Redemption value

A bond pays two kinds of cash: the coupons along the way and a final principal payment at the end. The final payment is the redemption value.

The workbook: Maturity / Redemption Value is the amount paid by the issuer other than the coupon payment. It then sets out three cases:

• redemption proceeds more than the face value — redeemed at a premium;
• less than the face value — redeemed at a discount;
• the same as the face value — redeemed at par.

Most plain bonds are redeemed at par. The workbook's example security has face value Rs 1,000, issue price Rs 1,000, a 7% coupon paid half-yearly, maturity 1 April 2031 and redemption value Rs 1,000. The workbook's definition of face value adds that sometimes an issuer can pay a premium above face value at maturity.

Keep redemption value separate from issue price. A zero coupon bond is generally issued at a discount to face value and then redeemed at face value; that is a discount at issue, not a redemption at a discount.

Redemption value is the last cash flow in every bond price. The workbook's yield equation discounts it alongside the coupons.

Bond price (workbook, section 1.10.2.2):

PV = Σ Cn / (1 + r)^n  +  Redemption Value / (1 + r)^N

Short form with the annuity factor (section 1.11):

Value = (Annual coupon × PVIF) + (Par / Face / Redemption Value × PV factor of the last year)

Zero coupon securities: the redemption value is F and the purchase price is P, so the true return can be read directly, because there are no interim cash flows to reinvest.

T-Bills: issued at a discount and redeemed at par (₹100); the return is the redemption value minus the issue price.

BEY = (Face value − Price) / Price × 365 / Days to maturity × 100

The workbook's bond. Face value ₹100, annual coupon 10%, 5 years left, market yield 8%.

Short form: 10 × 3.9927 + 100 × 0.6806 = 39.93 + 68.06 = ≈ ₹107.99.

Change only the redemption value (illustrative).

Coupons still run on the ₹100 face value in all three rows; only the final payment changes.

A T-Bill, from the workbook. Trading at ₹99.6898 on 22 October 2021, redeemed at ₹100 on 25 November 2021 (34 days): yield = (100 − 99.6898) / 99.6898 × 365 / 34 = 3.34%.

Chapter 1 (Introduction to Interest Rate, Interest Rate Instruments and Fixed Income Markets) defines redemption value among the key components of fixed income securities in section 1.2.1, uses it as F in zero coupon returns, places it in the yield to maturity equation in section 1.10.2.2 and values a bond with it in section 1.11. Expect a definition question on premium, discount and par redemption, and a bond price calculation where the redemption value is the final cash flow.

• Redemption value excludes the coupon. It is the amount paid other than the coupon.
• Above face value = redeemed at premium; below = at discount; equal = at par.
• Issued at a discount is not redeemed at a discount. T-Bills and zero coupon bonds are issued below face value and redeemed at face value.
• Coupons are calculated on face value, not on redemption value.
• In the last year the cash flow is coupon plus redemption value — ₹110 in the workbook table, not ₹100 or ₹10.
• A higher redemption value raises the price, all else equal, by its present value.