Bond pricing and premium/discount

A level-coupon bond can be valued by moving every promised cash flow to the purchase date. If the face value is F, the coupon rate per coupon period is r, the redemption value is C, the investor yield per coupon period is j, and there are n coupon periods, then the coupon is Fr and

P = Fr × [1 − (1+j)⁻ⁿ] / j + C(1+j)⁻ⁿ when j is nonzero. At zero yield, the coupon stream is nFr, so P = nFr + C.

The first term is the present value of the coupon annuity. The second is the present value of redemption. If price exceeds redemption value, the bond is at a premium; if price is below redemption value, it is at a discount.

This lab is deliberately supplemental because bonds occur in older Chapter 3 material but are not named in the current core Financial Mathematics outline.