Question

6. Please calculate the value (Price) of the following corporate bond with a coupon rate of 7% (annual), and a face value of $1000.00. The maturity of the bond is 15 years. The market interest rate of similar bonds (Yield to maturity) is 6%. the bond value now? Why? Suppose the market interest rate increases to 9%, what will happen to

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 = 7%

                YTM or Required rate = 6%

                Time to maturity (n) = 15 years

                Annual coupon C = $70

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

P = 70* [{1 - (1 + 0.06) ^ -15}/ (0.06)] + [1000/ (1 + 0.06) ^15]

P = 70* [{1 - (1.06) ^ -15}/ (0.06)] + [1000/ (1.06) ^15]

P = 70* [{1 - 0.41727}/ 0.06] + [1000/ 2.39656]

P = 70* [0.58273/ 0.06] + [417.26475]

P = 70* 9.71217 + 417.26475

P = 679.8519 + 417.26475

P = 1097.11665

So price of the bond is $1097.12

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When the market rate changes to 9% bond price will be

                Face value = $1000

                Coupon rate = 7%

                YTM or Required rate = 9%

                Time to maturity (n) = 15 years

                Annual coupon C = $70

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

P = 70* [{1 - (1 + 0.09) ^ -15}/ (0.09)] + [1000/ (1 + 0.09) ^15]

P = 70* [{1 - (1.09) ^ -15}/ (0.09)] + [1000/ (1.09) ^15]

P = 70* [{1 - 0.27454}/ 0.09] + [1000/ 3.64248]

P = 70* [0.72546/ 0.09] + [274.53823]

P = 70* 8.06067 + 274.53823

P = 564.2469 + 274.53823

P = 838.78513

So price of the bond is $838.79

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Change in price = 1097.12 - 838.79 = 258.33

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