### Solutions to Capital Budgeting Techniques Practice Questions and Problems

#### Solutions to Capital Budgeting Practice Questions

1. A payback period of two years simply means that the cash flows sum to the original amount of the investment. It is possible for the net present value to be negative for this project if the cash flows appear later, rather than earlier (that is, most in the second year) and the discount rate is sufficiently high.
2. The profitability index criteria is that a project should be accepted if its PI is greater than 1.0. This is equivalent to saying that the project should be accepted if its NPV is greater than zero. The criteria for the PI and NPV are directly relate d since both techniques require comparisons of the present value of the inflows with the present value of the outflows.
3. A project's IRR will be less than its MIRR if the reinvestment rate is greater than the project's IRR. This is not likely to occur, because the firm will invest its funds in these higher yielding investments (where the intermediate cash flows would be invested) instead of the project. However, if there is some type of restriction in investing in this alternative investment (that is, a limit on when or how much to invest), then this could occur.
4. A project that does not pay back (in the discounted payback period method) by construction cannot have a positive net present value. A project does not pay back if its discounted cash flows over its entire useful life do not sum to its original invest ment (thus, a NPV < \$0).

#### Solutions to Capital Budgeting Problems

1. Initial outlay = \$200,000
1. If r = 0%, NPV = \$200,000 + 50,000 + 50,000 - 200,000 = \$100,000
2. If r = 5%, NPV = +\$65,730
3. IRR = 18%
4. MIRR @ 5% = 15.43%

PV of outflows = \$200,000
FV of inflows = \$50,000 (1 + 0.05)2 + \$50,000 (1 + 0.05) + \$200,000 = \$307,625

FV = PV (1 + r)n
\$307,625 = \$200,000 (1 + MIRR)3

2. Initial outlay is \$50,000.
1. This project will have two values that cause the NPV to be equal to zero: 0% and approximately 41.5%. Neither is meaningful for decision-making: For discount rates below 0%, the net present value is negative; for discount rates above 0% but below 41 .5%, the net present value is positive; for discount rates above 41.5%, the net present value is negative.
2. NPV = \$1,938.24 = -\$50,000 + \$47,619 + \$90,703 - \$86,384

3. 0.96 = \$x/\$1,000,000
NPV = \$960,000 - \$1,000,000 = -\$40,000