# problems on finance engineering

Question 1 (based on Chapter 10) A city in the Midwest has made a decision to expand the electricity production in its area by building a new power plant. The city government must decide whether the plant will be powered by coal or whether the plant will be built on a river and use hydropower. The planning horizon is 40 years, and the assumed cost of capital is 7%. Compute a conventional B/C ratio, using AW, with disbenefits in the numerator for each of the two alternatives, determine which one should be chosen, and explain why.

The coal alternative would require a $50 million capital investment, a $500,000 annual operating expense, and bring about $2 million in annual operating revenue. In addition, the environmental harm and pollution impact caused by the plant is estimated to amount to $1 million annually. The plant is estimated to have a $400,000 worth of positive annual impact on the economic development of the city.

The hydroelectric alternative would require a $90 million capital investment, a $200,000 annual operating expense, and bring $1.5 million in annual operating revenue. The plant is expected to have no significant negative impact on the environment. The benefits of improved flood protection, water management, as well as fishing and recreation are expected to total $6 million annually.

Question 2 (based on Chapter 9) An existing project is nearing its end. The machine that is currently being used and will not be replaced. It could be sold today for $50,000, or kept for up to 5 more years. Determine whether the project should be abandoned now, or whether the machine should continue to be used, and if so determine the end- year when it should be sold. The table below gives the projected annual revenues and expenses attributed to the machine, and its projected end-of-the-year market values. Assume 6% cost of capital.

Year Revenues Expenses Machine year-end market value

1 75,000 15,000 40,000

2 70,000 16,000 30,000

3 60,000 17,000 25,000

4 45,000 18,000 20,000

5 25,000 20,000 15,000

FIN 5203, Trine University, Fall 2019, Dr. Kolar

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Question 3 (based on Chapter 9) A new machine will cost $80,000. The expected market value of the machine at the end of each year, and the annual maintenance costs are given in the table below. Assuming 8% cost of capital, what is the economic life of the machine?

Year Market Value at the End

Annual Maintenance Cost

0 80,000

1 65,000 9,000

2 55,000 8,000

3 47,500 9,000

4 42,500 11,000

5 37,500 14,000

6 30,000 18,000

Question 4 (based on Chapters 11 and 12) Lakeland Motors is contemplating an expansion of its production. The expansion would require a purchase and installation of a new machine with a cost of $400,000. The machine will be depreciated straight-line over 10 years with zero market value assumed at the end of the 10 year period. Nevertheless, the estimated duration of the expansion project is only 7 years, and the machine is expected to be sold for $175,000 at the end of year 7. The expansion project is expected to result in additional 10,000 units produced each year, and the expected selling price per unit is $35, while the expected variable cost per unit is $25. Use cost of capital of 7%, and a 20% tax rate.

a) Using the information given above, compute the after-tax annual cash flows for years 0-7. Based on the resulting present worth (NPV) of the expansion project, should the project be accepted? Why?

b) Perform sensitivity analysis, using a Monte Carlo simulation, with the following assumptions. Assume the selling price per unit is normally distributed, with $35 mean and $1.00 standard deviation. Assume the number of units sold is normally distributed, with 10,000 mean and 500 standard deviation. Assume the re-sale price of the machine at the end of year 7 is normally distributed with $175,000 mean and $2,000 standard deviation. Assume there is no correlation between the three random variables just described. Keep all of the other variables at their expected values. Re-compute the present worth (NPV) of the project 100 times (using 100 trials). Compute the average NPV, and determine the estimated cutoff point for the 5% of worst possible outcomes. Comment on the project uncertainty and the resulting desirability of the project.

c) Perform sensitivity analysis, varying the number of units sold and the variable cost per unit. Construct a table showing the present worth (NPV) of the expansion project for all possible combinations of the number of units sold and the variable cost per unit, using the following values: number of units sold (6,000 7,000 8,000 9,000 10,000 11,000 12,000 13,000 14,000) and variable cost per unit (21, 22, 23, 24, 25, 26, 27, 28, 29). Keep all of the other variables at their expected values. Comment on the project’s sensitivity to the number of units sold, and to the variable cost per unit. How does this sensitivity analysis affect the desirability of the project?