Excel : Avoiding Seven Common Errors Joint contribution by: Ms. Rubaina Shrivastava, Prof. Saini Das, and Prof.

Transcription

1 Excel : Avoiding Seven Common Errors Joint contribution by: Ms. Rubaina Shrivastava, Prof. Saini Das, and Prof. Madhukar Dayal Millions of MicroSoft Excel (MSE) users across the World use the NPV() function. There are many errors which common users (and even advanced users) make in using this function. The purpose of this article is to enlighten the readers about these errors and how to avoid them. We list below demonstrating through simple examples, the most common of these errors and how to avoid them. NPV assumes cash flows at the END of the time period, hence, it is not very good (without mathematical acrobatics) in handling middle of the time period cash flows (the beginning of time period cash flows can be conveniently handled by treating them as cash flows at end of the previous period). Error 1 and its rectification: NPV() function does not calculate the net present value correctly. This error has been highlighted by several others before, for example, see the link below by Timothy R Mayes: Briefly, net present value by definition also includes the cash (out-)flow(s) at time t=0, which the MSE NPV() function does not consider, and hence, this adjustment has to be made outside the function s operational area as expalined with the example below: 1 Year0 Year1 Year2 Year :Applicable yearly rate of interest :Correct NPV Table 1.1 Correct Usage of NPV() Error 2 and its rectification: NPV() function assumes that all "time periods" for which cash flows are given, are same (equal). Hence, users must avoid possible mistakes as in example below. 1 Quarter0 Quarter1 Year2 Quarter % :Applicable quarterly rate of interest :Incorrect NPV Table 2.1 Incorrect NPV() results due to non-coherent time periods

2 1 Quarter0 Quarter1 Quarter2 Quarter % :Applicable quarterly rate of interest :Correct NPV Table 2.2 Correct NPV() computed with coherent time periods Error 3 and its rectification: Discounting rate of interest per time period applicable is not adjusted to actual time periods of cash flows given (such as, annual rate of interest applied to quarterly cash flows). As NPV does not recognize quarterly, half-yearly, or other time periods, the user has to ensure that the applicable discounting rate of interest is for the correct time period for which all cash flows are provided (see examples below). 1 Quarter0 Quarter1 Quarter2 Quarter3 4 10% :Annual Rate :Incorrect NPV Table 3.1 NPV yields wrong results due to discounting rate of interest applied being for an incorrect time period 1 Quarter0 Quarter1 Quarter2 Quarter % :Adjusted Quarterly Rate 5 10% :Annual Rate :Correct NPV Table 3.2 Corrected NPV computation with adjusted quarterly rate

3 Error 4 and its rectification: NPV does not recognise missing months, quarters, or years. For example, (Please see table 4.1 & 4.2) in this example, NPV will assume Year 3 to be as Year2, Year4 to be as Year3 and compute (due to missing Year2 value). This is because NPV will assume and consider the next year to be a consecutive year and calculate NPV accordingly. For rectifying such errors, we need to provide a dummy '0' value for a time period which has NIL cash flow. Hence, always keep 0 cash flows instead of missing/escaping the said NIL cash flow period, else NPV results are wrong. 1 Year0 Year1 Year3 Year :Incorrect NPV Table 4.1: Wrong Computation of NPV due to missing time period (here, a year) E 1 Year0 Year1 Year2 Year3 Year :Incorrect NPV =NPV(E4,B3:E3)+A2 :Formula used Table 4.2: Partially Rectified NPV() calculation - missing time period (year) added, but 0 (zero) not entered E 1 Year0 Year1 Year2 Year3 Year :Cash Inflows :Correct NPV =NPV(E4,B3:E3)+A2 :Formula used Table 4.3: Rectifying the missing time period (year) error The examples above explain that the NPV() function assumes that: (i) all "time periods" for which cash flows are given, are the same (equal); (ii) no time period is missing (even if with zero cash flow); (iii) zero (0) value is entered in the cell representing the time period(s) with zero (0) cash flows; and, (iv) the discounting rate used is as applicable (adjusted) to the time periods considered.

