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studynotesPAPER F3Financial StrategyStudents tend to find discussing debt finance far easier than doing thecalculations. Andrew Howarth explains how to deal with yield on debt.CORBISAn investor who purchases a corporatebond receives a return from that bond in theform of annual interest (or coupon) paymentsand, if the bond is redeemable, the finalredemption payment. The total effectivereturn is referred to as the yield. The yield ofa redeemable bond is also known as the yieldto maturity (YTM) or redemption yield.In F3 exams you will often be asked tocalculate the yield or YTM of a bond. In somecases – eg, if the bond is irredeemable – thecalculations are simple. But they are morecomplex if the bond is redeemable ordenominated in a foreign currency.As well as being the effective return tothe investor, the yield on a bond is importantin many other calculations. For example, anentity’s cost of debt, which is used incalculating the weighted-average cost ofcapital, can be derived by adjusting the yieldfor the tax relief on debt interest. This posttax cost of debt, derived from the yield, isalso used as the discount rate whenevaluating a lease-versus-buy decision.42Irredeemable bondsLet’s start with the simplest of all yieldcalculations. An irredeemable corporate bondthat has just been issued at par (the face, ornominal, value) will have a yield equal to itscoupon rate.Consider a company called Kite, whichhas just issued some irredeemable 5%coupon-rate bonds at their par value of 100.It is clear that if an investor were to purchaseone of these Kite bonds, they would receivea return of 5% x 100 5 every year intoperpetuity. So their average annual return,as a percentage of the current value of thebond ( 100) is 5 100 5%.In short, for an irredeemable bond, thepercentage yield (annual interest received current bond price) x 100.Owing to factors of supply and demand inthe marketplace, bond prices fluctuate overtime. So it could be that, say, one year laterKite’s bonds are trading at 95. An investorpurchasing a bond now has to pay 95 infinancial management

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studynotesPAPER F31 Calculating the internal rates of return for Kite’s redeemable bondTime Discount factors at adiscount rate of 8%Year 0(100)1.000Years 1-513.993Year 51500.681order to receive the intereststream of 5% x 100 5every year intoperpetuity. Theinterest is alwayscalculated byapplying thecoupon rate to thebond’s par value,irrespective of its currentprice. So the yield in this caseis ( 5 95) x 100 5.26%.It’s notable that bond prices andbond yields are inversely related – ie,the lower the price of a bond, the higher itsyield will be. This is because the actualamount of interest (coupon amount) staysconstant. So, if the bond’s price falls, theinterest represents a higher proportion ofthe price.Redeemable bondsThe yield on a redeemable bond – ie, onewith a specified maturity or redemptiondate – is a more complex calculation,because the redemption amountand the remaining time beforematurity will also influence the yield.To see why, consider the followingsimple example.Assume that Kite is about toissue some more 100 bonds at par,this time with a coupon rate of 1%Present valueDiscount factors at aat 8%discount rate of 10%(100.00)1.0003.993.791102.150.6216.14and a redemption amountof 150 after five years. Aninvestor buying one of thesebonds for 100 will be entitledto 1 in interest each year andthen 150 in five years’ time.Using the logic from our previouscalculations for irredeemablebonds – ie, bonds with anindefinite life – it would be easy toassume that the yield on these newKite bonds is 1%. After all, aninvestor buying a bond for 100 onissue will receive interest of 1% x 100 1 each year, making a return of 1%of the current bond price. But the returnis no longer received in perpetuity. In fact,in five years’ time the investor will alsoreceive a lump sum of 150, which issignificantly greater than the original costof the bond. If we are to calculate the yieldproperly, it is important to incorporate theimpact of this premium on redemption.In effect, the investor’s yield is a 1% returneach year and then an extra 50% return inthe fifth year. The yield calculation replacesthis cumbersome statement with a singleeffective annual percentage figure,which incorporates both elements ofthe return. The yield of a redeemablebond equals the internal rate of return (IRR)of the bond price, the annual interest receivedand the final redemption amount.Present valueat 10%(100.00)3.7993.15(3.06)Using the figures from the Kite example,we need to calculate the IRR of:n Year 0: current bond price paid: ( 100).n Years 1-5: annual interest received: 1.n Year 5: redemption amount received: 150.The yield can now be calculated bydiscounting these amounts at any twodiscount rates and using interpolation, asshown in table 1 above. By interpolation, theannual percentage yield works out as 8% [2% x (6.14 {6.14 3.06})] 9.33% a year.So, instead of saying that the investorreceives 1% every year in interest and then a50% return in five years’ time, we say thatthe effective annual return to the investor –ie, the YTM – in this case is 9.33%.As with irredeemable bonds, the price ofredeemable bonds can fluctuate over time.So, if one year later these Kite bonds werepriced at 90 in the market, the yield ofthese four-year bonds could once againbe calculated by interpolation. Using thefigures derived from table 2 below, we canuse interpolation to work out the percentageyield as 12% [3% x (8.44 {8.44 1.34})] 14.59% a year.Again we can see the inverse relationshipbetween yield and bond price: because thebond price has fallen, the yield has increased.Irredeemable foreign currency bondsYield calculations become more complicatedwhen foreign currency loans are involved.2 Calculating the internal rates of return for Kite’s redeemable bond taking account of change in market value after year oneTime Discount factors at adiscount rate of 12%Year 0(90)1.000Years 1-413.037Year 41500.63644financial managementPresent valueDiscount factors at aat 12%discount rate of 15%(90.00)1.0003.042.85595.400.5728.44Present valueat 15%(90.00)2.8685.80(1.34)

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