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QuestionSolar Designs is evaluating two expansions. Find the return ranges, assess risk, choose an investment, and analyze changes if rates shift.

Studdy Solution

STEP 1

Assumptions1. The initial investment for both Expansion A and Expansion B is \$12,000. . The annual rates of return for Expansion A areessimistic -16%, Most likely -20%, Optimistic -24%.
3. The annual rates of return for Expansion B areessimistic -10%, Most likely -20%, Optimistic -30%.

STEP 2

First, we need to determine the range of the rates of return for each of the two projects. The range is calculated as the difference between the optimistic and pessimistic estimates.
For Expansion ARange A=Optimistic A−essimistic ARange\, A = Optimistic\, A -essimistic\, AFor Expansion BRange B=Optimistic B−essimistic BRange\, B = Optimistic\, B -essimistic\, B

STEP 3

Now, plug in the given values for the optimistic and pessimistic estimates for Expansion A and Expansion B to calculate the ranges.
For Expansion ARange A=24%−16%Range\, A =24\% -16\%For Expansion BRange B=30%−10%Range\, B =30\% -10\%

STEP 4

Calculate the range for Expansion A and Expansion B.
For Expansion ARange A=24%−16%=8%Range\, A =24\% -16\% =8\%For Expansion BRange B=30%−10%=20%Range\, B =30\% -10\% =20\%

STEP 5

To determine which project is less risky, we compare the ranges. The project with the smaller range is less risky because its returns are less variable.
Comparing the rangesRange A<Range BRange\, A < Range\, B

STEP 6

Since the range of Expansion A is less than the range of Expansion B, Expansion A is less risky.

STEP 7

If you were making the investment decision, you would need to consider your risk tolerance. If you are risk-averse, you would choose Expansion A because it is less risky. If you are risk-seeking, you might choose Expansion B because it has a higher potential return (30% vs24%). This decision implies your feelings toward risk.

STEP 8

Assume that expansion B's most likely outcome is21% per year and that all other facts remain the same. We need to recalculate the range for Expansion B and compare it with the range for Expansion A to determine if this changes the decision.
Recalculate the range for Expansion BRange B=Optimistic B−essimistic B=30%−10%=20%Range\, B = Optimistic\, B -essimistic\, B =30\% -10\% =20\%Compare the rangesRange A<Range BRange\, A < Range\, B

STEP 9

Even with the change in the most likely outcome for Expansion B, Expansion A is still less risky because its range of returns is smaller. Therefore, the answer to part c does not change.

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