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Valuing a New Computer System

Obsolete Technologies is considering the purchase of a new computer system to help handle its warehouse inventories. The system costs $50,000, is expected to last 4 years, and should reduce the cost of managing inventories by $22,000 a year. The opportunity cost of capital is 10 percent. Should Obsolete go ahead?

Don t be put off by the fact that the computer system does not generate any sales. If the expected cost savings are realized, the company s cash flows will be $22,000 a year higher as a result of buying the computer. Thus we can say that the computer increases cash flows by $22,000 a year for each of 4 years. To calculate present value, you can discount each of these cash flows by 10 percent. However, it is smarter to recognize that the cash flows are level and therefore you can use the annuity formula to calculate the present value:

The net present value is NPV = $50,000 + $69,740 = $19,740 The project has a positive NPV of $19,740. Undertaking it would increase the value of the firm by that amount.

The first two steps in calculating NPVs forecasting the cash flows and estimating the opportunity cost of capital are tricky, and we will have a lot more to say about them in later material. But once you have assembled the data, the calculation of present value and net present value should be routine. Here is another example.

Calculating Eurotunnel s NPV

One of the world s largest commercial investment projects was construction of the Channel Tunnel by the Anglo-French company Eurotunnel. Here is a chance to put yourself in the shoes of Eurotunnel s financial manager and find out whether the project looked like a good deal for shareholders. The figures in the column headed cash flow in Table 4.1 are based on the forecasts of construction costs and revenues that the company provided to investors in 1986.

The Channel Tunnel project was not a safe investment. Indeed the prospectus to the Channel Tunnel share issue cautioned investors that the project involves significant risk and should be regarded at this stage as speculative. If for any reason the Project is abandoned or Eurotunnel is unable to raise the necessary finance, it is likely that equity investors will lose some or all of their money.

To induce them to invest in the project, investors needed a higher prospective rate of return than they could get on safe government bonds. Suppose investors expected a return of 13 percent from investments in the capital market that had a degree of risk similar to that of the Channel Tunnel. That was what investors were giving up when they provided the capital for the tunnel. To find the project s NPV we therefore discount the cash flows in Table 4.1 at 13 percent.

Since the tunnel was expected to take about 7 years to build, there are 7 years of negative cash flows in Table 4.1. To calculate NPV you just discount all the cash flows, positive and negative, at 13 percent and sum the results. Call 1986 Year 0, call 1987 Year 1, and so on. Then Net present value of the forecast cash flows is АВАі251 million, making the tunnel a worthwhile project, though not by a wide margin, considering the planned investment of nearly АВАі4 billion.

Of course, NPV calculations are only as good as the underlying cash-flow forecasts. The well-known Pentagon Law of Large Projects states that anything big takes longer and costs more than you re originally led to believe. As the law predicted, the tunnel proved much more expensive to build than anticipated in 1986, and the opening was delayed by more than a year. Revenues also have been below forecast, and Eurotunnel has not even generated enough profits to pay the interest on its debt. Thus with hindsight, the tunnel was a negative-NPV venture.

Note: Cash flow for 2010 includes the value in 2010 of forecast cash flows in all subsequent years. Source: Eurotunnel Equity II Prospectus, October 1986. Used by permission. Some of these figures involve guesswork because the prospectus reported accumulated construction costs including interest expenses.