Question

Assume that you wish to purchase a 16-year bond that has a maturity value of $1,000 and a coupon interest rate of 9%, paid semiannually. If you require a 6.34% rate of return on this investment (YTM), what is the maximum price that you should be willing to pay for this bond? That is, solve for PV.

Answer 1

In this case we need to find the price of the bond, the price of the bond is PV of all the cash inflows generated by the bond.

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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 = 9%

                YTM or Required rate = 6.34%

                Time to maturity (n) = 16 years

                Annual coupon C = $90

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

P = 90/ 2 [{1 - (1 + 0.0634/2) ^-2*16}/ (0.0634/ 2)] + [1000/ (1 + 0.0634/2) ^2*16]

    = 45 [{1 - (1 + 0.0317) ^ -32}/ (0.0317)] + [1000/ (1 + 0.0317) ^32]

    = 45 [{1 - (1.0317) ^ -32}/ (0.0317)] + [1000/ (1.0317) ^32]

    = 45 [{1 - 0.36838}/ (0.0317)] + [1000/ 2.71462]

    = 45 [0.63162/ 0.0317] + [368.37568]

    = 45 [19.92492] + [368.37568]

    = 896.6214 + 368.37568

    = 1264.99708

So price of the bond is $1265

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Hope that helps.

Feel free to comment if you need further assistance J