An existing client in her late 20s comes to the RR's office with her boyfriend. The couple are not married but they want to open
1 answer:
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Answer:
City 2% 10% 20% 30% 50% 100%
Denver 80.93 -22.58 -100.47 -147.92 -200.06 -248.20
Dallas 453.59 180.88 -24.31 -149.32 -286.69 -413.54
SanAntonio 407.08 174.19 -1.05 -107.81 -225.13 -333.46
LosAngeles 473.36 140.93 -109.19 -261.57 -429.03 -583.65
Cleveland -18.14 -53.97 -80.93 -97.36 -115.40 -132.07
Atlanta 158.95 61.41 -11.98 -56.69 -105.82 -151.19
Chicago 0.00 0.00 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 453.59 180.88 -24.31 -149.32 -286.69 -413.54
SanAntonio 407.08 174.19 -1.05 -107.81 -225.13 -333.46
LosAngeles 473.36 140.93 -109.19 -261.57 -429.03 -583.65
Cleveland -18.14 -53.97 -80.93 -97.36 -115.40 -132.07
Atlanta 158.95 61.41 -11.98 -56.69 -105.82 -151.19
Chicago 0.00 0.00 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%)