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## Net Present Value

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**Net Present Value**RWJ-Chapter 9**Overview**• In late 2010, Foxconn, electronics contract manufacturing company (which manufactures many of the Apple products and Kindle), announced its plans to open a factory in China at a cost of $10 billion. • Foxconn’s new plant is an example of capital budgeting decision. Decisions such as these, with a price tag of $10 billion, are major undertakings, and risks and rewards must be carefully weighed. • In this chapter, we discuss the basic tools used in making such decisions.**Mutually Exclusive vs. Independent Projects**• Mutually Exclusive Projects: only ONE of several potential projects can be chosen, e.g. acquiring an accounting system. • RANK all alternatives and select the best one. • Independent Projects: accepting or rejecting one project does not affect the decision of the other projects. • Must exceed a MINIMUM acceptance criteria.**The Net Present Value (NPV)**• Net Present Value (NPV) = Total PV of future CF’s + Initial Investment • Estimating NPV: 1. Estimate future cash flows: how much? and when? 2. Estimate discount rate 3. Estimate initial costs • Minimum Acceptance Criteria: Accept if NPV > 0 • Ranking Criteria: Choose the highest NPV**NPV Example**• Alpha Corp. is considering investing in a risklessproject costing $100. The project receives $107 in one year and has no other cash flows. The risk-free interest rate is 6%. • NPV of the project is: $0.94= -100 + (107/1.06) • NPV is positive, accept the project. • NPV leads to good decisions. Why?**NPV Example (Contd.)**• Consider these two strategies: • Use $100 of corporate cash to invest in the project. The $107 will be paid as a dividend in one year. • Forgo the project and pay the $100 of corporate cash as a dividend today. • If strategy 2 is employed, the shareholders might deposit the dividend in the bank for one year. With the interest rate of 6 percent, strategy 2 will produce cash of $100 x 1.06 =$106 at the end of year 1. • Which strategy would the shareholders prefer?**How do We Interpret NPV?**• In the previous example, NPV of the project was $0.94. • Let’s say the firm today has productive assets worth $V and has $100 of cash. If the firm foregoes the project, the value of the firm today would be: $V +100 • If the firm accepts the project, the firm will receive $107 in one year but will have no cash today. V + 107/1.06 • The difference between the two equations is $0.94, i.e. NPV The value of the firm rises by the NPV of the project.**Discount Rate in NPV Calculations**• In the previous example, we assumed that the project was riskless. In real life, the future cash flows from a project are estimated rather than known. • Let’s say, Alpha Corp. estimates that with 50% chance the cash flow will be $117, or it will be $97. The expected cash flow will be (0.5) (117) +(0.5) (97)= $107 • Suppose the project is as risky as the market and expected return on the market is 10%. • NPV= -100 + 107/1.10 = -$2.73 • Expected return on the project is 7%. If the investors gets the cash in dividends and invest it at the market, the expected return is 10%.**Why Use Net Present Value?**• Accepting positive NPV projects benefits shareholders. • NPV uses cash flows • NPV uses all the cash flows of the project • NPV discounts the cash flows properly**9.2 The Payback Period**• How long does it take the project to “pay back” its initial investment? • Payback Period = number of years to recover initial costs • Minimum Acceptance Criteria: • set by management • Ranking Criteria: • set by management**Example-Payback Period**• Here are the projected cash flows from a proposed investment: • This project costs $100. • What is the payback periods?**The Payback Period Rule (continued)**• Disadvantages: • Ignores the time value of money • Fails to consider risk • Ignores cash flows after the payback period • Biased against long-term projects • Requires an arbitrary acceptance criteria • A project accepted based on the payback criteria may not have a positive NPV • Advantages: • Easy to understand • Biased toward liquidity**The Payback Period - Uses**• In relatively small decisions since it is simple. • Firms with good investment opportunities but no available cash. Quick cash recovery enhances the reinvestment possibilities for such firms. • Firms prefer NPV when they look at bigger projects.**The Discounted Payback**• How long does it take the project to “pay back” its initial investment taking the time value of money into account? • Still has some of the major flaws as payback. • By the time you have discounted the cash flows, you might as well calculate the NPV.