2. Consider the following cash flow [-100, + 230, -132]. We want to decide under what range of discount rate this is an advantageous investment. But noting the change in sign, we conclude IRR is not a suitable instrument. (10 marks)
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Write the expression for NPV using the unknown r as discount rate.
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Write this expression as a function of [1/(1+r)].
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Show that the expression in (b) as a quadratic equation. Look this up if necessary.
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Solve the quadratic equation for its two roots.
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Prepare a table of NPV vs. r for r= 0,10,20,40,100%.
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Draw the graph of NVP vs. r.
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Under what range of r values is this an acceptable investment?
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Noting that NPV increases then declines as r grows from 0 to 40%, determine at what level of r NPV is a maximum (recall that d(NPV)/ds = 0, where NPV is a maximum). If you have sufficient background, solve this using calculus. If not, graphically find the top of the NPV hill (where slope = 0).
What is the maximum value of NPV? (There is one bonus point for the correct answer using calculus).
7. A firm is considering bidding on a project to produce eight widgets per year for the next four years. In order to complete the project, the firm must lease facilities for $30,000 per year, purchase equipment that costs $100,000, as well as pay labour and material costs of $19,000 per unit produced. The equipment can be depreciated at the Class 8 CCA rate of 20%. At the end of the fourth year, it can be sold for $10,000, and the asset class will remain open after the disposal of the equipment. In addition, net working capital will increase by $50,000 if the project is undertaken, but these can be recovered at the end of the project. The company’s tax rate is 40%.
What is the minimum bid per widget if the firm requires 18% return on its investment? (10 marks)
8. You are evaluating a project for Ultimate Inc. The project produces chew-resistant doghouses. You estimate the sales price of these doghouses to be $500 and sales volume to be 2,500 units per year over the project’s three-year life. Variable costs amount to $300 per unit and fixed costs (not including depreciation) are $150,000 per year. The project requires an initial investment of $250,000 and this will be depreciated on a straight-line basis to zero over the three-year project life. There will be an initial net working capital investment of $90,000 (t0) and two further investments of $90,000 at the beginning of each year thereafter. The full amount of working capital will be recovered at the end of the project’s life (i.e., $270,000 at t3). The tax rate is 35% and the required return on the project is 15%. (10 marks)
- What is the EBIT for the project in the first year?
- What is the operating cash flow for the project in year 2?
- Suppose the actual market value of the initial investment at the end of year 3 is $50,000. What is the effect of the $50,000 salvage value on year 2 cash flows?
- What is the NPV of this project?
10. A project requires an initial investment of $10,000, straight-line depreciable to zero over four years. The discount rate is 10%. The firm’s tax bracket is 34%, and they receive a tax credit for negative earnings in the year in which the loss occurs. Additional information for variables with forecast error is shown below: (10 marks)
|
Item |
Base Case |
Lower Bound |
Upper Bound |
|
Unit Sales |
3,000 |
2,750 |
3,250 |
|
Price/Unit |
$14 |
$13 |
$16 |
|
Variable cost/unit |
$9 |
$10 |
$8 |
|
Fixed costs |
$9,000 |
$10,000 |
$8,500 |
- What is the base case NPV for the project?
- What is the worst case NPV for the project?
- What is the best case NPV for the project?
- Suppose you want to conduct a sensitivity analysis for the possible changes from the base case in unit sales. What is the IRR when the sales level equals 3,250 units?
- Suppose you are interested in the project’s sensitivity to unit price. What is the NPV for the base case at a price of $13 per unit?
- What is the base case accounting break-even point?
- What is the base case cash break-even point?
- What is the base case financial break-even point? Ignore taxes.
11. A firm is considering the purchase of equipment which will cost $3 million. This equipment will last for 10 years, at the end of which it can be sold for $800,000. The CCA rate for this asset class is 30%, and the firm expects to have other assets in this asset class at the end of year 10. This equipment is expected to increase before-tax operating cash flows by $750,000 per year. However, in order to put the equipment to use, an additional $150,000 will need to be invested in net working capital initially (i.e., at t=0). The required rate of return is 16% and the firm’s marginal tax rate is 35%.
(12 marks)
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Should the firm purchase this equipment?
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Suppose that to arrive at the before-tax operating cash flows in part (a), we have used the following estimates:
Fixed costs = $120,000
Variable costs = 60% of sales
What is the Net Present Value of the new equipment if, in the best-case scenario, we estimate that fixed costs could be lower by 20% and sales revenues could be higher by 25%?
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Given the information in (a), and assuming that fixed costs are $120,000 and variables costs are 60% of sales, what is the sales level at which Net Present Value equals zero? (In other words, what is the financial break-even sales level?)
12. A project has the following estimated data: price = $65 per unit; variable costs = $33 per unit; fixed costs = $4,000; required return = 16%; initial investment = $9,000;
life = three years.
Ignore the effect of taxes and assume straight-line depreciation to zero. (10 marks)
- What is the accounting break-even quantity?
- What is the cash break-even quantity?
- What is the financial break-even quantity?
- What is the degree of operating leverage at the financial break-even level of output?
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