Net Present Value (NPV): How to Calculate NPV

NPV of each project 

Net Present Value gives the value of cash flows resulting from an investment made. The NPV figure is expressed as a currency and helps figure out the worth of investment, thus a good basis for investment decisions. NPV appreciates the effect of investment duration on the cash flow. 

Strategic decision makers calculate the NPV of a project in order to match the investment capability to match the long-term goals of the organization. NPV main advantage is that it is more likely to give a reliable prediction of the currency value at a future time. It, however, cannot offer an honest opinion on the comparison of two projects of different magnitudes (Gotze, Northcott, & Schuster, 2016).  

The data given was used to compute NPV of three different projects in three different scenarios: 

Project 1 

Scenario 1 

-30,000 + 11,000/(1+0.05)^ 1 + 11,000/(1+0.05)^ 2 + 11,000/(1+0.05)^ 3 + 11,000/(1+0.05)^ 4 + 11,000/(1+0.05)^ 5 

=-30,000+10,476.19+9,977.32+9,502.21+9,049.72+8,618.78 

=17,624.16 

Scenario 2 

-30,000 + 11,000/(1+0.055)^ 1 + 11,000/(1+0.055)^ 2 + 11,000/(1+0.055)^ 3 + 11,000/(1+0.055)^ 4 + 11,000/(1+0.055)^ 5 

=16,973.13 

Scenario 3 

-30,000 + 11,000/(1+0.06)^ 1 + 11,000/(1+0.06)^ 2 + 11,000/(1+0.06)^ 3 + 11,000/(1+0.06)^ 4 + 11,000/(1+0.06)^ 5 

=16,336.00 

Project 2 

Scenario 1 

-32,000 + 15,000/(1+0.05)^ 1 + 14,000/(1+0.05)^ 2 + 11,000/(1+0.05)^ 3 + 2,000/(1+0.05)^ 4 + 500/(1+0.05)^ 5 

=6,523.51 

Scenario 2 

-32,000 + 15,000/(1+0.055)^ 1 + 14,000/(1+0.055)^ 2 + 11,000/(1+0.055)^ 3 + 2,000/(1+0.055)^ 4 + 500/(1+0.055)^ 5 

=-32,000+14,218.01+12,578.33+9,367.75+1,614.43+382.56 

=6,161.08 

Scenario 3 

-32,000 + 15,000/(1+0.06)^ 1 + 14,000/(1+0.06)^ 2 + 11,000/(1+0.06)^ 3 + 2,000/(1+0.06)^ 4 + 500/(1+0.06)^ 5 

=5,804.85 

Project 3 

Scenario 1 

-35,000 + 11,000/(1+0.05)^ 1 + 11,000/(1+0.05)^ 2 + 11,000/(1+0.05)^ 3 + 11,000/(1+0.05)^ 4 + 11,000/(1+0.05)^ 5 

=-35,000+10,476.19+9,977.32+9,502.21+9,049.72+8,618.78 

=12,624.22 

Scenario 2 

-35,000 + 11,000/(1+0.055)^ 1 + 11,000/(1+0.055)^ 2 + 11,000/(1+0.055)^ 3 + 11,000/(1+0.055)^ 4 + 11,000/(1+0.055)^ 5 

=11,973.13 

Scenario 3 

-35,000 + 11,000/(1+0.06)^ 1 + 11,000/(1+0.06)^ 2 + 11,000/(1+0.06)^ 3 + 11,000/(1+0.06)^ 4 + 11,000/(1+0.06)^ 5 

=-35,000+10,377.35+9,789.96+9,235.81+8,713.03+8,219.83 

=11,335.98 

Payback period for each project 

Payback period is the investment window whereby the capital invested will have been recovered by the yield of the asset. It defines the viability of capital expenditures in reference to the length of the investment releasing capital. Besides the notion of profitability, an investment should be able to pay back within the shortest time possible (Wessel, & Burcher, 2004). However, a combination of payback, NPV and IRR factors in calculating return on investment provides a reliable yardstick for measuring the real worth of an investment. 

Payback’s simplicity is a reason for its high adoption for quick decision making in small projects. But it does not take into account any cash inflows executed after the return on investment has been established. 

Project 1 

=30,000/11,000 = 2.72 years 

Project 2 

Year Cash flow Cumulative Cash flow 

0 (32,000) (32,000) 

1 15,000 (17,000) 

2 14,000 (3,000) 

3 11,000 8,000 

4 2,000 1,000 

5 500 1,500 

= 2 + 3000/11,000 

=2.27 years 

Project 3 

Year Cash flow Cumulative Cash flow 

0 (35,000) (35,000) 

1 11,000 (24,000) 

2 11,000 (13,000) 

3 11,000 (2,000) 

4 11,000 9,000 

5 11,000 20,000 

=3 +2,000/ 11,000 

= 3.18 years 

IRR for each project 

Internal Rate of Return (IRR) is a percentage expression of the expected returns from an investment. IRR does not show a significant implication on the cash flows. IRR denotes equilibrium value of the present value of future cash flows and the cost of capital investment (Abor, 2017). 

