Question

the bonds have an 8.2% coupon rae, payable semiannually, and a par value of $1000. They mature exactly 10 years from today. the yield to maturiy is 11% so the bonds now sell below par. what is the current market vllue of the fimrs debt?

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 = 8.2%

                YTM or Required rate = 11%

                Time to maturity (n) = 10 years

                Annual coupon C = $82

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

P = 82/ 2 [{1 - (1 + 0.11/2) ^-2*10}/ (0.11/ 2)] + [1000/ (1 + 0.11/2) ^2*10]

    = 41 [{1 - (1 + 0.055) ^ -20}/ (0.055)] + [1000/ (1 + 0.055) ^20]

    = 41 [{1 - (1.055) ^ -20}/ (0.055)] + [1000/ (1.055) ^20]

    = 41 [{1 - 0.34273}/ (0.055)] + [1000/ 2.91776]

    = 41 [0.65727/ 0.055] + [342.72867]

    = 41 [11.95036] + [342.72867]

    = 489.96476 + 342.72867

    = 832.69343

So price of the bond is $832.69

Long-term debt = 10,000,000

The face value of a bond = 1000

Number of bond issued = 10000000/1000 = 10000

Current market value of bonds = 10000* 832.69 = 8,326,900

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