Question

Toreal Metals, Inc. has a bond outstanding that has a $1,000 par value and a market price of $1,000. The bond has 10 years remaining to maturity. Assuming an annual market interest rate of 12% and that the bond pays interest semiannually, what is the ANNUAL coupon rate on the bond?

Answer 1

Market value and par value of the bond is equal that means YTM and coupon rate is equal, when this happens par value of the bond will be equal to the bond current price.

Let’s see hoe

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 = 12%

                YTM or Required rate = 12%

                Time to maturity (n) = 10 years

                Annual coupon C = $120

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

P = 120/ 2 [{1 - (1 + 0.12/2) ^-2*10}/ (0.12/ 2)] + [1000/ (1 + 0.12/2) ^2*10]

    = 60 [{1 - (1 + 0.06) ^ -20}/ (0.06)] + [1000/ (1 + 0.06) ^20]

    = 60 [{1 - (1.06) ^ -20}/ (0.06)] + [1000/ (1.06) ^20]

    = 60 [{1 - 0.3118}/ (0.06)] + [1000/ 3.20714]

    = 60 [0.6882/ 0.06] + [311.80429]

    = 60 [11.47] + [311.80429]

    = 688.2 + 311.80429

    = 1000.00429

So price of the bond is $1000

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