Question 1.  A newly-discovered oil-bearing geologic formation is estimated to contain 500,000 barrels (bbl) of crude oil.  You have been asked to evaluate potential development of the field over a five year period.  If developed, the field is expected to produce 100,000 barrels (bbl) of crude oil during its first year of operation. Production in succeeding years is expected to decline by 10% from the previous year's production.   Investment required to initiate and sustain production for five years is

$5,000,000. (Assume that the investment can be made in year 0 and that no further investments are needed over the five year period). The price of crude oil is estimated to be $103.23 / bbl and will remain at that price for the next five years.  Using present worth analysis and a MARR of 8%,

would you recommend that the firm invest to develop production from the opportunity? (You may neglect the value of the crude oil left in the field after five years of production).

(a)  Draw an appropriate cash flow diagram.

(b)  Indicate the formulas and factors used to evaluate the cash flow diagram.

(c)  Perform the calculations and indicate your results.  What recommendation do you make and why?

Question 2. You are part of a team preparing a bid for a civil engineering project. The project requires that a roadcut be completed for which approximately 1,000,000 tons of rock and soil must be removed over a period of four years. Regardless of the alternative selected, the rock and soil removal will require four years to complete. You have been asked to compare the costs of using two different items of equipment so that the lower cost alternative may be chosen. Using the data below, recommend the lower cost choice.  Note that the life of the Model 5237 Rock Raptor is two years, while that of the Model 4389 Big Bite is four years.  Use an Annual Equivalent Cost (AEC) analysis to support your answer. (Use MARR = 10%)

(a) Draw an appropriate cash flow diagram for each alternative to cover the four-year analysis period.

(b) Indicate the formulas and factors used to evaluate the cash flow diagrams.

(c) Perform the calculations and indicate your results.  Which alternative do you recommend and why?

Question 3. Examine the alternative investments below.

(a) Classify each alternative as simple or non-simple.  Justify your answer in each case. (b)  For which of the alternatives does a unique, positive i* exist?  Justify your answer.

Question 4. Southwest Airlines reportedly achieves competitive advantage by smart purchasing of fuel contracts, which "lock in" fuel prices for a given period of time. Suppose the price of jet fuel is $3.50 per gallon today and is expected to increase by $0.25 per gallon each year over the next four years. Assume that Southwest uses 800,000 gal of fuel per year on one of its flights between Baltimore- Washington International (BWI) and Louisville, KY (SDF) and that usage will remain constant over the next four years.  Southwest has an opportunity to enter into a fuel contract which will guarantee a $3.99 / gal price for the next four years. Southwest owns no fuel storage facilities, so it cannot simply buy fuel today and store it for future use. At a MARR of 5%, should Southwest enter into a contract at $3.99 / gal for four years or should it buy fuel at the prevailing market price each year? (a)  Draw an appropriate cash flow diagram for each alternative.

(b) Indicate the formulas and factors used to evaluate the cash flow diagrams. (c)  Perform the calculations and indicate your results.

Question 5. In developing a formula for the gradient series present worth factor on page 102 of his text, Park states that the arithmetic-geometric series has the finite sum

0 + x + 2x²   + ... + (N-1)x^N-1     =  x [ (1-Nx^N-1 + (N-1)x^N ) / (1-x)² ) ]

Demonstrate that the expression on the right in fact represents the sum of the series on the left.