NPV

Net Present Value and its Calculations

Net Present Value and its Calculations

Valuations

Part 1a

Initial Investment

Year 1

Year 2

Year 3

$ (400,000.00)

$ 100,000.00 $ 120,000.00 $ 850,000.00

This chart shows an initial investment of a project equaling $400,000. The negative number denotes outflows by the company. The positive numbers in year 1, year 2, and year 3 indicate cash inflows.

Net Present Value (NPV) = Present Value of all Future Cash Flows - Initial Investment

Present Value of Future Cash Flows = Cash Flow of Year 1 / {(1 + Rate) ^ 1} + Cash Flow of Year 2 / {(1 + Rate) ^ 2} ……. + Cash Flow of Year n / {(1 + Rate) ^ n}

Discount Rate

0%

2%

6%

11%

NPV

$670,000.00

$602,307.31

$485,675.08

$368,466.18

This Graph shows the NPV of the investment at ranging values of Discount Rates. In almost all cases, as the discount rate increases, the value of the NPV falls. The reason for such a phenomenon is that money loses value as time passes, and if the discount rate is higher, then money's value will lower at a much faster rate.

Based on calculations, the curve will intersect the horizontal axis when the discount rate is 45.7%. This value is also known as the Internal Rate of Return. IRR denotes the discount rate require for the NPV of the project to be zero. The higher is the IRR the better is the project because a higher IRR would take a higher discount rate to push the NPV of the project below zero. The modified IRR (MIRR) would be 39.52% based on the company's cost of capital to be at 5%.

Part 1b

Initial Investment

Year 1

Year 2

Year 3

$ (815,000.00)

$ 141,000.00 $ 320,000.00 $ 440,000.00

This chart shows an initial investment of a project equaling $815,000. The positive numbers in year 1, year 2, and year 3 indicate cash inflows.

Discount Rate

1%

4%

10%

18%

NPV

$64,711.25

$7,301.26

($83,433.51)

($167,704.98)

In contrast to the previous project, this project's cash flows are not sufficient enough to cover the project's initial investment cost at a much lower discount rate. Compared to the previous project, whose IRR was 45.7%; this project's IRR is a very low 4.42%. This means that a discount rate above this value would cause the NPV of this project to go below zero. Based on calculations, the MIRR of this project would be 4.55%. If you notice, the MIRR is greater than the IRR (4.42%) of this project. The main reason for this phenomenon is that the cost of capital (5%) is higher than the IRR of the project.

Part 1c

Profitability Index = PV of Future Cash Flows / Initial Investment

PI = 0.94 and Investment = $4.2 million

PV of Future Cash Flows = $4.2 million * 0.94 = $3.948 million

Part 2

The Internal Rate of Return provides us with the Discount Rate which causes the NPV of the future cash flow streams to reach zero. By comparing the IRR with the cost of capital, we can safely reject all project's whose IRR is below the cost of capital of a ...