 217.62928

P = 1156.47328

So price of the bond is $1156.47

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Interest rate might have decrease by the federal bank, making the Complex system good investment that is generating more return than the market.

Another reason is good credibility of the company, that has earned it good rating.

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If the required rate is 12 % (equal to bond coupon rate), the price will be equal to its par value.

                Face value = $1000

                Coupon rate = 12%

                YTM or Required rate = 12%

                Time to maturity (n) = 16 years

                Annual coupon C = $120

Let's put all the values in the formula to find the bond current value

P = 120* [{1 - (1 + 0.12) ^ -16}/ (0.12)] + [1000/ (1 + 0.12) ^16]

P = 120* [{1 - (1.12) ^ -16}/ (0.12)] + [1000/ (1.12) ^16]

P = 120* [{1 - 0.16312}/ 0.12] + [1000/ 6.13039]

P = 120* [0.83688/ 0.12] + [163.12176]

P = 120* 6.974 + 163.12176

P = 836.88 + 163.12176

P = 1000.00176

So price of the bond is $1000

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