Question

Suppose that a project generates the cash flows at the bottom, where payments are negative cash flows and revenues are positive cash flows.

1. Assuming the cost of capital is 7.5% and using the net present value method, find the value of the project and give a recommendation on whether the project should be undertaken.
2. Does your recommendation change if the costs of capital rises to 20%? Explain, and what is your recommendation?
3. Now suppose that after the 12th period the project continues on forever, with a constant flow of net cash flows equal to the twelfth period. That is the net cash in the twelfth period is repeated in the 13th period, and the 14th, and so on. Now include this feature into your valuation of the project. Calculate the NPV. Does your recommendation change? Explain.
4. Similar to the previous problem, suppose that the 12th period net flow continues on into the future, but instead of continuing forever, it only continues for 12 more years. Evaluate the NPV of this project, make a recommendation, and explain.
5. Assets are used to generate revenues and may incur some costs. Explain how the NPV method could be used to value assets, like a house for example.

Period	Payments	Revenues
0	-14	0
1	-6321	3896
2	-2600	4235
3	-6985	6013
4	-6032	1528
5	-4037	704
6	-672	10654
7	-5305	8865
8	-9345	1296
9	-5858	3817
10	-2612	5408
11	-3402	11803
12	-8522	10778

Answer 1

NPV formula in EXCEL is,

=NPV(rate, Year1 to Year n cashflows)-Initial cost

1&2. NPV at 7.5% and 20% cost of capital are as follows

At 7.5%, we can accept the project because of positive NPV but reject at 20% cost of capital due to its negative NPV.

3. If cashflows grows at constant growth rate after 12 years, we need to calculate the terminal value at Year12.

Year12 terminal value= Year13 cashflow/cost of capital=2256/7.5%=30080

Add this 30080 to Year12 cashflow

Then find NPV. Please find the below table

As NPV is positive, we can accept this project

4. Please find the below table if cashflows continue for another 12 years

In this case also, NPV is positive. We can accept the project

5. For assets like Houses, we have to first find the cashflows that will be generated in the future.

We should arrive at Net operating income (NOI) by subtracting maintainance costs from the rental income. This would be used as future cashflows and we can assume the inflation too.

While arriving at the required return, we have to find the capitalization rate. For this we need some houses Net operating income and the value of the house in the nearby premises.

Capitalization rate=NOI/value of the asset.

Now, you can value your asset with this capitalization rate, formula =NOI/Capitalization rate

NPV(rate,NOI cashflows)