The Yield One Year Later

The same corporate bond, a year on. The price has moved, so the yield has moved with it - and the number that comes out is not an annual one. The bond: par 400, a nominal coupon of 10% a year paid twice a year (so 20 every six months), five years, and a comparable yield of 14% a year. Its price on the day of issue is 349.72. 1. The price confirmed in the calculator: n = 10 periods, rate 6.77% a half year, payment 20, future value 400 → 349.72. 2. The keying that fails, and why. Putting 420 in as the future value with n = 9 pays the principal at period NINE - half a year early. A present-value function will not move a payment in time for you. The 420 belongs at period ten, and keyed there both forms give 349.72. 3. Pay more, earn less. At 349.72 the bond yields 14% a year. At 400 - par - it yields 5% a half year, which compounds to 10.25% a year, not 10%. At 500 it would yield 4.43%. That IS what pricing a bond means. 4. Part (c). One year after issue the bond trades at 340. One year is TWO periods, so eight of the ten are left: seven payments of 20 and then 420. 5. What was paid never matters. A bond is priced on what is still to come. 6. A price on one side and a cash flow on the other make an internal rate of return - and because the periods are half-years, the IRR is a half-yearly rate: 7.57%. 7. Back to a year, by compounding, exactly as at the start: 1.0757² − 1 = 15.71% a year. English narration and presentation.