What is the worth of the revenues in today’s …………..

Question

7. A mining company has discovered nickel deposits on land it already owns. However, forging working relationships with the many varied stakeholders near the land will take time, along with negotiating a set of very complex environmental impact statements with the government. The company expects the agreements and environmental approval will take a full three years, during which nothing can happen onsite. Then there will be another full year of blasting and digging, and then in the year after that the revenues should start to roll in. (Assume the revenues are counted at the end of years.) The mine should be operable for 12 years, and should bring in around $27 million per year. What is the worth of the revenues in today’s dollars, if the appropriate rate to use in your analysis is 8%?

Answer 1

The best way to answer this question is to draw a timeline. We are currently in year 0, and no revenues will take place in years 1-4. After that, revenues will be $27 million in years 5-16.

Valuing each cash flow requires a discount rate specific to the number of years it takes place from today. For example, we need to discount the cash flow in year 5 by 8% over 5 years to get its value today. Since no cash flows happen in years 1-4, we can start with year 5.

The cash flow of $27 million in year 5 needs to be discounted back by 5 years at a yearly rate of 8%. Since discount rates compound, we need to use the formula: PV_{Cash Flow} = Cash Flow / (1+rate)^Periods

Filling the known information into this equation, we get PV_{Cash Flow} = $27,000,000 / (1+0.08)⁵ = $18,375,846. This means that the cash flow of $27 million in year 5 is equivalent to a cash flow of $18,375,846 today given an interest rate of 8%.

We repeat this process for years 6-16 and get the present values for each of those years. Once all of the cash flows are discounted to the present, they can be added up to get the value of the project's revenues in today's dollars. This equals $149,559,542.52.