4 Error 5 and its rectification: NPV needs a single (comprehensive) cash flow value for each time period, as it can not accept multiple cash flows (inflows or outflows) for the same time period. Hence, all cash outflows and inflows for a time period have to be aggregated and the single aggregated value used in the NPV function. Alternately, the NPV for cash outflows and for cash inflows can be computed separately and from these two values, the aggregated NPV computed (do not forget to enter a zero, if for a time period there is no cash flow). E 1 Year0 Year1 Year2 Year3 Year :Cash Outflows :Cash Inflows Table 5.1(a): Cash flows for computing NPV and discounting rate of interest per time period E 5 In E5: =NPV(E4,B2:E2)+A :Correct PV of cash outflows 6 In E6: =NPV(E4,B3:E3) :Correct PV of cash inflows 7 In E7: =SUM(E5+E6) :Correct NPV Table 5.1(b): Method 1 - computing NPV of cash outflows and inflows separately adjusted with initial capital outlay E :Correct NPV 6 In E5: =NPV(E4,B2:E2)+NPV(E4,B3:E3)+A2 Table 5.1(c): Method 2 - computing NPV of cash outflows, inflows and initial capital outlay integratedly E :Yearly net cash flows :Correct NPV 7 In E6: =NPV(E4,B5:E5)+A5 Table 5.1(d): Method 3 - computing NPV from time-period-wise aggregated cash flows

5 Error 6 and its rectification: Excel considers numeric values entered in a cell as follows: 0.1 as 10%, 10% as 10% but 10 as 1000%. Thus, it is necessary that with NPV, the chosen number format is used correctly in the formula as shown in examples below. 1 Year0 Year1 Year2 Year3 4 Applicable yearly rate of interest Formula used :Correct NPV =NPV(A5,B3:D3)+A2 6 10% :Correct NPV =NPV(A6,B3:D3)+A :Incorrect NPV =NPV(A7,B3:D3)+A :Correct NPV =NPV(A8/100,B3:D3)+A2 Table 6.1: Applying discounting rate of interest with correct number format in NPV Error 7 (advanced) and its rectification: NPV can not handle different rates for different time periods. Hence, use separate cells for each time period's applicable rate. Note: Here NPV has to be used multiple times (or other advanced usage is needed). Readers should note that the rate applicable for each year has to be applied to discounted future cash flows too! 1 Year0 Year1 Year2 Year % 9.9% 9.8% :Applicable yearly rate of interest :Correct NPV =NPV(B4,B3+NPV(C4,C3+NPV(D4,D3)))+A2 :Formula used Table 7.1: Applying different annual discounting rates for different years

6 NPV ignores cells with no value entered (as pointed above in Error 4 Table 4.2). However, this feature provides a benefit, too, which is: to incorporate multiple cash outflows and cash inflows for each time period (say, on account of different economic activities), aggregates can be computed as in the example below. E F G H 1 Year0 Year1 COFYear1 CIF Year2 COFYear2 CIF Year3 COF Year3 CIF Applicable rate of Int: % :Present value of cash outflows using =NPV(H3,B4:G4)+A4 (see * below) :Present value of cash inflows using =NPV(H3,B6:G6) (see * below) 8 :Correct NPV computed using =H4+H Aggregated (Net) cash flows: Year0 Year1 Year2 Year :Correct NPV computed using =NPV(H3,C10:G10)+A10 Table 7.2: Demonstrating horizontal and vertical aggregation of cash flows for each time period for NPV * Note, that in cells H4 and H5, the formula used is NPV(), however, the values computed are present values of cash outflows and inflows, respectively. Note also, that here, we take advantage of the fact that NPV() ignores empty cells in the cash flow range given as the second argument! The above example is demonstrated again with different discounting rates appllicable for each time period below. E F G 1 Year0 Year1 COFYear1 CIF Year2 COFYear2 CIF Year3 COF Year3 CIF % 9.90% 9.80% :Applicable rate/s of interest 7 Aggregated cash flows: (for each time period) :Correct NPV Formula used in G9: =NPV(C6,C8+NPV(E6,E8+NPV(G6,G8)))+A8 Table 7.3: Demonstrating aggregation of cash flows for each time period with different discounting rates for NPV We hope the above examples elaborate the correct use of NPV() function for all readers. For any suggestions, please, write to any one of us at: Ms. Rubaina Shrivastava at (rubainas@iimidr.ac.in, m @gmail.com), Prof. Saini Das (saini@vjsom.iitkgp.ernet.in) or Prof. Madhukar Dayal (madhukar@iimidr.ac.in).