The equivalent annual cost (EAC) approach

　　This approach computes the present value of costs for each project over a cycle and then expresses the present value in an annual equivalent cost using the appropriate annuity factors for each cycle. The annual equivalent of NPVs of the two or more projects can then be compared. Having calculated the EAC for each cycle and each project， then compare the EACs. The project that has the lowest EAC over the cycles is the better one if lowest outlay is the objective or the higher EAC would be preferred if the highest revenue were the objective.

　　Infinite re-investment approach

　　This approach is appropriate when projects of unequal lives and unequal risks are being considered. The first step to take will be to establish the net present value of the projects in the normal way and then calculate the net present value of projects to infinity using the formula：

　　NPV ? = NPV of project/PV of annuity for the life of project at discount rate

　　Discount rate for the project

　　The project， which has the highest NPV to infinity， is the one to recommend

　　Project appraisal under inflation

　　Inflation is a state of affairs under which prices are constantly rising. When this happens the purchasing power of money depreciates. The currency will buy fewer goods and services than previously and consequently the real returns on investments will fall. Investors understandably， will expect to be compensated for the fall in the value of money during inflation. When appraising investment opportunities the appraiser requires an understanding of three discount rates. These are Money Rates， Real Rates and Inflation Rates. Money rate (also known as Nominal rate) is a combination of the real rate and inflation rate and should be used to discount money cash flows. If on the other hand you were given real cash flows these must be discounted using the real discount rates. In order to be able to use either of these two rates， you need to know how to calculate both of them. They can be calculated from the following formula， devised by Fisher

　　1 + m =(1 + r) x (1 + i)

　　Where：

　　m = money rate

　　r = real rate

　　i = inflation rate

　　From the above formula it is possible to calculate m， r and i if you were given information about two of the three variables. For example if you were told that the money rate was 20% and real rate was 12% the inflation rate will be calculated as follows：

　　i =1 + m ? 1

　　1 + r

　　i =1 + 0.20? 1

　　1 + 0.12

　　i =1.0714?

　　= 7.14%

　　Equally m and r could be calculated as follows.

　　m =(1.12 x 1.0714) ? 1

　　(1.19999) ? 1

　　20%

　　r =1.20? 1

　　1.0714

　　12%

　　When the appropriate discount rate has been established the present value factors of this rate at different time periods can be obtained from the present value table or the present value factors calculated using the following formula：

　　11111

　　(1+r)(1+r)2(1+r)3(1+r)4(1+r)5?etc

　　Where r = discount rate.

　　Present value tables are only available for whole numbers， so if your r is not a whole number you will have to use the formula to calculate the required present value factors. Let us calculate for example the present value factors of 7.14% for years 1 to 5.

　　11111

　　(1.0714)(1.0714) 2(1.0714) 3(1.0714) 4(1.0714)5?etc

　　0.9330.8710.8130.7590.708

　　Having either obtained or calculated the present value factors for the relevant discount rates， these are then used to discount the future cash flows to give the net present values of the projects. It is important to understand when to use which rate. If the question gives you money cash flows， then use the money rate; if the question gives real cash flow it follows then that the real rate must be used. To confuse one with the other would give the wrong answer.