Finance To evaluate the project for T-Mobile, we need to take into account the present-day value of future cash flows. This means that the future cash flows need to be discounted. The case example gives both the future cash flows and the discount rate for T-Mobile, which is the company's cost of capital. The net present value calculation relies on the following equation:

PV of CF = CF1 / (1+r) 1 + CF2 / (1+r) 2 + CF3 / (1+r) 3 + CF4 / (1+r) 4 + CF5 / (1+r)

This is the present value of the future cash flows. Note that as the discount rate is compounding: the longer into the future the cash flow is the more heavily it is discounted. This reflects that time equates to risk, so the further into the future the flow is, the greater risk that the flow change. Thus, the discount rate for future flows must be higher than for flows closer to the present day.

The PV formula provides the present value of the future flows. The net present value calculation then subtracts the present value of the future flows from the known current flows, in this case the $4 million initial investment. The present value of the future flows is as follows:

Year

Cash Flow

350,000

1,700,000

2,000,000

500,000

3,000,000

PV

330,189

1,512,994

1,679,239

396,047

2,241,775

NPV

6,160,243

Discount Rate

0.06

To finish the NPV calculation, we must then subtract from this the current flows:

$6,160,243 - $4,000,000 = $2,160,243

The net present value of this project is $2.16 million. Therefore, the T-Mobile should accept this project. The rule of thumb with respect to using net present value to evaluate whether or not a project should be undertaken is that if the project has a positive net present value, it should be accepted. This is because the discount rate equates to the expected rate of return on the company's existing operations. Thus, any project that is more valuable to the company than its existing operations is one that the company should undertake.

There is a caveat to the assumption that the project should always be accepted if...

All NPV calculations are based on assumptions, so the company needs to perform a sensitivity analysis on those assumptions in order to truly understand if the project is going to add value. It helps to be conservative when setting these assumptions. For example, this project has a positive NPV but if the project does not generate the expected cash flows, the NPV might not be positive anymore. The management of T-Mobile will need to understand how changes to its assumptions will affect the NPV of the project.
The shareholders should understand that the NPV is a means of understanding the value of a project. There are other methodologies that can be used but NPV is the best because it takes a number of important factors into consideration. For example, the NPV is based on the concept of the time value of money. Given that T-Mobile has a cost of capital of 6%, this implies that if the company plowed this money back into its current operations, the return would be around 6%. But this project is going to generate revenues for the next five years. A dollar earned in the future is not as valuable as a dollar earned today. Thus, it cannot be considered to have the same value. What the NPV calculation does is it gives those future dollars an equivalent value today, based on the risk that is associated with the company's cash flows.

So the NPV calculation essentially weighs the value of those future cash flows against the value of the initial cash flows. In this example, T-Mobile is spending $4 million to initiate the project and its shareholders need to know what they can expect to gain from that. We have estimates of future cash flows, in future dollars. By discounting those future dollars back to present day to account for the risk associated with the fact that those flows are in the future, we are able to make a more accurate comparison between the initial cost of the project and the cash flows that come from the project in the future. Because the value of those flows in the future is greater than the initial cost, we are recommending that T-Mobile accept the project.

Part II.

I believe that a merger between Sprint and T-Mobile would not add value to the shareholders of each corporation. When analyzing the worth of a…