Discounted Capital Budgeting Techniques

Discounted Capital Budgeting Techniques

• Capital investment evaluation methods consider the time value of money.
• Cash inflows and outflows are discounted to their present value.

Net Present Value (NPV)

• The difference between the present value of net cash inflows and the present value of net cash outflows (initial investment).

Net Present Value (NPV) Illustration

• An investment opportunity costing $180,000 is expected to yield net cash flows of $60,000 annually for five years with a hurdle rate of 12%.

• To find the net present value, calculation of the present value of net cash inflows and outflows is required.

• The investment occurs at the current time, it is already at present value.

• Present value of cash inflows = $60,000 * 3.605 = $216,300

• Net Present Value = $216,300 - $180,000 = $36,300

• The investment should be pursued if the present value of net cash inflows is greater than or equal to the present value of net cash outflows.

• The investment should be pursued if the net present value is at a positive amount (greater than zero) or equal to zero.

• Salvage value should form part of the present value of net cash inflows if it exists for an investment because the investment can be sold at salvage value at the end of its useful life.

• Present value of cash inflows = $60,000 * 3.605 = $216,300

• Present value of salvage value = $5,000 * 0.567 = $2,835

• Present value of net cash inflows = $216,300 + $2,835 = $219,135

• Net Present Value = $219,135 - $180,000 = $39,135

• The PV factor used to compute the present value of salvage value is based on PV of 1 because the salvage value will only be realized when it is sold at the end of the useful life of the investment.

• Salvage value should be after tax before multiplying to the PV factor if there is a given tax rate.

Internal Rate of Return (IRR)

• It equates the present value of net cash inflows with the net investment.
• The discount rate is required for the net present value to be exactly zero.
• At the internal rate of return, the net investment and the annual net cash inflows are equal.
• PV factor using PV of ordinary annuity at internal rate of return with the annual net cash inflows should equal the value of the net investment.
• To find the rate equal to the PV factor of 3 with a period of 5 years, trial and error should be used.
• With a rate of 19%, the PV factor would be 3.058, and the present value of net cash inflows at this rate would be $183,480.
• Increasing the rate decreases the present value.
• The present value at 19% is greater than the amount that is wanted, meaning the IRR is greater than 19%.
• With a rate of 20%, the PV factor is 2.991, and the present value of net cash inflows at this rate would be $179,460.
• The IRR is between 19% and 20%, and interpolation should be used to find the exact rate.
• The IRR would be 19.866%.
• The investment should be pursued if the IRR is greater than or equal to the company’s cost of capital, otherwise, it must be rejected.

Profitability Index

• The ratio of the present value of cash inflows to the initial investment.
• An investment or a project greater than or equal to 1 should be pursued, otherwise, it is rejected
• A project with a higher profitability index is preferred.

Discounted Payback Period

• Recognizes the time value of money.
• Periodic net cash inflows are discounted using an appropriate required rate of return
• The payback period is computed using the discounted cash flows.
• With a new machine costing P50,000 with a three-year useful life, and no salvage value at the end of three years, is expected to bring after tax cash inflows of P25,000 per year.
• To compute for the discounted payback, calculation of the discounted periodic cash inflows is needed.
• Multiply the PV factor using PV of 1 for each year even if cash inflows are uniform
• Year 1: Periodic cash flows=25,000, PV factor=0.833, Discounted cash flows=20,825
• Year 2: Periodic cash flows=25,000, PV factor=0.694, Discounted cash flows=17,350
• Year 3: Periodic cash flows=25,000, PV factor=0.579, Discounted cash flows=14,475
• After computing the discounted periodic cash inflows, the discounted payback period is determined by using the same method of determining payback period under uneven cash flows.
• 50,000 investment balance with 20,825 discounted cash flows is paid back in one year.
• Year 2: 29,175 investment balance with 17,350 discounted cash flows is paid back in one year.
• Year 3: 11,825 investment balance with 14,475 discounted cash flows at 0.817.
• Discounted Payback Period is 2.817

Equivalent Annual Annuity (EAA)

• A method which can be used to compare projects of unequal lives.
• Comparing the NPV for the whole life of projects with unequal lives is misleading.
• The remedy for comparing projects like this is the equivalent annual annuity approach.
• Using the equation helps compare the NPV for 1 year, and not NPV for the whole life of the project.
• Desirability of projects can be compared even if they have unequal lives.
• The PV factor is based on PV of ordinary annuity.
• The project with higher EAA is preferred.

Fisher’s Rate or Net Present Value Point of Difference

• Fisher’s rate means the interest rate where the net present values of two mutually exclusive projects become equal.
• Fisher’s rate only means useful information in practice if the ranking is made based on the net present value.
• The principle of ranking is in contradiction with the concept of long-term profit maximization.
• The transformed net present value, which is free of distorting effects (and assuming equal required rates of return,) gives the same ranking list as the internal rate of return.
• Fisher’s rate has no importance in business decisions.