Hello, y'all. The topic today is what happens to a firm's risk when a new project is undertaken. In class we had an example looking at the profitability of adding a new project with an expected cash flow in year one of $58M and a volatility of $50M. It was determined that the new project looked profitable until we looked at the added risk to the firm. Now, I am going to look at changing our expected cash flow from $58M to $75M and the volatility from $50M to $55M. I will assume all other variables remain unchanged, i.e. initial cost is $50M and the cost of capital is 6%.
The net present value of the project is $20,754,717. It looks very profitable. Let's look now at the added risk. The volatility of the existing projects and the new one is $90,967,027. The CaR of the existing projects is 1.65 times the volatility of $50M and that is $82,500,000. The CaR of the new and the existing projects is 1.65 times $90,967,027, which is $150,095,595. It costs the firm some money to hold the extra risk. Let’s suppose that cost is 10%.If we assume that the cost of the firm holding the extra risk is 10%, then our new NPV is 20.8M - .1*(150.1M-82.5M) which is $13,995,198. This project would be accepted since we have a positive net present value.
The risk of the firm always goes up when a new project is added that has a positive correlation with the existing projects. A new project carries a certain volatility which puts a certain amount of money at risk. When adding new projects that are positively correlated to the old ones, the risk of the firm will go up. Projects that are negatively correlated will lower the risk of the firm since it does the opposite of the other projects, thus canceling out some of the fluctuations between new and old projects.
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