These are the forecasts of revenues over the lifetime of a project. Assume all c

Question

These are the forecasts of revenues over the lifetime of a project. Assume all cash flows occur at the end of the year.

Yearly expenses from year 1 to year 3: $30 Million

Yearly revenues from year 1 to year 3: $0

Yearly expenses from year 4 to year 10: $55 Million

Yearly expected revenues from year 4 to year 10: $105 Million

The discount rate for the firm is 7.8% for all cash flows (net cash flows from projects, recovered NWC, salvage, etc.).

In the first part of this question, you are asked to only calculate the present value of the discounted costs and revenues. What is this value?

Hint: This hint is optional; you don't have to read this. This is only to help you, if you are confused by this hint just ignore it and solve the question as you would. This will have two parts. Part 1 would be discounted value of costs for the first 3 years of $30 Million each, which is an annuity. You know the formula for an annity for (negative) cash flows that iwll come the next 3 years.

Part 2 is an annuity of $50 Million a year for 7 years, the first cash flow which will occur at the end of the 4th year, and the last one which will occur at the end of the 10th year. Now position yourself at the end of year 3. You should be able to use the annuity formula for the 7 cash flows which will occur from the end of year 4 to the end of year 10. However, you will have the value at the end of year 3 by using the annuity formula. You will have to use discounting again to find the present value, that is today.

Once you have calculated the above, answer would be Part 1- Part 2= Discounted Net Cash Flows from year 4 to year 10- discounted costs from year 1 to year 3.

Explanation / Answer

The hint is clearly provided.

Net cash flows from Year 4 - year 10 = $105m - $55m = $50m every year

Discounted cash flows from year 4 - year 10 (1+0.078)^n in $m years cash flows Discount factor Discounted cash flows 4 50 1.3504                        37.02 5 50 1.4558                        34.35 6 50 1.5693                        31.86 7 50 1.6917                        29.56 8 50 1.8237                        27.42 9 50 1.9659                        25.43 10 50 2.1193                        23.59                     209.23 Discounted costs from year 1 - year 3 years cash flows Discount factor Discounted cash flows 1 30 1.0780                        27.83 2 30 1.1621                        25.82 3 30 1.2527                        23.95                       77.59 Discounted value of net cash flows of project                     131.64

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