The exam is in two parts. The first, in-class, part is closed-book. The second, take-home, part consists of the Extended case study, `Welcome to the Real World', on pp. 255-260 of Fraser, Bernhardt, Jewkes and Tajima, and is due on Monday, February 28. The in-class exam is worth a total of 40 points, and the take-home is worth 60 points.

Closed Book Section: 40 minutes

Assume the inflation rate is zero unless the question says it isn't. Assume all interest rates are rates per year, compounded annually on the year-end balance. Questions 1-15 are worth 2 points each, and Question 16 is worth 10 points. Note that Question 16 offers a choice of two parts, A or B. Only do one or the other. Don't do both.

  1. What is leverage? If you own a company, would you prefer to have a high or a low amount of leverage? Why?

    It's the ratio of debt to equity. If you expect the company to increase in value, high leverage will increase your personal gains; on the other hand, it will also increase your losses if the company loses value.

    Questions 2-5 are about inflation. The inflation rate is f%, and on January 1, 2000, a real dollar and an actual dollar are worth exactly the same amount. (You'll need to know the difference between real and actual dollars in each question; since the two words are easily confused, it may help to remember that real dollars are also known as `constant dollars' or `now dollars', while actual dollars are also known as `then-current dollars' or `then dollars'.)

  2. On January 1, 2000, a loonie falls out of your pocket and rolls under the couch. You find it a year later. When you find it, it is worth:

    1. A real dollar
    2. An actual dollar
    3. Both (a) and (b).
    4. Neither (a) nor (b).

    An actual dollar

  3. On January 1, 2000, you deposit $100 in a bank that pays interest at f%. A year later, you have in the bank:

    1. 100 real dollars
    2. 100 actual dollars
    3. Both (a) and (b).
    4. Neither (a) nor (b).

    100 real dollars

  4. If you deposit a dollar on Jan 1, 2000, in a bank that pays interest at i%, the value of your investment ten years in the future, in actual dollars, will be:

    1. (1+f)10
    2. (1+i)10/(1+f)10
    3. (1+f)10/(1+i)10
    4. (1+i)10
    5. (1+i)10(1+f)10

    d

  5. If you deposit a dollar on Jan 1, 2000, in a bank that pays interest at i%, the value of your investment ten years in the future, in real dollars, will be:
    1. (1+i)10(1+f)10
    2. (1+i)10/(1+f)10
    3. (1+f)10/(1+i)10
    4. (1+if)10

    b

  6. In 1981, a change occurred in the way Revenue Canada calculates depreciation on assets. What was this change? Did the change increase or reduce the tax burden on a typical company?

    In 1981, the rules changed so that only 50% of the cost of an item bought in any given year could be included in the depreciation calculation for that year, the other 50% being included in the depreciation calculation for the subsequent year. This increased the tax burden on all companies affected.

  7. Give two advantages and two disadvantages of being a corporation rather than a single proprietorship.

    See notes, ``The Company".

  8. If I invest $2,000 at 12% interest, compounded annually, about how long will it be before I have $8,000?

    This can be solved using the (P/F,i,N) formula, but it's quicker and easier to use the Rule of 72: an investment doubles in 72/i years, where i is the interest rate.

  9. My MARR is 25%. I am considering two proposals: Proposal X involves an immediate expenditure of $10,000, which will yield a large single influx of cash in ten years time. Proposal Y involves the same initial expenditure, and an annual influx of cash every year for the next eight years. Both proposals have the same present worth. If my MARR is reduced to 20%, which proposal will I favour?

    This is the most important question on the quiz, and you should make sure you have a firm grasp of the principle involved. The principle is that as the interest rate grows, future cashflows become less and less visible. (You could envisage the interest rate as a kind of fog that obscures your view of the future.) So if at the poor visibility of 25% interest, the ten-years-distant payback from X looks as big as the next-eight-years payback from Y, then when the visibility improves to 20% interest, the payback from X will loom larger still.

