The in-class section is closed-book and is worth 40% of the points for the mid-term, and the mid-term itself is worth 15% of the points for the course.

Questions 8 and 12 are worth 6 and 8 points respectively, all the other questions are worth 3 points.

1. What is the Fundamental Equation of Accounting? (3 points)

   Equity = Assets - Liabilities

2. You have a small company that has grown by 15% every year for the last three years. You sell that company for $500,000 in order to start a new company. You borrow $500,000 at 10% interest, and sell $500,000 worth of stock in the new company, to members of the public who were impressed by the performance of your last company; so the new company starts off with $1,500,000 in assets. What is the weighted cost of capital to the new company, and what should the pre-tax MARR be? (3 points)

   The tricky question here is what rate of return you want on the $500,000 you're putting in. Some people wanted 15%, some wanted 10%, some were satisfied not to earn anything at all on it. I counted all these as correct, though I can't see why you'd be going into business if you don't want to make any money.

3. Briefly define and distinguish between a company's Balance Sheet and Income Statement. (3 points)

   The Income Statement is an account of company cash flows over a fixed period, usually a year. It would normally include income from sales, and expenditures on labour, materials, etc.

   The Balance Sheet is a snapshot of the company's state at an instant in time. It should list all assets and debts, and show the company's equity as the difference between them.

4. What is an aspiration level, and when would you use it? (3 points)

   In the most general terms, the aspiration level for any one of the inputs to an economic analysis is the value of the input parameter at which the verdict of the analysis changes from `No Go' to `Go'. Identifying the aspiration level for the important parameters can help to focus market research -- instead of asking, ``Do we have any idea what the sales price might be?'', we can ask, ``Do we expect the sales price to be above or below $12.35?'' (which may be an easier question to answer.)

   A particular example of an aspiration level is the break-even point for sales. This is the point where the verdict changes from ``We'll lose money'' to ``We'll make money''.

5. What is the acid-test ratio, and how is it used? (3 points)

   It's the ratio (cash + accounts receivable)/(total liabilities). It gives a measure of how capable the company is of meeting its debts from cash on hand, excluding resources tied up in inventory which may be difficult to liquidate at short notice. Its importance, and the value it needs to have for the company to be healthy, vary from industry to industry. In some industries, for example, inventory is easy to move and doesn't decay over time (for example, stockpiles of oil), whereas in other industries, inventory may be hard to move and perishable (stockpiles of milk; 1998-model cars in January 1999).

6. 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 is the strongest conclusion you can reach 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%

   This question is explored in the last question of Assignment 7, due on March 5.

7. Why does ranking proposals in order of their IRR sometimes give misleading results? How can your analysis be modified to allow for this? (3 points)

   The problem I had in mind was that a ranking in order of IRR maximizes rate of return, whereas what we want to do is to maximize dollars of profit. This can be solved using an incremental analysis.

   Some people mentioned that use of IRR can lead to multiple solutions. I also counted this as right, and this problem can be solved by using the ERR instead of the IRR. Suggesting incremental analysis as the answer to this problem is wrong, though -- we can still get multiple IRR's from an incremental analysis.

8. 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? (6 points)

   This is just 80,000 * 10 * (CCTF(d=20%) - CCTF(d=30%)).

   (You can work out the solution one year at a time instead, but this is very tedious.)

9. What is the effective annual rate corresponding to a nominal annual rate of 12%, compounded monthly? (3 points)

   A nominal annual rate of 12% is a nominal monthly rate of 1%. And we're compounding monthly, so this is also the effective monthly rate. So the effective annual rate is (1.01)¹²-1.

10. 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%? (3 points)

    Let the amount be F. Then, equating present values, we have

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

    from which we can find F.

11. 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? (3 points)

    A nominal rate of 8% per year is a nominal rate of 4% per six months, and the compounding interval is six months, so 4% is also the effective six-monthly interest rate. So the amount is

    F = 4000(F/P,0.04,40)

12. Alice is considering the purchase of a new lawn-mower. The two models she is considering have the following characteristics:

    	Model A	Model B
    Cost	350.00	120.00
    Maintenance / year	90.00	100.00
    Life	10 years	4 years

    Alice's MARR is 5%.

    1. Choosing a study period which is the least common multiplier of the mower lifetimes, which mower has the lower equivalent annual uniform cost? (4 points)
    2. Suppose model A has a salvage value of $ x after 4 years. What is the minimum value that x must have for A to be the better buy? (4 points)

    The difficult part of this analysis is to come up with a fair basis for comparison. For the first part of the question, we need to consider a study period of 20 years. So whichever option we go with, we must make sure that the grass gets cut for 20 years. This means buying a new model A after 10 years, or new model B's after 4, 8, 12, and 16 years. Calculate the present value of these purchases:

    PW(A) = 350 + 350(P/F,i,10)

    PW(B) = 120 + 120(P/F,i,4) + 120(P/F,i,8) + 120(P/F,i,12) + 120 (P/F i,16)

    (Note that I've left out the maintenance costs.) Now, we spread this cost evenly over the twenty years and add maintenance:

    EUAC(A) = PW(A)(A/P,i,20) + 90

    EUAC(B) = PW(B)(A/P,i,20) + 100

    These come out to be almost exactly equal: $135 and $133 respectively. B is a bit cheaper, so we can go with B. (Though it would also be plausible to say that the two options are indistinguishable, given that the uncertainties in the analysis almost certainly amount to more than $2.)

    For part (ii), we can go to a 4-year study period. To find the break-even point for the salvage value of A, solve the equation

    350 + 90(P/A,i,4) - x(P/F,i,4) = 120 + 100(P/A,i,4)

    for x.