Net Present Value and Other Investment Criteria Chapter 8 Brealey-Myers-Marcus 6th Edition Business Finance 620 Topics Covered Net present value (NPV) Understand why the NPV rule is consistent with the goals of financial management Alternative investment criteria Internal rate of return (IRR) Payback rule Capital rationing and the profitability index Investment timing decisions Equivalent annual cost Assets with different lives Asset replacement decisions Investment Project Analysis The objective is to determine whether an investment project is profitable. We need to know: the benefits of the project, and the costs of the project. The key question: Do the benefits exceed the costs, measured in today’s dollars? Net Present Value Basic Illustration You invest $50 today and will receive $60 in one year. The benefit is the $60 payoff. The cost is the $50 payment today. Your expected (desired) rate of return is 10%. Initial Investment Added Value $50 $4.55 The $4.55 added value is the NPV of this one-year investment – Your profit in today’s dollars. Net Present Value Formula Net Present Value (NPV) The difference between the PV of a project’s future after-tax cash flows and the project’s initial cost. General formula for NPV: where Ci is a project’s ith cash flow (may be positive or negative), N is the length of the project in time periods, and R is the project’s required rate of return. Net Present Value Decision Rule Net Present Value Rule Accept all projects with a positive net present value. Reject all other projects. Why? The goal of management is to increase shareholder wealth. Managers should accept all projects worth more than their cost. Only projects with a positive NPV leave the firm with more value than they cost. NPV is the source of the term “valued added.” A Cost Savings Project NPV Application Possible costs to consider: Costs resulting from running the project Costs paid regardless of whether the project runs The benefits of the project After-tax savings of $50,000 at the end of Year 1. These first-year savings will growth at 2% per year for the next two years (2 and 3), remaining constant for Year 4 (at the Year 3 level). Plans call for the project to run 4 years. The appropriate discount rate is 12%. Should the project be undertaken? A Cost Savings Project NPV Application Period Cash Flow PV of Cash Flow 1 $ 50,000 44,643 = 50,000 / 1.12 2 51,000 = 50,000 (1.02) 40,657 = 51,000 / (1.12)2 3 52,020 = 50,000 (1.02)2 37,027 = 52,020 / (1.12)3 4 52,020 = 50,000 (1.02)2 33,060 = 52,020 / (1.12)4 TOTAL $ 155,387 (PV of cash flows) PROJECT BENEFITS A Cost Savings Project NPV Application Project Costs: Consulting fees to evaluate the various projects under consideration = $75,000 Project administration = $85,000 Taxes generated by the project = $35,000 Other costs of running the project = $25,000 Which costs are relevant to this project? Total Project Costs equal $145,000. NPV = –145,000 + 155,387 = $10,387 Other Investment Criteria Internal Rate of Return (IRR) Discount rate which equates the PV of a project’s future cash flows to its initial cost (thus, NPV = 0). In effect, IRR is the average annual rate of return a project actually earns. Payback Period Time required for a project’s periodic cash flows to recover the project’s initial investment cost. Conceptually and mechanically simple measure. Less analytical refinement than other measures. Internal Rate of Return Basic Illustration You can purchase a building today for $350,000. During the first three years of operation, the building will generate $16,000 annually in net cash inflows. At the end of the third year, you will sell the building for $450,000. What rate of return will you earn on the investment? To determine the investment project’s IRR, you will need to solve the following expression: Internal Rate of Return Basic Illustration The investment project’s IRR is 12.96%. Solving the formula for IRR requires either Excel or a financial calculator. The Excel approach: How should the 12.96% IRR be interpreted? Internal Rate of Return Basic Illustration IRR=12.96% Another View of the Internal Rate of Return (IRR) Payback Period Basic Illustration $50,000 $51,000 $52,020 – $145,000 0 1 2 4 Returning to the cost savings project used to illustrate NPV, we can calculate the project’s payback period. If we spend $145,000 at the start of the project (initial investment), and we earn the cash flows shown below in each year, then the $145,000 cost will be recovered by cash flows in 2.85 years (2 years, 10 months); the result is found by linear interpolation. $52,020 3 Project Time Period (years) Comparison of Payback and NPV Compared with NPV, the payback period: is easy to understand ignores the time value of money ignores cash flows beyond the payback period is biased against long-term projects requires an arbitrary cut-off period for a decision The payback rule is popular among