56:054 Engineering Economy

Prof. O'Grady

 

  1. Jessica Young, an UI student, considers herself an average cigarette smoker, for she consumes about a carton a week. She wonders how much money she could accumulate by the time she reaches 60 if she quit smoking now and put her cigarette money into a saving account. Cigarettes cost $10 per carton. Ron expects that a savings account would earn 6% interest, compounded semi-annually. Compute Jessica's future worth at age 60. (Jessica is now 20 yrs old) (10 points)
  2. Solution: Semi-annual saving $10/carton x 26 weeks = $260

    FW = A(F/A,3%, 80) = 260 x 321.363 = 83,554.38

     

  3. A firm is trying to decide which of two devices to install to reduce costs in a particular situation. Both devices cost $1000 and have useful lives of 5 years and no salvage value. Device A can be expected to result in $300 savings annually. Device B will provide cost savings of $500 the first year, but will decline $50 annually, making the second-year savings $450, the third-year savings $400, and so forth. With interest at 6%, which device should the firm purchase? (Use benefit/Cost ratio to solve this problem) (20 point)
  1. PW of cost = $1000
  2. PW of benefits = 300(P/A, 6%, 5) = 300x4.212 = 1263.6

    B/C ratio = 1.263

  3. PW of cost = $1000

PW of benefits = 500(P/A, 6%, 5) - 50(P/G, 6%,5) = 500x4.212 - 50 x 7.934 = 1709.3

B/C ratio = 1.709

 

  1. Consider the three mutually exclusive alternatives below. Each alternative has a 10-year life and no salvage value. If the minimum attractive rate or return is 5%, which alternative should be selected? (20 points)

 

 ABC
Initial cost$2000$4000$6000
Uniform400650700
  1. Complete the following Benefit-cost graph
  2.  

    A: PW Benefits = 400(P/A, 10, 5%) = 400 x 7.722 = 3089

    B: PW Benefits = 650(P/A, 10, 5%) = 5019

    C: PW Benefits =700(P/A,10,5%) = 5405

  3. Based on this graph, which alternative should be selected? Why?
  4. C has a B/C ratio less than 1, C is out

    Consider Upgrade from A to B, The incremental B/C ratio (the slop of line AB ) = (5019-3089)/(4000-2000) is less than 1, should still go with A.

  5. Suppose B is the preferred at its current initial cost of $4000, how much higher than $4000 can the initial cost be and still have B the preferred alternative?

 

NPW of alternative A = 3089 - 2000 = 1089

NPW of alternative B = 5019 -x

NPW of alternative C = 5405 - 6000 = -595** ç Since it is negative, you should never upgrade from B to C, as a result you don't spend any money more than $4000 to upgrade B to C. Sorry this question is very confusing.)

 

 

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  [ Professor O'Grady ]