Question

You buy a 9 percent, 20-year, $1,000 par value floating rate bond in 1999. By the year 2014, rates on bonds of similar risk are up to 11 percent. What is your one best guess as to the value of the bond?

Answer 1

Year remaining till maturity = 20 – (2014 – 1999) = 5 years

We have assumed that the coupon is paid annually.

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 = 9%

                YTM or Required rate = 11%

                Time to maturity (n) = 5 years

                Annual coupon C = $90

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

P = 90* [{1 - (1 + 0.11) ^ -5}/ (0.11)] + [1000/ (1 + 0.11) ^5]

P = 90* [{1 - (1.11) ^ -5}/ (0.11)] + [1000/ (1.11) ^5]

P = 90* [{1 - 0.59345}/ 0.11] + [1000/ 1.68506]

P = 90* [0.40655/ 0.11] + [593.45068]

P = 90* 3.69591 + 593.45068

P = 332.6319 + 593.45068

P = 926.08258

So price of the bond is $926.08
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