**The Average Accounting Return**• Another attractive but fatally flawed approach. • Ranking Criteria and Minimum Acceptance Criteria set by management • Disadvantages: • Ignores the time value of money • Uses an arbitrary benchmark cutoff rate • Based on book values, not cash flows and market values • Advantages: • The accounting information is usually available • Easy to calculate**Example-AAR**• You are deciding whether to open a store in a new shopping mall. The required investment is $500,000. • The required investment would be 100% depreciated (straight-line) over the five years. • The following table provides yearly revenue and costs for average accounting return:**Example-AAR**or**The Internal Rate of Return (IRR)**• IRR: the discount rate that sets NPV to zero • Minimum Acceptance Criteria: • Accept if the IRR exceeds the required return. • Ranking Criteria: • Select alternative with the highest IRR • Reinvestment assumption: • All future cash flows assumed reinvested at the IRR. • Disadvantages: • Does not distinguish between investing and borrowing. • IRR may not exist or there may be multiple IRRs. • Problems with mutually exclusive investments. • Advantages: • Easy to understand and communicate**$50**$100 $150 0 1 2 3 -$200 The Internal Rate of Return: Example • Consider the following project: • The internal rate of return for this project is 19.44%**The NPV Payoff Profile for This Example**• If we graph NPV versus discount rate, we can see the IRR as the x-axis intercept.**Problems with the IRR Approach**• General problems affecting both independent and mutually exclusive projects: • Investing or Financing • Multiple IRRs • Problems specific to mutually exclusive projects: • The Scale Problem • The Timing Problem**Investing or Financing?**• Two different projects • Project A (Investing type) • CF0 = -100 • CF1 = 130 • NPV @10% = $18.2 • IRR = 30% • Project B (Financing type) • CF0 = 100 • CF1 = -130 • NPV @10% = -$18.2 • IRR = 30% IRR is greater than discount rate in both cases. But Project B’s NPV is negative. IRR rule is reversed for financing type projects.**100% = IRR2**0% = IRR1 Multiple IRRs Which one should we use? • There are two IRRs for this project:**How Do We Solve Multiple IRR Problem?**• Rely on NPV when cash flows are non-normal. • OR calculate Modified Internal Rate of Return (MIRR) • Three steps to calculate MIRR (Combination approach): • Find the PV of cash outflows • Find the FV of cash inflows • Find the rate of return which makes the FV of cash inflows equal to PV of cash outflows (MIRR)**$200 $800**0 1 2 3 - $800 -$200 Example - MIRR • Let’s assume the discount rate is 10% • PV of cash outflows = -200 + [-800/(1.10)3] = $ -801.06 • FV of cash inflows = 200 * (1.1)2 + 800 *(1.1) = $1,122 • 801.06 = 1,122/(1+MIRR)3 • MIRR= 11.886%**Problems with MIRR**• “Meaningless internal rate of return”? • There are three methods of calculating MIRR (we have seen only one). • MIRR requires compounding and discounting. If we have the discount rate, why not calculate NPV? • MIRR depends on the discount and compound rate, so it is not truly an internal rate of return, which should depend on only the project’s cash flows.**The Scale Problem (of IRR)**• Suppose that a friend promises to pay you $2 tomorrow if you lend him $1 today. This deal promises a return of 100% (IRR). • Another friend asks you to lend him $100 today in exchange of $150 tomorrow. IRR on this deal is 50%. • Which one would you choose? • The first deal increases your wealth by $1 (NPV), the second deal increases your wealth by $50.**How Do We Solve the Scale Problem?**• Compare NPVs**The Timing Problem**• The preferred project in this case depends on the discount rate. NPV of project B is higher with low discount rates and the NPV of project A is higher with high discount rates.**Calculating the Crossover Rate**• Compute the IRR for either project “A-B” or “B-A”**IRR vs. NPV**• Either due to differences in timing or in size, the project with the highest IRR need not have the highest NPV. • When working with mutually exclusive projects, it is very common that you will face scale or timing problem. Then you should simply use NPV.**IRR vs. NPV**• Consider these two statements: • You must know the discount rate to compute NPV of a project but you can compute the IRR without referring to the discount rate. • Hence, the IRR rule is easier to apply than the NPV rule because you don’t use the discount rate when applying IRR. • First statement is true, while the second statement is not.