companies. Often used when the capital investment is small, and when the merits of a project are so obvious that more formal analysis is really unnecessary. Capital Rationing When financing for new projects is limited, and the firm cannot launch all the investment projects with a positive NPV, simply relying upon NPV to select projects to be undertaken may mislead managers. In the case of limited funding, management should choose those positive-NPV projects which offer the highest NPV per dollar of funds invested. The Profitability Index measures a project’s NPV in relation to the dollar amount invested. You want a measure capable of identifying projects that offer the “the biggest bang for the investment dollar.” Profitability Index Basic Illustration Although Project D has the highest NPV, Project E offers the highest profit (NPV) per dollar of funds invested. Investment Timing Decisions Sometimes you have an opportunity to defer an investment, and select a time better suited to an investment decision. A common example is a tree farm. You can defer harvesting of the trees, but by doing so, you defer the receipt of the cash flow, yet increase the cash flow. Because the cost of technology tends to decline over time, acquisition of most technology can be evaluated using investment-timing analysis. Investment Timing Decisions Basic Illustration You can purchase a new machine today for $5,000. The machine provides benefits worth $1,000 a year. The machine’s expected life is 10 years. New machines of this sort are expected to decline in price by 20% a year. The discount rate (“hurdle rate) for the machine is 10%. Should you purchase the machine today, or wait? When is the best time to purchase the machine? Investment Timing Decisions Basic Illustration Example Solution Determine the cost of the machine for each of the next 10 years (the price drops by 20% annually). Compute the NPV of the machine purchase for each of the next 10 years. Because the NPVs are future values, you need to discount them to the present, using the 10% discount rate. Investment Timing Decisions Basic Illustration Years until Purchase Machine Cost NPV Purchase Date NPV Today 0 5,000 1,145 1,145 1 4,000 2,145 1,950 2 3,200 2,945 2,434 3 2,560 3,585 2,693 4 2,048 4,097 2,798 5 1,638 4,507 2,799 6 1,311 4,834 2,729 7 1,049 5,096 2,615 The best time to purchase the machine is the number of years associated with the largest discounted NPV today. Assets with Different Lives We frequently need to decide among assets (often equipment) designed to do exactly the same thing, but which have different characteristics. A common example is the choice between leasing and purchasing an asset. To bring assets with different financial terms on the same financial footing, we compare their costs with a measure called equivalent annual cost. Calculating Equivalent Annual Cost General Rule for Calculating EAC Regardless of the particular application, you can always use the following rule to calculate EAC: STEP 1, calculate the PV of all future cash flows using the discount rate provided in the problem. STEP 2, calculate the constant annual cash flow associated with the PV from STEP 1, again with the discount rate provided in the problem. Use the annuity formula for this calculation. Assets with Different Lives Basic Illustration A firm can lease a truck for 5 years at an annual cost of $26,360. Alternatively, the firm can buy a truck for $67,450, with an annual maintenance of $9,880. If the truck is purchased, the firm can arrange to sell at the end it can be sold for $23,275. At a discount rate (hurdle rate) of 10.6%, should the firm buy a truck or lease one? Assets with Different Lives Basic Illustration Example Solution Find the PV of the costs associated with buying the truck. The equivalent annual cost is the payment with the same PV (as ownership). In this case, the payment is $24,180. The annual cost of owning is $24,180. Because the cost of leasing is more ($26,360), purchasing is a better deal. EAC = $24,180 Asset Replacement Decisions The decision to replace assets is almost always an economic decision, not one driven by the complete physical collapse of equipment. While replacement equipment is more efficient than existing equipment, new equipment costs more. The issue is whether greater efficiency warrants the cash investment, especially when older assets may still be operational. Asset Replacement Decisions Basic Illustration A forklift, which can be used only for 3 more years, costs $6,750 a year to maintain. A new forklift, with a useable life of 10 years, costs $25,280, plus $3,375 a year for maintenance. With an 8.5% hurdle rate should managers replace the old forklift now? Asset Replacement Decisions Basic Illustration Example Solution Find the equivalent annual cost of the new forklift: The old forklift now costs $6,750 a year. The new forklift is more expensive by about $480. EAC = $7,228