If IRR rises above standard charge on the capital expenditure, it signifies that the project is worth being pursued. IRR is undoubtedly the simplest method and a well-understood way of calculating the rates of return. The disappointing fact about IRR is that it only recognizes the high percentage rates of return with no consideration on the economies of scale. 

Below are computations for three different projects in three different rate scenarios: 

Project 1 

Scenario 1 

=30,000+10,476.19+9,977.32+9,502.21+9,049.72+8,618.78 

=77,624.16 

(17,624.16/77,624.16)*100% 

=22.7% 

Scenario 2 

=30,000+ 11,000/(1+0.055)^ 1 + 11,000/(1+0.055)^ 2 + 11,000/(1+0.055)^ 3 + 11,000/(1+0.055)^ 4 + 11,000/(1+0.055)^ 5 

=76,973.13 

(16,973.13/76,973.13)*100% 

=22.1% 

Scenario 3 

=30,000+ 11,000/(1+0.06)^ 1 + 11,000/(1+0.06)^ 2 + 11,000/(1+0.06)^ 3 + 11,000/(1+0.06)^ 4 + 11,000/(1+0.06)^ 5 

=76,336.0 

(16,336/76,336)*100% 

=21.4% 

Project 2 

Scenario 1 

=32,00015,000/(1+0.05)^ 1 + 14,000/(1+0.05)^ 2 + 11,000/(1+0.05)^ 3 + 2,000/(1+0.05)^ 4 + 500/(1+0.05)^ 5 

=70,523.51 

(6,523.51/70,523.51)*100% 

=9.3% 

Scenario 2 

=32,000+14,218.01+12,578.33+9,367.75+1,614.43+382.56 

=70,161.08 

(6,161.08/70,161.08)*100% 

=8.8% 

Scenario 3 

=32,000+ 15,000/(1+0.06)^ 1 + 14,000/(1+0.06)^ 2 + 11,000/(1+0.06)^ 3 + 2,000/(1+0.06)^ 4 + 500/(1+0.06)^ 5 

=69,804.85 

(5,804.85/69,804.85)*100% 

=8.3% 

Project 3 

Scenario 1 

=35,000+ 11,000/(1+0.05)^ 1 + 11,000/(1+0.05)^ 2 + 11,000/(1+0.05)^ 3 + 11,000/(1+0.05)^ 4 + 11,000/(1+0.05)^ 5 

=82,624.22 

(12,624.22/82,624.22)*100% 

=15.3% 

Scenario 2 

=35,000+ 11,000/(1+0.055)^ 1 + 11,000/(1+0.055)^ 2 + 11,000/(1+0.055)^ 3 + 11,000/(1+0.055)^ 4 + 11,000/(1+0.055)^ 5 

=81,973.11 

(11,973.13/81,973.13)*100% 

= 14.6% 

Scenario 3 

=35,000+10,377.35+9,789.96+9,235.81+8,713.03+8,219.83 

=81,335.98 

(11,335.98/81,335.98)*100% 

=13.93% 

Project to be selected using NPV in scenario 1 

Project 1: This is because it has a positive and the highest Net Present Value at $17,624 

Project to be selected using NPV in scenario 2 

Project 1: This is because it has a positive and the highest Net Present Value at $ 16,973 

Project to be selected using NPV in scenario 3 

Project 1: This is because it has a positive and the highest Net Present Value at $16,336 

The above projects were selected since they all have positive NPVs which translate to profit for the project investors. A project with the highest NPV yields the most benefits (Holland, & Matthews, 2018). 

Project to be selected using payback period 

Project 2: this is because it takes the least number of years to recover the cost of investment at 2.27 years. The shorter the time taken by a capital investment to yield, the better it is for investors. This will untie capital for re-investing. 

Project to be selected using the IRR method 

Project 1 at the rate of 5%: This is because it has the highest return on investment at 22.7%. 

A high IRR signifies high yields in cash flows for the investor. 

References 

Abor, J. Y. (2017). Evaluating Capital Investment Decisions: Capital Budgeting. In  Entrepreneurial Finance for MSMEs  (pp. 293-320) . Springer International Publishing. 

Gotze, U., Northcott, D., & Schuster, P. (2016).  Investment Appraisal . Springer-Verlag Berlin An. 

Holland, D. A., & Matthews, B. A. (2018). Never Forget The Golden Rule.  Beyond Earnings: Applying the HOLT CFROI® and Economic Profit Framework , 1-30. 

Wessel, G., & Burcher, P. (2004). Six Sigma for small and medium-sized enterprises.  The TQM Magazine ,   16 (4), 264-272.