The equivalent annual cost (EAC) approachThis 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 rateDiscount rate for the project

The project， which has the highest NPV to infinity， is the one to recommendProject 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 Fisher1 + 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?etc0.9330.8710.8130.7590.708

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.

Effects of taxation on project appraisal

Investment in capital assets has taxation implications， which should be included in the analysis.To ignore the effect of taxation could affect the quality of the decision， which is consequently made about an investment opportunity. If the resulting project from the appraisal is profitable then taxation becomes payable on these profits thus reducing the net cash inflows by the amounts of tax payable. Capital allowances are given by the Inland Revenue at about 25% on a reducing balance basis over the life of the project. Capital allowances reduce the amount of tax which becomes payable. If the project has a terminal value at the end of its useful life， it will be necessary to establish whether this gives rise to a balancing allowance or a balancing charge. Net cash inflows are used in pay back，net present value and Internal rate of return methods. If the entity will not be in a tax-paying position during the entire life of the project then it is known as tax exhausted and tax can be ignored but this situation is most unlikely to occur.

Now that we have looked at these possible areas of complication let us look at a fictitious company we shall call Samco Plc.

Case

Samco Plc is a manufacturer of electric drills. The company has just developed two new models of electric drills. Model 1 is called Automatic and model 2 is called Super. Senior managers have resolved that if production were to commence in making the automatic model， 200，000 drills per annum will be produced and sold over the next five years at a price of ?200 per drill， whereas if production were to commence with the super model， 150，000 drills per annum will be sold over the next seven years at a price of ?140 per drill. Budgeted operating costs of each of the two models at today?s prices are as stated below：

Automatic model

Direct material70

Direct Labour20

Variable overhead

Fixed production overhead

Selling， Distribution etc20

Net Cash inflow per unit =(?200 ? ?140)= ?60Super model?

Direct material20

Direct labour12

Variable overhead15

Fixed production overhead

Selling， distribution， etc.

Net Cash inflow per unit =(140  70)= 70Net present value to infinity

Automatic model

NPV= NPV of the project/PV of annuity of appropriate years and rateDiscount Rate

= 17，130，000/3.736

0.155

= 29，581，405

Super model

= 18，920，000/3.605

0.20

= 26，241，332

Having calculated the net present values of the two projects to infinity clearly one can see that the automatic model has a net present value of about 29.5m whereas super has a lower net present value of about 26.2m. This means that the automatic model will give a higher return to the shareholders of Samco plc. This is the model the Board should manufacture and sell to their customers，because shareholders wealth will be maximised by taking this course of action.

Conclusion

The main objective of this second article in the area of project appraisal was to demonstrate to readers that cases might not necessarily be straightforward. Aspects such as inflation， taxation and unequal life spans must be understood in order that candidates can competently answer questions requiring an understanding of these further aspects. The scenario in Samco plc should be carefully followed ensuring that you understand how the author has used the available information to answer the question.

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