A firm is considering moving its manufacturing plant from Chicago to a new location. The industrial engineering department was asked to identify the various alternatives together with the costs to relocate the plant and the benefits. The engineers examined six likely sites, together with the do-nothing alternatives of keeping the plant at its present location. Their findings are summarized as follows: Plant Location First Cost ($000s) Uniform Annual Benefit($000s) Denver $300 $52 Dallas 550 137 San Antonio 450 117 Los Angeles 750 167Cleveland 150 18Atlanta 200 49Chicago 0 0The annual benefits are expected to be constant over the 8-year analysis period. Required:(a) Construct a choice table for interest rates from 0% to 100%.(b) IT the firm uses a 10% annual interest in its economic analysis, where should the manufacturing plant be located. Use MARR=15%, and only use Excel to check your results.

City                    2%10%         20%  30%          50%100%

Denver        80.93-22.58-100.47-147.92-200.06-248.20

Dallas        453.59180.88-24.31-149.32-286.69-413.54

SanAntonio407.08174.19-1.05-107.81-225.13-333.46

LosAngeles473.36140.93-109.19-261.57-429.03-583.65

Cleveland-18.14-53.97-80.93-97.36-115.40-132.07

Atlanta       158.9561.41-11.98-56.69-105.82-151.19

Chicago         0.000.00   0.00    0.00     0.00     0.00

b) The manufacturing plant should be located in Dallas (IRR=19%).

Explanation:

We have the cost and uniform annual benefits for each city:

Plant Location First Cost ($000s) Uniform Annual Benefit($000s)

Denver 300 52

Dallas 550 137

San Antonio 450 117

Los Angeles 750 167

Cleveland 150 18

Atlanta 200 49

Chicago 0 0

The cash flow can be written as:

where:

I0: first cost.

CF: uniform annual benefit

i: discount rate

A: annuity factor

The annuity factor that multiplies the CF is equal for every city, so it can be calculated beforehand:

For some rate of returns, we have:

r=2% A=7.33

r=10% A=5.33

r=20% A=3.84

r=30% A=2.92

r=50% A=1.92

r=100% A=1.00

a) Then, for each city, we have this NPV, in function of differents discount rates:

City                    2%10%         20%  30%          50%100%

Denver        80.93-22.58-100.47-147.92-200.06-248.20

Dallas        453.59180.88-24.31-149.32-286.69-413.54

SanAntonio407.08174.19-1.05-107.81-225.13-333.46

LosAngeles473.36140.93-109.19-261.57-429.03-583.65

Cleveland-18.14-53.97-80.93-97.36-115.40-132.07

Atlanta       158.9561.41-11.98-56.69-105.82-151.19

Chicago         0.000.00   0.00    0.00     0.00     0.00

b) The firm uses a 10% annual interest. For this situation, we can look up in the table from the previos question and see that Dallas has the higher NPV at this discount rate.

So the manufacturing plant should be located in Dallas.

(NOTE: the IRR of the project relocating to Dallas is 19%)  

d. low interest rates