# CAPITAL BUDGETING. Net Present Value and Other Investment Criteria

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1 CAPITAL BUDGETING Net Present Value and Other Investment Criteria

2 Net Present Value (NPV) Net present value is the difference between an investment s market value (in today s dollars) and its cost (also in today s dollars). Net present value is a measure of how much value is created by undertaking an investment. Estimation of the future cash flows and the discount rate are important in the calculation of the NPV.

3 Net Present Value Steps in calculating NPV: The first step is to estimate the expected future cash flows. The second step is to estimate the required return for projects of this risk level. The third step is to find the present value of the cash flows and subtract the initial investment.

4 NPV Illustrated Initial outlay (\$1100) Revenues \$1000 Expenses 500 Cash flow \$500 Revenues \$2000 Expenses 1000 Cash flow \$1000 \$ \$500 x \$1000 x \$ NPV

5 NPV An investment should be accepted if the NPV is positive and rejected if it is negative. NPV is a direct measure of how well the investment meets the goal of financial management to increase owners wealth. A positive NPV means that the investment is expected to add value to the firm.

6 Payback Period The amount of time required for an investment to generate cash flows to recover its initial cost. Estimate the cash flows. Accumulate the future cash flows until they equal the initial investment. The length of time for this to happen is the payback period. An investment is acceptable if its calculated payback is less than some prescribed number of years.

7 Payback Period Illustrated Initial investment = \$1000 Year Cash flow 1 \$ Year Accumulated Cash flow 1 \$ Payback period = 2 2/3 years

8 Advantages of Payback Period Easy to understand. Adjusts for uncertainty of later cash flows. Biased towards liquidity.

9 Disadvantages of Payback Period Time value of money and risk ignored. Arbitrary determination of acceptable payback period. Ignores cash flows beyond the cut-off date. Biased against long-term and new projects.

10 Discounted Payback Period The length of time required for an investment s discounted cash flows to equal its initial cost. Takes into account the time value of money. More difficult to calculate. An investment is acceptable if its discounted payback is less than some prescribed number of years.

11 Example Discounted Payback Initial investment = \$1000 R = 10% PV of Year Cash flow Cash flow 1 \$200 \$

12 Example Discounted Payback (continued) Accumulated Year discounted cash flow 1 \$ Discounted payback period is just under three years

13 Ordinary and Discounted Payback Initial investment = \$300 R = 12.5% Cash Flow Accumulated Cash Flow Year Undiscounted Discounted Undiscounted Discounted \$ \$ \$ \$ Ordinary payback? Discounted payback?

14 Advantages and Disadvantages of Discounted Payback Advantages Disadvantages - Includes time value of money - Easy to understand - Does not accept negative estimated NPV investments - Biased towards liquidity - May reject positive NPV investments - Arbitrary determination of acceptable payback period - Ignores cash flows beyond the cutoff date - Biased against long-term and new products

15 Accounting Rate of Return (ARR) Measure of an investment s profitability. ARR average net profit average book value A project is accepted if ARR > target average accounting return.

16 Example ARR Year Sales \$440 \$240 \$160 Expenses Gross profit Depreciation Taxable income Taxes (25%) Net profit \$105 \$30 \$0 Assume initial investment = \$240

17 Example ARR (continued) Average \$105 net profit \$30 3 \$0 \$45 Average book value Initial investment 2 Salvage value \$240 2 \$120 \$0

18 Example ARR (continued) Average net profit ARR Average book value \$45 \$ %

19 Disadvantages of ARR The measure is not a true reflection of return. Time value is ignored. Arbitrary determination of target average return. Uses profit and book value instead of cash flow and market value.

20 Advantages of ARR Easy to calculate and understand. Accounting information almost always available.

21 Internal Rate of Return (IRR) The discount rate that equates the present value of the future cash flows with the initial cost. Generally found by trial and error. A project is accepted if its IRR is > the required rate of return. The IRR on an investment is the required return that results in a zero NPV when it is used as the discount rate.

22 Example IRR Year Initial investment = \$200 Cash flow 1 \$ Find the IRR such that NPV = = (1+IRR) 1 + (1+IRR) 2 + (1+IRR) = (1+IRR) 1 + (1+IRR) 2 + (1+IRR) 3

23 Example IRR (continued) Trial and Error Discount rates NPV 0% \$100 5% 68 10% 41 15% 18 20% 2 IRR is just under 20% about 19.44%

24 NPV Profile Net present value Year Cash flow 0 \$ Discount rate 2% 6% 10% 14% 18% IRR 22%

25 Problems with IRR More than one negative cash flow multiple rates of return. Project is not independent mutually exclusive investments. Highest IRR does not indicate the best project. Advantages of IRR Popular in practice Does not require a discount rate

26 Multiple Rates of Return Assume you are considering a project for which the cash flows are as follows: Year Cash flows 0 \$

27 Multiple Rates of Return What s the IRR? Find the rate at which the computed NPV = 0: at 25.00%: NPV = 0 at 33.33%: NPV = 0 at 42.86%: NPV = 0 at 66.67%: NPV = 0 Two questions: u 1. What s going on here? u 2. How many IRRs can there be?

28 Multiple Rates of Return NPV \$0.06 \$0.04 \$0.02 IRR = 25% \$0.00 (\$0.02) (\$0.04) IRR = 33.33% IRR = 42.86% IRR = 66.67% (\$0.06) (\$0.08) Discount rate

29 IRR and Non-conventional Cash Flows When the cash flows change sign more than once, there is more than one IRR. When you solve for IRR you are solving for the root of an equation and when you cross the x axis more than once, there will be more than one return that solves the equation. If you have more than one IRR, you cannot use any of them to make your decision.

30 IRR, NPV and Mutually-exclusive Projects Net present value Crossover Point 2% 6% 10% 14% 18% Year Project A: \$ Project B: \$ % 26% Discount rate IRR A IRR B

31 Present Value Index (PVI) Expresses a project s benefits relative to its initial cost. PVI PV of Initial inflows cost Accept a project with a PVI > 1.0.

32 Example PVI Assume you have the following information on Project X: Initial investment = \$1100 Required return = 10% Annual cash revenues and expenses are as follows: Year Revenues Expenses 1 \$1000 \$

33 Example PVI (continued) 500 NPV 1.10 \$ PVI Net Present Value Index = =

34 Example PVI (continued) Is this a good project? If so, why? This is a good project because the present value of the inflows exceeds the outlay. Each dollar invested generates \$ in value or \$ in NPV.

35 Advantages and Disadvantages of PVI (and NPVI) Advantages Disadvantages - Closely related to NPV, generally leading to identical decisions. - Easy to understand. - May lead to incorrect decisions in comparisons of mutually exclusive investments. - May be useful when available investment funds are limited.

36 Capital Budgeting in Practice We should consider several investment criteria when making decisions. NPV and IRR are the most commonly used primary investment criteria. Payback is a commonly used secondary investment criteria.

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