Question

 Solar Designs is considering an investment in an expanded product line. Two possible types of expansion are under review. After investigating the possible​ outcomes, the company made the estimates shown in the following​ table:

Initial investment   $13,000   $13,000
Annual rate of return      
Pessimistic   12%   10%
Most likely   23%   23%
Optimistic   24%   26%

The pessimistic and optimistic outcomes occur with a probablity of​ 25%, and the most likely outcome occurs with a probability of​ 50%.

a.  Determine the range of the rates of return for each of the two projects.

b.  Which project is less​ risky?

c.  If you were making the investment​ decision, which one would you​ choose? What does this imply about your feelings toward​ risk?

d.  Assume that expansion​ B's most likely outcome is 24​% per year and that all other facts remain the same. Does this change your answer to part ​c?

Answer 1

In the given question, let's assume the two projects are:- Project A and Project B

a. Range of rates of return

Project A

Pessimistic return = 13000*12%*25% = 390

Most likely return = 13000*23%*50% = 1495

Optimistic return = 13000*24%*25% = 780

Total return under Project A = 2665

Rate of return = Total return/Total investment = 2665/13000 = 20.5%

Project B

Pessimistic return = 13000*10%*25% = 325

Most likely return = 13000*23%*50% = 1495

Optimistic return = 13000*26%*25% = 845

Total return under Project A = 2665

Rate of return = Total return/Total investment = 2665/13000 = 20.5%

b) Since the return of both the projects is same, both the projects are equally risky.

c) Since the return in both the projects is same, we are indifferent in choosing between Project A and Project B.

d) If B's most likely outcome is 24%, our calculation is revised as under:-

Pessimistic return = 13000*10%*25% = 325

Most likely return = 13000*24%*50% = 1560

Optimistic return = 13000*26%*25% = 845

Total return under Project A = 2730

Rate of return = Total return/Total investment = 2665/13000 = 21%

In the light of above, project B is yielding more return, hence we would invest in Project B.