Suppose you purchase a 20-year treasury bond with a 6% annual coupon ten years ago at par. Today the bond's yield to maturity has risen to 8% (EAR). Consider a bond that pays annually an 8% coupon with 20 years to maturity. The amount that the price of the bond will change if its yield to maturity increases from 5% to 7% is closest to:

The amount that the price of the bond will change if its yield to maturity increases from 5% to 7% is closest to: 6.0%

Explanation and Solution:

The IRR you would pay for keeping this bond for 10 years is the amount (one of the four options) that allows the current value of all cash flows you would earn equal to the price you initially charged for the contract.

What are the relevant cash flows to you?

First of all, you were told that you purchased the bond at par; let's presume that's 1,000. Then you can earn 10 discount fees, one at the end of each year, for 10 years. At the end of the day, you offer the bond as it has 10 remaining to maturity.

Therefore, the cash inflows become 10 coupon transactions plus sales profits (which will be earned around the same period as the 10th coupon payment, so that you can merge the 10th coupon payment with sales profits and view it as a single cash inflow at year 10).

In order to determine the selling profits, you notice that the seller of the bond has 10 further coupon payments to be earned, plus 1,000 to be paid at maturity (or, equivalently, a coupon fee each year for the next 9 years and 1,060—coupon and maturity — to be provided as a last inflow 10 years after you buy the bond.

Discount the cash inflows of the seller at that point to calculate the purchasing price (ergo, the sale price) of the loan.

By doing that, you already realize all the cash dividends you've got during your ten-year ownership span. To tie things up, identify the discount rate that renders the current value of this cash flow equivalent to the 1,000 you initially charged. This would be your IRR keeping time, and see if any of the four options most closely suit this IRR.

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