Net present Value

Definition Of Net Present Value

Net Present Value (NPV) is a project appraisal method which takes into account ALL the cash flows, (Inflows & Outflows) discounted at Shareholder’s required rate of return. The project is normally considered as financially viable if the discounted sum of inflows exceed outflows.

Calculation Of Net Present Value

Suppose that a machine is to be bought at 4 million dollars and will be used in the business for 6 years. Each year, the revenue generated from the machine is 1 million with no scrap value.
Let us assume, Shareholder’s required rate of return is 10%.

The above simple approach can be used to find whether the project is financially viable.
Year1-  1m*.909= 0.909m
year2-  1m*.826= 0.826m
year3-  1m*.751= 0.751m
year4-  1m*.683= 0.683m
year5-  1m*.621= 0.621m
year6-  1m*.564= 0.564m

SUM = 0.909+0.826+0.751+0.683+0.621+0.564= 4.354m
NPV = 0.354m (4.354m – 4m) is positive and hence the machine is worth purchasing on the basis of NPV.
NOTE: The discount rates used can be found on the discount table or can be calculated using the present value formula which is; (1+r)^-n   (1+.10)^-2= 0.909 

However, a much quicker approach can be used when the inflows are the same every year.
Equal Cash flows arising every year are called annuities and are discounted using a single annuity rate.
In the above example, 1m will be discounted using a sixth-year annuity rate of 10% which is 4.355
1m * 4.355 = 4.355m.
(Annuity Factor can also be calculated by adding discount rates for the given time period)

Care must be taken in calculating cash flows that relate to the project, ie only relevant cash flows are considered. Depreciation, Sunk costs & General Overheads are irrelevant for NPV purposes.

Explanation

The above was just a simple illustration of NPV. The complication occurs when we incorporate the effect of working capital and Tax savings made on the project. Let’s first define what these terminologies are;
Working Capital is simply the net current assets employed in a business calculated as current assets less current liabilities. Throughout the life of a project, additional current assets will be employed which will be released after the end of the project and will be subject to the time value of money.  A question might Pop up, why would the additional current assets relate to the project? There is an apparent answer to that. With great power comes great responsibility!
Additional Sales made will result in increased receivables and inventory, subject to inventory holding costs.

Tax Saving on an asset is when the Tax authorities allow a company to deduct a certain amount each year from profit figures to allow for the use/impairment of an asset. It might be on a straight-line basis (same amount each year) or a Reducing Balance Basis. For instance, in the above example, a straight-line Tax relief is given on the machine and the rate of Tax is 30%.
Each year, 0.2m (4m/6*30%) will be added to inflows to arrive at the resultant NPV figure.
Reducing the balance basis 20% relief will give differing figures and will be as follows;
year1–  4m*20%*30%= 0.24m
Remaining Value = 3.2m [(4m-0.8)(20% of 4m)]
year2-  3.2m*20%*30%=  0.192m
And so on till disposal of the machine…
However, if for example there is a scrap value of the machine say 0.5m at the end of the year6, calculating Tax savings for the year6 will be different in that the scrap value will be deducted from the remaining value of the asset from year5 and 30% tax will be calculated without applying the reducing balance rule. Suppose the remaining value is 1m, the calculation will be 1m-0.5m*30%= 0.15m Tax saving amount.