Principles of Microeconomics / Unit 15 MIC 1414 worked example, 60 to 90 seconds
Pricing a Bond When Rates Move
The idea
A bond has a face value, a coupon rate and a maturity. List its payments: the coupon each year and the face value plus the last coupon at maturity. Discount each at the market rate and add: that is the bond's price. At a market rate equal to the coupon rate the price equals face value. When the market rate rises above the coupon, the price falls below face; when it falls, the price rises above.
In practice
Worked example: a two-thousand-dollar two-year bond with a five percent coupon pays one hundred after year one and two thousand one hundred after year two. At five percent, one hundred divided by one point oh five is ninety-five twenty-four, and two thousand one hundred divided by one point one oh two five is one thousand nine hundred four seventy-six: two thousand, the face value. Rates rise to eight percent: ninety-two fifty-nine plus one thousand eight hundred forty-one: about one thousand eight hundred ninety-three. The payments did not change; their present value did.
Where people slip
Discount the second payment by one plus the rate squared, not doubled; that is the error that makes the price come out wrong. And the bond's coupon rate is fixed at issue while its yield moves with the market; the two are equal only on the day the market rate equals the coupon.
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