The quiz is closed-book. You don't need a calculator; you can write the answer in terms of unevaluated formulas, such as (F/P,i,N).

1. Define the internal rate of return. How is it calculated?

   It is the rate of return at which the present worth of a series of cash flows would be zero.

2. Define the external rate of return. How is it calculated? What is the auxiliary rate of return, and what role does it play in this calculation?

   The external rate of return is the rate of return at which the present worth of a series of cashflows would be zero, where all cash flowing in during the project is re-invested at the auxiliary rate of return, that being the best rate available in practice.

3. What is the MARR? What determines its value?

   The minimum acceptable rate of return; its value is determined by the cost of capital to the company.

4. Which of the following statements are true?
   • For a given investment, the IRR is always equal to or greater than the ERR.

     False.

   • For a given investment, the MARR is always greater than or equal to the auxiliary rate of return.

     True

   • A correct calculation of the ERR will always yield exactly one solution.

     True

5. A given investment yields an immediate income of $1,000, followed by expenses of $900, $800 and $200 over the next 3 years, followed by a final income of $1,500. What is the present worth of the investment if the interest rate is zero? What limit does the present worth of the investment approach as the interest rate grows without limit? What can you say about the IRR calculation for this investment. [Do NOT attempt to calculate a value of the IRR.]

   $600; $1,000; IRR will have two solutions.

6. Investment strategy A requires an initial investment of $500, and yields an income of $1,000 two years in the future. Strategy B requires an initial investment of $1,000 to yield $1,900 two years in the future. If the two strategies are mutually exclusive, and these are the only investment opportunities available, which one should we choose? (Our MARR is 10%).

   Choose B.

7. How is the benefit/cost ratio for a project defined?

   PW(benefits)/PW(costs)

8. In considering a project which requires an indefinite series of payouts -- for example, maintenance work on a nuclear waste repository -- how is the cost of this series represented in calculations?

   By the capitalized cost, P = A/i.

9. Name two difficulties faced in the analysis of public projects which are not faced in the private sector.

   Need to consider effect on all interest groups; need to consider all of the non-monetary consequences; need to get re-elected.

10. Distinguish between the physical life and the economic life of an asset.

    The physical life is how long it will last, the economic life is how long it's worth keeping.

11. An asset will need to be replaced some time over the next few years, and the only reasonable replacement is another device of the identical type. Describe, in outline, how you would decide when to make the replacement.

    (See lecture on replacement analysis.)

12. If the nominal annual interest rate on an investment is 12%, and the interest is compounded continuously, what is the effective monthly interest rate?

    Effecctive monthly rate is j, where

    j = e^0.01-1