  10. Three women are having breakfast: the CEO of an insurance company, the CEO of a mortgage company, and a retired CEO. The morning paper has a headline: ``Inflation rates expected to rise sharply!''. For whom is this good news, and for whom is it bad news?

    It's definitely bad news for the retired CEO, unless her pension is inflation-linked.

    I had been thinking of the insurance company as a life insurance company, in which case inflation is good news, since life insurance companies usually promise a fixed sum on death, and that sum can now be paid out in inflated dollars. But the question leaves open the possibility that the company insures against fire or theft; in which case, if the amount to be paid out is set at replacement cost, the news is nether good nor bad. (Since the replacement cost in real dollars will be constant.)

    For the mortgage company, it's bad news: they've lent a sum of money in the past, and they're now going to get paid back in deflated dollars. (If the mortgages are variable-rate, they may be able to put the rates up to cushion the effect.)

  11. What is the effective annual rate corresponding to a nominal annual rate of 12%, compounded monthly?

    A nominal annual rate of 12% compounded monthly is an effective monthly rate of 1%, compounded monthly. So the equivalent effective annual rate is (1.01)12-1.

  12. What single amount, paid to you five years from now, is equivalent to a uniform annual series of $1,000/year paid to you over the next 12 years, when the effective annual interest rate is 7%?

    Suppose the amount is x, then equate present worths:

    x(P/F,0.07,5)=1000(P/A,0.07,12)

  13. What amount will accumulate in 20 years from an initial investment of $4,000 at a nominal interest rate of 8% per year, compounded semi-annually?

    This is an effective interest rate of 4% per six months, so the accumulated amount will be 4000(F/P,0.04,40).

  14. When a proposal is analysed to find the IRR, two solutions are obtained: IRR = 5% and IRR = 45%. If the auxiliary rate of return is 10%, what can you conclude about the ERR?

    1. You can conclude nothing about the ERR
    2. The ERR will be between 5% and 10%.
    3. The ERR will be between 10% and 45%
    4. The ERR will be between 5% and 45%

    (d)

  15. Why does ranking proposals in order of their IRR sometimes give misleading results? How can your analysis be modified to allow for this?

    If the proposals being considered are the ONLY ones available, you need to consider which makes the best use of your TOTAl investment funds. It's better to get a medium rate of return on a large sum than an excellent rate of return on a small sum, if the latter choice leaves a lot of funds uninvested. To take this into account, you should do an incremental analysis.

    `

    Section 2: Long Answer Questions, 10 points each. Answer 1 out of 2.

    1. Your company needs to purchase ten oscilloscopes during the coming year. The oscilloscopes are top-of-the-line models, with a built-in Pentium processor, and cost $80,000 each. You are presenting an argument to Revenue Canada that they should be considered as computers, and depreciated at 30% per annum. Revenue Canada thinks that they're generic electronic equipment, which is depreciated at 20% per annum. Your company pays tax at 50%, and your pre-tax cash flow every year is at least $500,000. Your after-tax MARR is 5%. What is the present value of convincing Revenue Canada that they're computers?

      The present cost of the purchase is 800,000*CCTF. The value of the CCTF factor depends on the depreciation rate, according to the formula provided in the cribsheet. So you need to calculate 800,000(CCTF(20%)-CCTF(30%)).

    2. A city is installing a new swimming pool at a recreation centre. Two designs are under consideration:

      Design A has an initial cost of $1,500,000, and will need to be overhauled every ten years at a cost of $200,000. Design B has an initial cost of $500,000, and requires $5,000 of maintenance at the end of evey year. Every fifth year it will require an additional major overhaul, costing $100,000, and every fifteenth year it will require an even more major overhaul, costing $150,000.

      If the city's MARR is 5%, which design should they go with?

      Just compare present worths over a suitable time frame. Thirty years is a good choice, since it's a multiple of the overhaul periods. Remember not to include the cost of overhauls in the thirtieth year, since these would cover a period beyond the time horizon.