"Discounted cash flow MethodsDiscounted cash flow methods combine theconcepts of cash flow and time value for theeconomic analysis of investment opportunities. Theobjectives of the economic analysis is as follows:a. To indicate the intrinsic economic value of eachinvestment opportunity. Is the return oninvestment as reflected by the time distributionof the cash flows adequate to cover the cost ofcapital to finance it?b. To select the best investment opportunity.c. To rank investment alternatives in order ofrelative attractiveness down to the cost of capitalcut off. Below this cut off opportunities wouldnot be desirable.For the evaluation, comparison and selection ofinvestment opportunities using discounted cashflow or DCF methods it is important to distinguishamong different types of investment opportunity. When the selection of an investment opportunityfrom a set of opportunities has no effect on theselection of any other opportunities, theopportunity is independent.In many cases investment opportunities are relatedto one another in such a way that selection of oneinfluences the selection of others, suchopportunities are dependent. Interdependenciesoccur for a number of reasons.If investment opportunities are related so that theacceptance of one precludes the selection of any ofthe others, the opportunities are mutually exclusive. Another relationship arises that once some initialproject is undertaken there are a number ofauxiliary investments that become feasible as aresult of the original investment. Such auxiliaryinvestments are called contingent opportunitiesbecause their selection is contingent or conditionalon the selection of the prior opportunity.Where there are limits on the amount of moneyavailable for investment and the capital cost of allinvestments exceeds the money available forinvestment, financial interdependencies areintroduced between proposals. Theseinterdependencies are usually complex and theywill occur whether the opportunities areindependent, mutually exclusive or contingent. Most investment decisions are of the followingtypes:a. Chose the best of a group of mutually exclusiveopportunities.b. Make accept or reject decisions for opportunitiesthat are independent. Equivalent annual value The economic attractiveness of an investmentopportunity can be measured by the equivalentannual value of its anticipated cash flows. Theequivalent annual value can be either a positivereturn or a negative cost depending on theeconomic characteristics of the opportunity beingevaluated. The alternative with the maximumequivalent annual return or minimum equivalentannual cost is preferred.To apply the equivalent annual value method allestimated cash flows are converted into a series ofequal annual values over a specified time frame,the time frame usually being the lifetime of thealternative. To do this the appropriate cost ofcapital rate and compound interest rate formulaeare applied. This method is of particular use in comparingdifferent types of equipment to perform a giventask where the equipment alternatives havedifferent lives.In this type of application where only costs arebeing considered and where minimising costs is thecriterion, capital expenditure is converted toequivalent annual costs over the life of theequipment being considered and added to theannual operating costs and maintenance costs. To illustrate the method consider thefollowing: A new mine equipment alternativewhere a capital expenditure of $ 100,000would now result in operating andmaintenance costs of $ 15,000 over ananticipated 5 year life. The cost of capital is10%.Equivalent annual cost = 15,000 + 100,000 x (CRF ) 5 =15000 + 100000 x 0.2638= $41,380A special application of this method is inreplacement problems where the economic life ofnew equipment is determined before the equivalentannual cost comparison with existing equipmentcan be made. The equivalent annual value method can be alsoapplied to more broadly illustrate the economiccharacteristics of an investment. Consider thefollowing mineral deposit:Exploration investment : 12 years @ $1,500,000? ? per annumMine development investment: 2 years @? ? $23,000,000 per annumMine production: 15 years @ $ 41,000,000 per? ? annum revenue and operating costs of$17,000,000 per annum.If the cost of capital is 10%, what is the equivalentannual return on investment over the productivelife? 1.5 ? (CPVF ) ? (CRF ) 1.5 ? (6.814) ? (0.1315) 12 15 EAEI ? ? ? $5.1million PVF 0.2633 14 23 ? (CRF ) 23 ? (0.1315) 15 EAMI ? ? ? $6.4million SFF 0.4762 2 Equivalent Annual return? 41 - (17? 5.1 ? 6.4) ? $12.5millionNet present value Net present value converts the anticipated timedistribution of cash flows for an investmentopportunity to an equivalent value at a particularpoint in time, the present. The evaluation of Netpresent value (NPV) requires the following steps:1. Select a discount rate. The discount rate shouldbe the cost of capital that is appropriate for thetype of investment being evaluated. This cost ofcapital rate represents the minimum acceptablerate of return for the investment and the breakeven value for the investment.2. Discount each cash flow to a present value usingthe selected rate.3. Summing the present values gives the net presentvalue of the investment. Thus the NPV is thedifference between the discounted positive cashflows and the discounted investment. n CF x NPV ? ? x (1 ? i) x ?1In simple cases the discounting can be done in asingle step. For example, an investment of $3million is expected to generate cash flows of $1million per year for 5 years. The cost of capital is10%.NPV ? 1 ? (CPVF ) ? 3 ? 1 ? (3.791) ? 3 ? 0.791million 5 Normally each cash flow has to be discountedindividually. To illustrate this consider thefollowing mine development opportunity. Table 6details the time distribution of the cash flows. Thecost of capital is 10%. $ 000’sYear Cash flow PVF Present value1 -5,000 0.9091 -4,5452 -7,000 0.8264 -5,7853 4,000 0.7513 3,0054 4,000 0.6830 2,7325 3,800 0.6209 2,3596 3,400 0.5645 1,9197 3,000 0.5132 1,5408 2,400 0.4665 1,1209 2,100 0.4241 89110 2,800 0.3855 1,079 13,500NPV = 4,315 "