Toby purchased a 20-year par value bond with semiannual coupons at a nominal annual rate of 8% convertible semiannually at a price of 1,722.25. The bond can be called at par value 1,100 on any coupon date starting at the end of year 15. What is the minimum yield that Toby could receive, expressed as a nominal annual rate of interest convertible semiannually?

3.22%

Explanation:

Here, we are interested in calculating the minimum yield that Toby could receive.

To calculate this, we use the YTM formula.

Before we apply this formula, we write out the parameters which we were given in the question.

Given that number of years, n = 15*2 = 30, Price, P = 1722.25, Face value, F = 1100, C = 0.08/2*1100 = 44

Using YTM approximation formula,

YTM = [C + (F – P)/n]/ (F + P)/2

YTM = [44 + (1100 – 1722.25)/30]/ (1100+1722.25)/2

YTM = 23.2583/1411.125

YTM = 1.61%

YTM = 1.61% x 2 = 3.22%

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