Q7 Three mutually exclusive alternatives are being evaluated

Q7. Three mutually exclusive alternatives are being evaluated and their costs and revenues are listed in the following table Alt I Alt 11 Alt IIII Capital Investment Annual Revenues Annual Expenses Market Value Useful Life (vears $300,000 $200,000 $50,000 $50,000 10 $450,000 $100,000 $50,000 $50,000 10 $600,000 $200,000 $100,000 $100,000 10 1) If the MARR is 20% per year and the analysis period is 10 years, use the PW method to determine which alternatives are economically acceptable and which one should be selected(10 marks) 2) If the total capital investment budget available is $500,000, which alternative should be selected? (5 marks)

Solution

(a)

Alternative I:

Annual Revenue = $ 250000, Annual Expense = $ 50000

Net Income = 250000 - 50000 = $ 200000

Market Value (at project completion) = $ 50000

Capital Investment = $ 300000 and Project Tenure = 10 years

MARR = 20 %

PW of Market Value and Net Income = 200000 x (1/0.2) x [1-{1/(1.2)^(10)}] + 50000 / (1.2)^(10) = $ 846569.696

Net PW = 846569.696 - 300000 = $ 546569.696

Alternative II:

Annual Revenue = $ 100000, Annual Expense = $ 50000

Net Income = 100000 - 50000 = $ 50000

Market Value (at project completion) = $ 50000

Capital Investment = $ 450000 and Project Tenure = 10 years

MARR = 20 %

PW of Market Value and Net Income = 50000 x (1/0.2) x [1-{1/(1.2)^(10)}] + 50000 / (1.2)^(10) = $ 217698.883

Net PW = 217698.883 - 450000 = - $ 232301.117

Alternative III:

Annual Revenue = $ 200000, Annual Expense = $ 100000

Net Income = 200000 - 100000 = $ 100000

Market Value (at project completion) = $ 100000

Capital Investment = $ 600000 and Project Tenure = 10 years

MARR = 20 %

PW of Market Value and Net Income = 100000 x (1/0.2) x [1-{1/(1.2)^(10)}] + 100000 / (1.2)^(10) = $ 435397.767

Net PW = 435397.767 - 600000 = - $ 164602.233

As Alternative I is the only option that gives a positive NPW, the same is economically acceptable and should be chosen.

(b) Although the total capital investment budget is $ 500000, only one alternative generates value for the firm (has positive NPW) and therefore only Alternative 1 should be selected at a capital investment of $ 300000. The other two investments generate negative value (negative NPW) and should not be taken up even if the budget is available.