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Chapter 8

Chapter 8. Investment Decision Rules. Chapter Outline. 8.1 The NPV Decision Rule 8.2 Using the NPV Rule 8.3 Alternative Decision Rules 8.4 Choosing Between Projects 8.5 Evaluating Projects with Different Lives 8.6 Choosing Among Projects When Resources Are Limited

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Chapter 8

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  1. Chapter 8 Investment Decision Rules

  2. Chapter Outline 8.1 The NPV Decision Rule 8.2 Using the NPV Rule 8.3 Alternative Decision Rules 8.4 Choosing Between Projects 8.5 Evaluating Projects with Different Lives 8.6 Choosing Among Projects When Resources Are Limited 8.7 Putting it All Together

  3. Learning Objectives • Calculate a Net Present Value • Use the NPV rule to make investment decisions • Understand alternative decision rules and their drawbacks • Choose between mutually exclusive alternatives

  4. Learning Objectives • Evaluate projects with different lives • Rank projects when a company’s resources are limited so that it cannot take all positive- NPV projects

  5. 8.1 The NPV Decision Rule • Most firms measure values in terms of Net Present Value–that is, in terms of cash today. NPV = PV (Benefits) – PV (Costs) (Eq. 8.1)

  6. 8.1 The NPV Decision Rule • Logic of the decision rule: • When making an investment decision, take the alternative with the highest NPV, which is equivalent to receiving its NPV in cash today.

  7. 8.1 The NPV Decision Rule • A simple example: • In exchange for $500 today, your firm will receive $550 in one year. If the interest rate is 8% per year: • PV(Benefit)= ($550 in one year) ÷ ($1.08 $ in one year/$ today) = $509.26 today • This is the amount you would need to put in the bank today to generate $550 in one year. • NPV= $509.26 - $500 = $9.26 today

  8. 8.1 The NPV Decision Rule • You should be able to borrow $509.26 and use the $550 in one year to repay the loan. • This transaction leaves you with $509.26 - $500 = $9.26 today. • As long as NPV is positive, the decision increases the value of the firm regardless of current cash needs or preferences.

  9. 8.1 The NPV Decision Rule • The NPV decision rule implies that we should: • Accept positive-NPV projects; accepting them is equivalent to receiving their NPV in cash today, and • Reject negative-NPV projects; accepting them would reduce the value of the firm, whereas rejecting them has no cost (NPV = 0).

  10. Example 8.1 The NPV Is Equivalent to Cash Today Problem: • After saving $1,500 waiting tables, you are about to buy a 42-inch plasma TV. You notice that the store is offering “one-year same as cash” deal. You can take the TV home today and pay nothing until one year from now, when you will owe the store the $1,500 purchase price. If your savings account earns 5% per year, what is the NPV of this offer? Show that its NPV represents cash in your pocket.

  11. Example 8.1 The NPV Is Equivalent to Cash Today Solution: Plan: • You are getting something (the TV) worth $1,500 today and in exchange will need to pay $1,500 in one year. Think of it as getting back the $1,500 you thought you would have to spend today to get the TV. We treat it as a positive cash flow. Today In one year Cash flows: $ 1,500 –$ 1,500 • The discount rate for calculating the present value of the payment in one year is your interest rate of 5%. You need to compare the present value of the cost ($1,500 in one year) to the benefit today (a $1,500 TV).

  12. Example 8.1 The NPV Is Equivalent to Cash Today Execute: • You could take $1,428.57 of the $1,500 you had saved for the TV and put it in your savings account. With interest, in one year it would grow to $1,428.57  (1.05) = $1,500, enough to pay the store. The extra $71.43 is money in your pocket to spend as you like (or put toward the speaker system for your new media room).

  13. Example 8.1 The NPV Is Equivalent to Cash Today Evaluate: • By taking the delayed payment offer, we have extra net cash flows of $71.43 today. • If we put $1,428.57 in the bank, it will be just enough to offset our $1,500 obligation in the future. • Therefore, this offer is equivalent to receiving $71.43 today, without any future net obligations.

