A note on intra-period compounding and the valuation of semi-annual and quarterly bonds

Abstract

The valuation of redeemable semi-annual and quarterly bonds is a specialised and contentious subject in finance. While instructing on this subject, students frequently pose the subsequent four enquiries: Which semi-annual discount rate do we use to discount the bond’s cash flows to arrive at its present value? What time frame is utilised to compute the present value elements for discounting the bond's cash flows? Do we obtain the identical bond value when assessing it from the views of the corporation and the investors? What is the appropriate discount rate for scenarios involving numerous discount rates from the present to the bond's maturity date? This study illustrates that the semi-annual and annual percentage rate (APR) yield to maturity (YTM) rates are the most appropriate discount rates for valuing redeemable semi-annual and quarterly bonds. The present value factors are calculated using the time interval period, not the actual years.  Assessing bonds from a company's standpoint by employing post-tax cash flows and discount rates results in an undervaluation of the bonds. The arbitrage-free valuation method is the most appropriate technique for assessing redeemable semi-annual and quarterly bonds. This method use various annual APR YTM rates derived from the bond's benchmark spot rate curve, valuing the bond as a collection of cash flows, with each cash flow treated as a zero-coupon bond. This allows each cash flow to be discounted at its specific discount rate

Keywords: {'name': 'annual percentage rate, effective annual rate, arbitrage-free approach, semi-annual and quarterly bonds.'}

Authors & affiliations

Vusani Moyo
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