Net Present Value (NPV):

Internal Rate of Return (IRR):

To solve for each project's IRR, find the discount rates that set NPV to zero:

Profitability Index (PI):

PV Benefits _ $10,966.01

PV Costs $10,630.72 $10,000


B. Using all methods, project X is preferred over project Y. Because both projects are acceptable under the NPV, IRR, and PI criteria, both projects should be accepted if they are interdependent.

C. Choose the project with the higher NPV at k = 12%, or project X.

D. To determine the effects of changing the cost of capital, plot the NPV profiles of each project. The crossover rate occurs at about 6% to 7%. To find this rate exactly, create a project A, which is the difference in cash flows between projects X and Y:

Project X - Project Y = Year Project A Net Cash Flow

1 3,000

Then find the IRR of project A:

Thus, if the firm's cost of capital is less than 6.2%, a conflict exists, because NPVY > NPVX but IRRX > IRRy.

Graphically, the crossover discount rate is illustrated as follows:

4,500 4,000 3,500 3,000 2,500 2,000 1,500 1,000 500 0

NPV Profiles for Project Xand Project Y

NPV Profiles for Project Xand Project Y

4,500 4,000 3,500 3,000 2,500 2,000 1,500 1,000 500 0

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