Time value of money II | My Assignment Tutor -

1Topic 3Time value of money IIObjectivesOn completion of this topic, you should be able to: apply time value of money techniques to situations where compounding is more frequentthan annual distinguish between types of interest rates and convert between these different rates find the deposit needed to accumulate a future sum apply time value of money techniques to amortised loans.IntroductionThis week we continue our study of time value of money (TVM) by adding complexities such ascompounding that is more frequent than annual and finding payments. We also consider atechnique for comparing stated interest rates using effective annual rates. Finally, we apply TVMtechniques to amortised loans.More TVM toolsUp until now, we have considered only straightforward compounding such as annual compounding,where the interest is added to the principal once per year, or where the interest rate given was forthe same period as payments. Because the compounding period matched the period for which theinterest rate was stated, no complications arose and we could simply use the number of periodsand the rate given to perform the time value of money calculations.In practice, interest is often compounded more frequently than once a year. However, the interestrate is still stated as an annual rate. Interest may be compounded semi-annually (i.e. interest addedtwice a year), quarterly (i.e. interest added 4 times a year), monthly, weekly, daily or evencontinuously. If compounded more than once a year, there will be a difference between the statedannual rate and the effective annual rate leading to the need to use a periodic rate in most ofour calculations. Let’s work through this step-by-step, defining these terms as we go.Standard practice is to quote interest rates (and rates of return) as an annual rate, often called thenominal rate or annual percentage rate (APR) but note APR sometimes includes fees and charges.The compounding period is usually stated immediately afterward; e.g. ‘6% compounded monthly’.6% is the nominal annual rate, which is the interest rate based on simple interest for one year; i.e.the rate excluding the effect of compounding.2What happens when the stated annual rate is the same but the compounding periods differ? Toillustrate this, consider the two scenarios below. We assume in each scenario that we deposit $100for one year.Scenario 1: Rate quoted as 6%.Scenario 2: Rate quoted as 6% compounded semi-annually.In scenario 2, we have to divide the year and the rate by two because there are two compoundingperiods each year. Dividing the rate by two gives us the periodic rate of 3%.The periodic rate is the rate used in solving problems where interest is compounded morefrequently than annually and the payment periods correspond to the compounding periods. Theperiodic rate is the nominal annual rate (r) divided by the number of compounding periods peryear (m). Therefore, the periodic rate is r/m. In the case of scenario 2 above, there are twocompounding periods per year so the periodic rate is 6%/2 = 3% per half-year.You can see from the example above that more frequent compounding (scenario 2) gives moreinterest. In general, the more frequent the compounding, the greater is the interest, and this effectis more pronounced at higher interest rates.So, how can we easily compare interest rates with different stated rates, compounding periods orboth? The answer is by using the effective annual rate (EAR). This rate discloses the true ‘benefit’(from the perspective of a lender) or ‘cost’ (from the perspective of a borrower) of interest becausethe EAR is the exact annual rate effectively earned or paid, allowing for the compounding of interest.Your text explains how to calculate an EAR.It is worth noting that in Australia the National Credit Code requires credit providers to discloseinterest rates only as APR or as comparison rates. The National Credit Code specifies when and howa comparison rate must be provided. A comparison rate is an effective annual rate and includesknown fees and charges, as well as interest. However, the rate is based on a typical loan amount,term and payment frequency, so you must be careful in interpreting this rate in situations whereany of those three variables (amount, term and payment frequency) are likely to be different. For6%$100 $106$100 $103 $106.093% 3%3example, you might be considering a larger loan amount or a shorter term that the comparisonrates do not reflect.Amortised loansYou will have noted that many applications of TVM relate to loans, as well as to investments. Loansrequire that at some point in time the borrowed money (principal) is paid back to the lender andinterest is also paid. While there are an almost unlimited number of ways these payments might bestructured, there are three basic forms:Discount loanThe principal and interest is paid at the end of the loan period. An example is a zero coupon bond,which will see in Topic 4.Interest-only loanInterest is paid each period throughout the term of the loan and the principal is repaid at the endof the term, along with the final interest payment. An example is a fixed interest bond, which willsee in Topic 4.Amortised loanEqual payments are made each period throughout the loan term and these payments includeinterest and part repayment of principal. This results in a regular principal reduction or‘amortisation’. An example is a standard home mortgage.If allowable under the amortised loan agreement, making payments more frequently (say weeklyrather than monthly) or paying more than the set minimum payment can help reduce theoutstanding balance of the loan more quickly. For example, every dollar above the minimumpayment goes directly to paying off the principal and the faster the principal can be reduced theless interest is paid. Keep this in mind as you work through TVM examples and exercises. This is auseful tip for significantly reducing (over time so be patient!) the interest you may pay on a homemortgage, for example.Textbook readingWork through section 3-7, pages 95–103 of your text. We recommend you try to replicateexamples as you go using this week’s spreadsheet template, which you can downloadfrom the learning pathway.SummaryThis topic adds some complexities to your knowledge of TVM techniques and applies them toamortised loans. Once you have completed all the reading and activities for this topic, you will havecompleted your TVM toolkit needed for the remainder of this unit. In the next topic, we will applyyour TVM toolkit to the valuation of bonds and simple preferred shares. In a later topic, we willconsider the valuation of projects using TVM techniques and extend your valuation knowledge.