An investor purchased the following 5 bonds. Each of them had a face value of $1

Question

An investor purchased the following 5 bonds. Each of them had a face value of $1,000 and 8% yield to maturity on the purchase day. Immediately after she purchased them, interest rates fell and each then had a new YTM of 5%. What is the percentage change in price for each bond after the decline in interest rates? Fill in the following table. Round your answers to two decimal places.


A) $100 perpetuity, Price at 8%
B) $100 perpetuity, Price at 5%
C) Percentage Change between (A) and (B)


Please show how to derive answer, thanks!

Explanation / Answer

Perpetuities are nice and easy, no discounted cash flows to do. The formula is just Price = Annual coupon payment/interest rate. You don't say what the interest rate is on the bond, but I'm assuming it is 8% and the bonds were initially sold at par, or $1,000. So if interest rates fell to 5% the price would change from 1,000 to P= 1000*.08/.05=1,600. Percentage change on the price was (1,600-1,000)/1,000= 60%.

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