  14. Example 8.1a The NPV Is Equivalent to Cash Today Problem: • After saving $2,500 waiting tables, you are about to buy a 50-inch LCD TV. You notice that the store is offering “one-year same as cash” deal. You can take the TV home today and pay nothing until one year from now, when you will owe the store the $2,500 purchase price. If your savings account earns 4% per year, what is the NPV of this offer? Show that its NPV represents cash in your pocket.

  15. Example 8.1a The NPV Is Equivalent to Cash Today Solution: Plan: • You are getting something (the TV) worth $2,500 today and in exchange will need to pay $2,500 in one year. Think of it as getting back the $2,500 you thought you would have to spend today to get the TV. We treat it as a positive cash flow. Today In one year Cash flows: $ 2,500 –$ 2,500 • The discount rate for calculating the present value of the payment in one year is your interest rate of 4%. You need to compare the present value of the cost ($2,500 in one year) to the benefit today (a $2,500 TV).

  16. Example 8.1a The NPV Is Equivalent to Cash Today Execute: • You could take $2,403.85 of the $2,500 you had saved for the TV and put it in your savings account. With interest, in one year it would grow to $2,403.85  (1.04) = $2,500, enough to pay the store. The extra $96.15 is money in your pocket to spend as you like.

  17. Example 8.1a The NPV Is Equivalent to Cash Today Evaluate: • By taking the delayed payment offer, we have extra net cash flows of $96.15 today. If we put $2,403.85 in the bank, it will be just enough to offset our $2,500 obligation in the future. Therefore, this offer is equivalent to receiving $96.15 today, without any future net obligations.

  18. 8.2 Using the NPV Rule • A take-it-or-leave-it decision: • A fertilizer company can create a new environmentally friendly fertilizer at a large savings over the company’s existing fertilizer. • The fertilizer will require a new factory that can be built at a cost of $81.6 million. Estimated return on the new fertilizer will be $28 million after the first year, and last four years.

  19. 8.2 Using the NPV Rule • Computing NPV • The following timeline shows the estimated return:

  20. Given a discount rate r, the NPV is: We can also use the annuity formula: 8.2 Using the NPV Rule (Eq. 8.2) (Eq. 8.3)

  21. 8.2 Using the NPV Rule • If the company’s cost of capital is 10%, the NPVis $7.2 million and they should undertake the investment.

  22. 8.2 Using the NPV Rule • NPV of Fredrick’s project • The NPV depends on cost of capital. • NPV profile graphs the NPV over a range of discount rates. • Based on this data the NPV is positive only when the discount rates are less than 14%.

  23. 8.2 Using the NPV Rule FIGURE 8.1 NPV of Fredrick’s New Project

  24. 8.3 Alternative Decision Rules FIGURE 8.2 The Most Popular Decision Rules Used by CFOs

  25. 8.3 Alternative Decision Rules • The Payback Rule • Based on the notion that an opportunity that pays back the initial investment quickly is the best idea. • Calculate the amount of time it takes to pay back the initial investment, called the payback period. • Accept if the payback period is less than required • Reject if the payback period is greater than required

  26. Example 8.2 Using the Payback Rule Problem: • Assume the fertilizer company requires all projects to have a payback period of two years or less. In this case would the firm undertake the project under this rule?

  27. Example 8.2 Using the Payback Rule Solution: Plan: • In order to implement the payback rule, we need to know whether the sum of the inflows from the project will exceed the initial investment before the end of 2 years. The project has inflows of $28 million per year and an initial investment of $81.6 million.

  28. Example 8.2 Using the Payback Rule Execute: • The sum of the cash flows from year 1 to year 2 is $28m x 2 = $56 million, this will not cover the initial investment of $81.6 million. Because the payback is > 2 years (3 years required $28 x 3 = $84 million) the project will be rejected.

  29. Example 8.2 Using the Payback Rule Evaluate: • While simple to compute, the payback rule requires us to use an arbitrary cutoff period in summing the cash flows. • Further, also note that the payback rule does not discount future cash flows. • Instead it simply sums the cash flows and compares them to a cash outflow in the present. • In this case, Fredrick’s would have rejected a project that would have increased the value of the firm.

  30. Example 8.2a Using the Payback Rule Problem: • Assume a company requires all projects to have a payback period of three years or less. For the project below, would the firm undertake the project under this rule?

