Question

KIC, Inc., plans to issue $7 million of bonds with a coupon rate of 7 percent and 20 years to maturity. The current market interest rates on these bonds are 9 percent. In one year, the interest rate on the bonds will be either 8 percent or 4 percent with equal probability. Assume investors are risk-neutral.

  

a.	If the bonds are noncallable, what is the price of the bonds today? Assume a par value of $1,000 and semiannual payments. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

     

Price of the bonds

$

Answer 1

Price of the bond could be calculated using below formula.

P = C/ 2 [1 - {(1 + YTM/2) ^2*n}/ (YTM/2)] + [F/ (1 + YTM/2) ^2*n]

Where,

                Face value (F) = $1000

                Coupon rate = 7%

                YTM or Required rate = 9%

                Time to maturity (n) = 20 years

                Annual coupon C = $70

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

P = 70/ 2 [{1 - (1 + 0.09/2) ^-2*20}/ (0.09/ 2)] + [1000/ (1 + 0.09/2) ^2*20]

    = 35 [{1 - (1 + 0.045) ^ -40}/ (0.045)] + [1000/ (1 + 0.045) ^40]

    = 35 [{1 - (1.045) ^ -40}/ (0.045)] + [1000/ (1.045) ^40]

    = 35 [{1 - 0.17193}/ (0.045)] + [1000/ 5.81636]

    = 35 [0.82807/ 0.045] + [171.92884]

    = 35 [18.40156] + [171.92884]

    = 644.0546 + 171.92884

    = 815.98344

So price of the bond is $815.98

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