Question

The Sloan Corporation is trying to choose between the following two mutually exclusive design projects: Year Cash Flow (0) -$63,000 32,000 32,000 32,000 Cash Flow (11) $18,100 9.750 9,750 9.750 6.66 points eBook Print a-1 If the required return is 11 percent, what is the profitability Index for both projects? (Do not round Intermediate calculations. Round your answers to 3 decimal places, e.g., 32.161.) References Project Project II

Answer 1

a-1 PROFITABILITY INDEX

Project I	1.241
Project II	1.316

a-2 The project that should be accepted based on profitability index:

Project II

• since Project II has a higher profitability index than Project I.

b-1 NPV

Project I	$15,198.87
Project II	$5,726.22

a-2 The project that should be accepted based on NPV:

Project I

• since Project I has a higher NPV than Project II.

WORK

• Project I

	Cash Flow ($)	Present Value of 1 at 11%	Present Value ($)
Year 1	32,000.00	0.9009	28,828.83
Year 2	32,000.00	0.8116	25,971.92
Year 3	32,000.00	0.7312	23,398.12
Totals	96,000.00		78,198.87
Amount invested			(63,000.00)
Net present value			15,198.87

Profitability Index = PV of future cash flows ÷ Initial investment = 78,198.87 ÷ 63,000 = 1.241

• Project II

	Cash Flow ($)	Present Value of 1 at 11%	Present Value ($)
Year 1	9,750.00	0.9009	8,783.78
Year 2	9,750.00	0.8116	7,913.32
Year 3	9,750.00	0.7312	7,129.12
Totals	29,250.00		23,826.22
Amount invested			(18,100.00)
Net present value			5,726.22

Profitability Index = PV of future cash flows ÷ Initial investment = 23,826.22 ÷ 18,100 = 1.316

NPV

• Net present value (NPV) is the difference between the present value of cash inflows and the present value of cash outflows over the life of an investment project.
• NPV is used to evaluate investment projects in capital budgeting.
• A project with a positive NPV is accepted. A positive NPV indicates that the project will result in net cash inflows in today's dollars.
• A project with a negative NPV is rejected. A negative NPV indicates that the project will result in net cash outflows in today's dollars.
• The cash flows are discounted at a required rate of return. It may be a weighted average cost of capital, cost of debt, etc.
• In the case of mutually exclusive projects, a project with the highest NPV is accepted. However, if all projects have negative NPV, all such projects are rejected.

PROFITABILITY INDEX

• The profitability index is a ratio that expresses the relationship between the costs and benefits of a project.
• Profitability index = PV of future cash flows ÷ Initial investment
  • Profitability index greater than 1: Project should be accepted (it indicates the present value of anticipated future cash inflows are more than the present value of cash outflows)
  • Profitability index less than 1: Project should be rejected. (it indicates the present value of anticipated future cash inflows are less than the present value of cash outflows)
  • Profitability index equal to 1: Project is indifferent. (it indicates the present value of anticipated future cash inflows equals the present value of cash outflows)
• In case of mutually exclusive projects, the project with the highest profitability index is accepted.