  31. Example 8.2a Using the Payback Rule Solution: Plan: • In order to implement the payback rule, we need to know whether the sum of the inflows from the project will exceed the initial investment before the end of 3 years. The project has inflows of $1,000 for two years, an inflow of $12,000 in year three, and an initial investment of $10,000.

  32. Example 8.2a Using the Payback Rule Execute: • The sum of the cash flows from years 1 through 3 is $14,000. This will cover the initial investment of $10,000. Because the payback is less than 3 years the project will be accepted.

  33. Example 8.2a Using the Payback Rule Evaluate: • While simple to compute, the payback rule requires us to use an arbitrary cutoff period in summing the cash flows. • Further, also note that the payback rule does not discount future cash flows. • Instead it simply sums the cash flows and compares them to a cash outflow in the present.

  34. Example 8.2b Using the Payback Rule Problem: • Assume a company requires all projects to have a payback period of three years or less. For the project below, would the firm undertake the project under this rule?

  35. Example 8.2b Using the Payback Rule Solution: Plan: • In order to implement the payback rule, we need to know whether the sum of the inflows from the project will exceed the initial investment before the end of 3 years. The project has inflows of $1,000 for three years, an inflow of $1,000,000 in year four, and an initial investment of $10,000.

  36. Example 8.2b Using the Payback Rule Execute: • The sum of the cash flows from years 1 through 3 is $3,000. • This will not cover the initial investment of $10,000. • Because the payback is more than 3 years the project will not be accepted, even though the 4th cash flow is very high!

  37. Example 8.2b Using the Payback Rule Evaluate: • While simple to compute, the payback rule requires us to use an arbitrary cutoff period in summing the cash flows. • Further, also note that the payback rule does not discount future cash flows – in this case, a huge mistake! • Instead it simply sums the cash flows and compares them to a cash outflow in the present.

  38. 8.3 Alternative Decision Rules • Weakness of the Payback Rule • Ignores the time value of money. • Ignores cash-flows after the payback period. • Lacks a decision criterion grounded in economics

  39. 8.3 Alternative Decision Rules • The Internal Rate of Return Rule • Take any investment opportunity where IRR exceeds the opportunity cost of capital.

  40. Table 8.1 Summary of NPV, IRR, and Payback for Fredrick’s New Project

  41. 8.3 Alternative Decision Rules • Weakness in IRR • In most cases IRR rule agrees with NPV for stand- alone projects if all negative cash flows precede positive cash flows. • In other cases the IRR may disagree with NPV.

  42. 8.3 Alternative Decision Rules • Delayed Investments • Two competing endorsements: • Offer A: single payment of $1million upfront • Offer B: $500,000 per year at the end of the next three years • Estimated cost of capital is 10% • Opportunity timeline:

  43. The NPV is: Set NPV to zero and solve for r to get IRR. 8.3 Alternative Decision Rules

  44. 8.3 Alternative Decision Rules • 23.38% > the 10% opportunity cost of capital, so according to IRR, Option A best. • However, NPV shows that Option B is best • To resolve the conflict we can show a NPV Profile

  45. 8.3 Alternative Decision Rules FIGURE 8.3 NPV of Cole’s $1 Million QuenchIt Deal • For most investments expenses are upfront and cash is received in the future. • In these cases a low rate is best. • When cash is upfront a high interest rate is best.

  46. 8.3 Alternative Decision Rules • Multiple IRRs • Suppose the cash flows in the previous example change. • The company has agreed to make an additional payment of $600,000 in 10 years.

  47. 8.3 Alternative Decision Rules • The new timeline: • The NPV of the new investment opportunity is: • If we plot the NPV profile, we see that it has two IRRs!

  48. 8.3 Alternative Decision Rules FIGURE 8.4 NPV of Evan’s Sports Drink Deal with Additional Deferred Payments

  49. 8.3 Alternative Decision Rules • Modified Internal Rate of Return (MIRR) • Used to overcome problem of multiple IRRs • Computes the discount rate that sets the NPV of modified cash flows to zero • Possible modifications • Bring all negative cash flows to the present and incorporate into the initial cash outflow • Leave the initial cash flow alone and compound all of the remaining cash flows to the final period of the project.

  50. Figure 8.5 NPV Profile with Multiple IRRs

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