The questions in the first section are worth 4 points each; the questions in the second section are worth 15 points each. Total time for the exam is three hours.

Short Answer Section: 4 points each

1. A pre-tax analysis shows that, over a five-year study period, leasing and buying a particular machine are equally attractive options. If the company pays tax at 50%, and if the machine is in Asset Class 8 (20% declining-balance depreciation per year), which option will be favoured by an after-tax analysis over the same study period?

   Leasing. (If you buy the machine, you pay out now and can deduct diminishing fractions of the purchase price from pre-tax income over the next five years. If you lease it, you deduct the lease cost from pre-tax income every year. The latter option will always save you more tax than the former.)

2. An after-tax analysis shows that, over a five-year study period, leasing and buying a particular machine are equally attractive options. (The company pays tax at 50%, and the machine is in Asset Class 8 (20% declining-balance depreciation per year).) If the analysis is now modified to take into account inflation at 10% per annum, which option will be favoured?

   Leasing. (If you buy it, you deduct a diminishing fraction of the purchase price from your pre-tax income every year. But your pre-tax income grows with inflation, while the purchase price is fixed. If you lease, on the other hand, your lease cost grows with inflation, so the size of the deduction you can make from pre-tax income grows at the same pace as inflation.)

3. What are the tax advantages and disadvantages of forming a corporation, rather than being a single proprietor?

   Advantages: income is taxed at the corporate rate (20% for a small company, 50% for a big one), which will be less than the individual rate if income is high. If you take your share of the company's growth as an increase in stock value rather than as dividends, you can choose to sell stock when your income from other sources is low (e.g. while you're yachting round the world), and pay relatively low captital gains taxes.

   Disadvantages: Your dividend income gets taxed twice, once for the corporation, once as part of your personal income.

4. Give brief definitions of:
   • The internal rate of return
   • The external rate of return
   • The auxiliary rate of return
   • The minimum acceptable rate of return

   See Lecture 5: 5. Rates of Return*

5. What is the difference between microeconomics and macroeconomics?

   See Lecture 1: 1. Introduction

6. You are going to receive $1,000 over the course of a year, at a nominal interest rate of 10% per annum. Order these four methods of computing cashflow and interest from the one which gives you the greatest amount at the end of the year to the one which gives you the least. (You don't need to calculate any amounts explicitly.)
   • Discrete cash flow, annually compounded.
   • Continuous cash flow, annually compounded.
   • Discrete cash flow, continuously compounded.
   • Continuous cash flow, continuously compounded.

   This question is a bit ambiguous, as we don't specify when in the year you get the $1,000 in the case of discrete cash flow. If you get it on January 1, the discrete flow/continuous compounding gives you the most; if you get it on Dec 31, continuous cash flow, continuously compounded, gives you the most. The two `annually compounded' options give you the least.

7. I invest $1,500 at 4% interest, compounded annually. Approximately how many years will it be before I have $6,000?

   This is a case for the `Rule of 72': at an interest rate of i%, your principal doubles in 72/i time periods. Hence, in this case, it quadruples in 144/4 = 36 time periods.

8. Define capitalised cost.

   The capitalised cost of an infinite series of payments is the present worth of that series; if one payment in the series is A and the interest rate is i, the capitalised cost is A/i.

9. I have just bought an asset costing $80,000. There is a slight ambiguity in the tax rules: under one interpretation, I can depreciate it over ten years using the straight-line method. Under the second interpretation, I can depreciate it using the declining balance method at 10% per year. Which interpretation would I prefer?

   You would prefer the straight-line method; both methods eventually allow you to deduct the whole cost of the purchase from pre-tax income, but the declining balance method takes longer to do so, so the present worth of the series of deductions is less.

10. My MARR is 10%. I have two proposals in front of me: Proposal A involves a large immediate investment, and yields a substantial payback at the end of three years; Proposal B involves a fixed annual expenditure, and a (larger) annual return. Present-worth analysis ranks both equally. If my MARR increases to 12%, which proposal will I favour?

    B. (As the MARR increases, the importance of future paybacks diminishes the further in the future they are.)

    Long Answer Section

11. In a paragraph or less, describe the Monte Carlo method, the conditions under which you would use it, and how you would interpret its results.

    See Lecture 17: 16. Monte Carlo Method

12. Annual costs for two alternatives that perform the same service have been estimated as follows:

    End of Year	Alternative A	Alternative B
    	(Actual Dollars)	(Real Dollars)
    1	120	100
    2	132	110
    3	148	120
    4	160	130

    The inflation rate is 6% per year, and your real MARR is 9%. Which alternative would you choose?

    The key point here is remembering the difference between real dollars and actual dollars. Your best policy is to deflate the actual dollar amounts for A. Once you've done this, you can see that they're larger than the corresponding amounts for B every year except Year 4. It is thus not actually necessary to calculate the present cost of each option; A clearly costs more, so B is the better choice.

13. A company is considering the following four projects (all sums in $000's):

    End of Year	A	B	C	D
    0	-100	-20	-120	-30
    1	40	6	25	6
    2	40	10	50	10
    3	60	10	85	19

    The following limitations hold:

    • No more than $140,000 can be spent at time 0
    • A and C are mutually exclusive.
    • To do either B or D, you must also do either A or C
    • B and D are mutually exclusive.

    Your MARR is 15%.

    List all feasible combinations of projects, and identify the best combination.

    The feasible combinations are {A}, {A,B}, {A, D}, {C}, {B, C}. The present worth of a combination is the sum of the present worths of the projects involved, so you just need to calculate the present worth of each project. All the present worths except A turn out to be negative, so you should just do A.

14. A company is considering the purchase of a new machine. It costs $9,600, and has a useful life of twelve years, after which it will have a salvage value of $1,600. It costs $2,100/year to operate.

    The machine falls into Asset class 8: declining balance depreciation at 20% per annum. Your company pays taxes at 50%, and your after-tax MARR is 8%. What is the after-tax equivalent annual cost of the machine?

    The best approach is to figure out the present worth of the purchase price and salvage value, convert this to an equivalent annual cost, then add on the operating expenses, which are already expressed as an equivalent annual cost:

    The present worth of the purchase price is 9600 * CCTF, where CCTF is the capital cost tax factor. The present worth of the salvage is 1600 * CCTF * (P/F,0.08,12), (We multiply the salvage income by the CCTF because we have to deduct this income from the balance on the company books for asset class 8, and thus we lose the future tax deductions we could otherwise have made against this balance.)

    Now we multiply this present worth by (A/P,0.08,12) to get an equivalent annual cost, and add to it 2,100 * 0.5, representing the after-tax cost to us of the annual operating costs.