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(ECON115)[2010](f)midterm~kchungaa^_21200.pdf
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Econ 115 Engineering Economics and Finance Name:______________
Fall, 2010 ID:_________________
Midterm Exam
Instructor: YU, Yan Lecture #:____________

General instruction: This is a closed-book exam. You may use calculators. Steps of calculation must be shown, including functional symbol of factors (such as (P/A, 10%, 6)) and its value (here 4.3553). Draw cash flow diagram whenever possible (it counts for 10% of total marks). You have 120 minutes for this exam.

(2.2) Question 1 (10 points)
A basic lesson to be learned in life is to minimize annual maintenance fees (and sales commissions) on portfolios of securities (stocks and bonds). To illustrate this lesson, consider an actively managed stock market fund that charges 1% per year as its management fee. A less actively managed fund (e.g., an index fund) charges 0.5% per year. For a one-time investment of $100,000, how much will this decrease in annual management fee (i.e., 0.5%) save during a 20-year period? Let i=10% per year and express your answer as a percentage of the original $100,000.


If the management fee is charged on initial investment amount:
The reduction in management fees between an actively C managed fund and an index fund is 0.005 ($100,000) = $500 per year. The compound worth of this difference in 20 years is F = $500 (F/A, 10%, 20) = $500*57.275=$28,637.5. This is 28.64% of the original investment of $100,000.

If the management fee is charged on the investment balance at the end of each year (which usually is the case):
F1 = 100,000(F/P, 10%, 20) (1-1%)^20
F2 = 100,000(F/P, 10%, 20) (1-0.5%)^20

(F2-F1)/100,000 = 58.33%















(2.2, 4.8) Question 2 (20 points)
A foundation was endowed with $10,000,000 in July 2000. In July 2004, $3,000,000 was expended for facilities, and it was decided to provide $250,000 in the July of each year forever to cover operating expenses. The first operating expense was in July 2005, and the first replacement expense is in July 2009. If all money earns interest at 5% after the time of endowment, what amount would be available for capital replacements at the end of every fifth year forever? (Hint: Draw a cash-flow diagram first.)

$10,000,000






2000 2004 2005 2006 2009 2014 ~ Forever














$250,000/yr





X X
Amount at July 2004:

$100,000(1.05)4 . $3,000,000 = $12,155,000 C $3,000,000 = $9,155,000

$9,155,000







2004 2005