16 May WHAT ARE THE NET PRESENT VALUES OF PROJECT A AND PROJECT B?
We have two independent and mutually exclusive projects, A and B. Project A requires an initial investment of $1000, and will yield $500 of cash inflows for the next three years. Project B requires an initial investment of $3,500, and will yield $1,000 of cash inflows for the next five years. The required return on both projects is 10%. (13 marks total)
a. What are the net present values of Project A and Project B? (2 marks)
b. What is the problem with using the NPV investment criterion in this case? What alternative criterion should be used? (1 mark)
c. Which project should be chosen? (2 marks)
The cash flows and required return given are all in nominal terms. Given that the inflation rate is 3%, answer the following questions:
d. What is the real rate of return based on the exact Fisher equation? (1 mark)
e. What are the real cash flows from Project A and Project B? (2 marks)
f. What are the real net present values of Project A and Project B? (Hint: The real NPV should be the same as the nominal NPV.) (2 marks)
g. Which project should be chosen based on the real cash flows and real rate of return? (3 marks)
6. A new printing machine costs $19,000 and has an installation cost of $1,000. It belongs to CCA Class 8, which means that it has a CCA rate of 20%. The manufacturer of this machine guarantees that this machine will last for five years. Assume a tax rate of 40%. (9 marks total)
a. In the table provided, fill in the beginning undepreciated cost of capital (Beg UCC), the capital cost allowance (CCA), the ending undepreciated cost of capital (End UCC), and the CCA tax shield (CCATS) for each of the next five years. Remember to use the half-year rule. (2.5 marks)
Year Beg UCC CCA End UCC CCATS
1
2
3
4
5
b. Assuming a required return of 12%, calculate the present value of CCATS (PVCCATS) for each of the five years, using the numbers calculated in part (a). (2 marks)
c. Based on the numbers calculated in part (b) above, what is the total PVCCATS over the five years? (0.5 mark)
d. Assume that salvage value at the end of Year 5 is $1,000. What is the total PVCCATS if we use the long formula? (2 marks)
PVCCATS =
e. What is the reason for the difference between your answers in parts (c) and (d)? (2 marks)
7. For the following questions, assume no taxes and straight-line depreciation. (9 points total)
a. What is the cash break-even quantity, and how is it calculated? Use both words and an equation in your explanation. Include a discussion of payback period, NPV, and IRR at the cash break-even sales level. (3 marks)
b. What is the accounting break-even quantity, and how is it calculated? Use both words and an equation in your explanation. Include a discussion of payback period, NPV, and IRR at the accounting break-even sales level. (3 marks)
c. What is the financial break-even quantity, and how is it calculated? Explain using both words and an equation. Make sure that you discuss the two steps involved in finding the financial break-even point. Also, include a discussion of discounted payback period, NPV, and IRR at the financial break-even sales level. (3 marks)
8. You are considering a new product launch. The project will cost $680,000, have a four-year life, and have no salvage value; depreciation is straight-line to zero. Sales are projected at 160 units per year, price per unit will be $19,000, variable cost per unit will be $14,000, and fixed costs will be $150,000 per year. The required return on the project is 15%, and the relevant tax rate is 35%. (17 marks total)
a. Based on your experience, the unit sales, variable cost, and fixed cost projections given here are probably accurate to within 10%. What are the upper and lower bounds for these projections for unit sales, variable cost, and fixed cost? (3 marks)
b. What is the base-case NPV? (1 mark)
c. What are the NPVs in the best-case and worst-case scenarios? (2 marks)
d. Evaluate the sensitivity of your base-case NPV to changes in fixed costs. (2.5 marks)
e. What is this project’s cash break-even level of output (ignoring taxes)? (1 mark)
f. What is the accounting break-even level of output for this project, and what is the degree of operating leverage (DOL) at the accounting break-even point? How do you interpret this DOL number? (2.5 marks)
g. What is the financial break-even level of output for this project, and what is the degree of operating leverage (DOL) at the financial break-even point? How do you interpret this DOL number? (5 marks)
9. You are considering a project that will supply an automobile production facility with 35,000 tonnes of machine screws annually for five years. To get the project started, you will need an initial $1,500,000 investment in threading equipment. The project will last for five years. The accounting department estimates that annual fixed costs will be $300,000 and that variable costs should be $200 per tonne. The CCA rate for treading equipment is 20%. Accounting estimates a salvage value of $500,000 after costs of dismantling. The marketing department estimates that the auto makers will accept the contract at a selling price of $230 per tonne. The engineering department estimates you will need an initial net working capital investment of $450,000. You require a 13% return and face a marginal tax rate of 38% on this project. (14 marks total)
a. What is the NPV for this project? Should you pursue this project? (5 marks)
b. Suppose you believe that the accounting department’s initial cost and salvage projections are accurate only to within 15%; the marketing department’s price estimate is accurate only to within 10%; and the engineering department’s net working capital estimate is accurate only to within 5%. What is your worst-case scenario for this project? Your best-case scenario? (9 marks)
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