Question

A firm must choose from six capital budgeting proposals outlined below. The firm is subject to capital rationing and has a capital budget of​ $1,000,000; the​ firm's cost of capital is 15 percent. Please show the work.

Project Initial Investment IRR NPV
1 $200,000 19% $100,000
2 400,000 17 20,000
3 250,000 16 60,000
4 200,000 12 -5,000
5 150,000 20 50,000
6 400,000 15 150,000

Using the internal rate of return approach to ranking projects, which projects should the firm accept?

Using the net present value approach to ranking projects, which projects should the firm accept?

Answer 1

Using the IRR method, Projects 5, 1, and 2 should be accepted first. Under the NPV method, Projects 6, 1, 3, and 5 should be accepted, as they offer the highest combined NPV within the capital budget.

Step-by-step explanation:

When a firm is subject to capital rationing and needs to choose the best projects to invest in, it can use two primary approaches: the Internal Rate of Return (IRR) method and the Net Present Value (NPV) method.

Using the IRR method, a project is considered acceptable if its IRR exceeds the firm's cost of capital, which in this case is 15%. Therefore, the rankings based on IRR from highest to lowest for the projects are:

• Project 5: IRR 20%
• Project 1: IRR 19%
• Project 2: IRR 17%
• Project 3: IRR 16%
• Project 6: IRR 15%
• Project 4: IRR 12%

Therefore, with a budget of $1,000,000, the firm should accept Projects 5, 1, and 2 first, then look to Project 3 or 6 if the budget allows.

Now, when using the NPV method, a project is accepted if its NPV is positive - the higher the NPV, the better the project. The rankings based on NPV from highest to lowest are:

• Project 1: NPV $100,000
• Project 6: NPV $150,000
• Project 3: NPV $60,000
• Project 5: NPV $50,000
• Project 2: NPV $20,000
• Project 4: NPV -$5,000 ( should not be accepted)

With a budget of $1,000,000, using NPV, the firm should accept Projects 6, 1, 3, and 5, as they offer the highest combined NPV without exceeding the capital budget.

Answer 2

On IRR basis projects 1, 2, 3, and 5 will be selected.

On NPV basis projects 1, 3, 5, and 6 will be selected.

Step-by-step explanation:

The firm will accept or choose all the project that has a higher or equal internal rate of interest than cost of capital. However, in the given case project 4 has a lower internal rate of interest (12 percent) than the cost of capital. Thus, projects 1, 2, 3, and 5 will be chosen by the firm. While the firm has budget constraints so it will have no money for projects 4 and 6.

The firm will select all the projects with positive NPV when there is no budget constraint. But in case of budget constraint, the firm will select the project that has high NPV. Thus, Project 1, 6, 3, and 5 will be selected and there will be no money left for projects 2 and 4.