The Price On Issue Day

A corporate bond that pays twice a year, priced on the day it is issued - and the same price reached two different ways. The data: par value 400 shekels, a nominal coupon of 10% a year paid in two instalments, five years to redemption, the principal repaid in one payment at the end, and a similar bond in the market yielding 14% a year. 1. The two conversions, which decide everything that follows. The coupon is a NOMINAL rate, so it is divided: 10% / 2 = 5% a half year, and 5% of 400 = 20 shekels every six months. The yield is an EFFECTIVE rate, so it is compounded: 1.14^0.5 − 1 = 6.77% a half year. Check it: 1.0677^2 − 1 = 14% exactly. 2. Five years at two payments a year is 10 periods, not 5. 3. The cash flow: 20 at each of periods 1 to 9, then 420 at period 10 - the last coupon and the 400 of principal arriving together. 4. The price, payment by payment: 20/1.0677 + 20/1.0677² + ... + 20/1.0677⁹ + 420/1.0677¹⁰ = 349.72. 5. The same price as an annuity plus a single payment: 20/0.0677 × [1 − 1/1.0677¹⁰] + 400/1.0677¹⁰ = 349.72. Ten in both exponents. 6. And the question the room argues about: is nine coupons plus 420 at period ten the same as ten coupons plus 400 at period ten? It is - 349.72 either way, to eight decimal places. Both arrive at period ten, and 20 + 400 = 420, so nothing has moved in time. 7. A warning about precision: using 1.067 instead of 1.0677 gives 351.57, wrong by 1.85 shekels. A rounded factor compounds ten times over. English narration and presentation.