Investment Decision Rules: NPV, IRR, and Payback time Alternative Decision RulesThe NPV RuleExample: Using the NPV RuleExample: Using the NPV RuleWhat discount rate, r?Whether NPV is positive or negative depends strongly on the cost of capitalThe Internal Rate of ReturnIRR Rule and Differences in RiskIRR Rule vs. NPV RuleExample: If benefits upfront and costs laterExample: If multiple IRRsIRR Rule and Differences in ScaleThe Payback RuleExample: Using the Payback RuleProblems with the Payback RuleChoosing Between ProjectsExample: Choosing Between ProjectsSolutionSummary of decision rulesINVESTMENT DECISION RULES: NPV, IRR, AND PAYBACK TIMEAlternative Decision Rules FIGURE The Most Popular Decision Rules Used by CFOsThe NPV Rule • The NPV rule implies that we should: — Accept all projects with NPV>0 — Reject all projects with NPV<0; accepting them would reduce the value of the firm, whereas rejecting them has no cost (NPV = 0). • Similarly, buy a security if the PV of its future cash flows is greater than the purchase price NPV = PV (Benefits) – PV (Costs)Example: Using the NPV Rule • A fertilizer company is considering creating a new environmentally friendly fertilizer • The fertilizer will require a new factory that can be built at a cost of $81.6 million • The estimated profit on the new fertilizer will be $28 million in the first year, and these profits will last four years • What’s the NPV of this project?Example: Using the NPV Rule • Given a discount rate r, the NPV of this project is: 23428 28 28 2881.61(1 ) (1 ) (1 )NPVrrrr=−+ + + +++++What discount rate, r? • Assume that investing in an alternative project with equivalent risk has an expected return of 10% • 10% is therefore the opportunity cost of capital in this example – this is the correct discount rateWhether NPV is positive or negative depends strongly on the cost of capital If the company’s cost of capital is 10%, the NPV is $7.2 million and they should undertake the investmentThe Internal Rate of Return • IRR: Discount rate that sets the NPV of cash flows equal to zero • IRR Decision Rule: — Take any investment opportunity where IRR exceeds the cost of capital — Turn down any investment where IRR is less than the cost of capital • In the previous example, the IRR Decision Rule says: — Take the investment, because the IRR (14%) is greater than the cost of capital (10%)IRR Rule and Differences in Risk • An IRR that is attractive for a safe project need not be attractive for a riskier project.  Companies cannot use the same IRR cutoff to evaluate projects of different riskinessIRR Rule vs. NPV Rule • The NPV rule and IRR rule often give the same answer • BUT, the IRR rule sometimes disagrees with the NPV rule, for example: — Delayed investment: If negative cash flows follow positive cash flows (then a lower discount rate is better) — Multiple IRRs or No IRR  Cannot use the IRR Rule — Differences in scaleExample: If benefits upfront and costs laterExample: If multiple IRRsIRR Rule and Differences in Scale • If a project’s size is doubled, its NPV will double. This is not the case with IRR.  IRRs cannot be used to compare projects of different scalesThe Payback Rule • Based on the idea that an investment opportunity that pays back the initial investment quickly is the best • Payback period: The amount of time it takes to earn back the initial investment • The Payback Rule implies that we should: — Take any investment opportunity where the payback period is less than a required cutoff — Turn down any investment where the payback period is greater than this cutoffExample: Using the Payback Rule Problem: • Assume the fertilizer company in the previous example requires all projects to have a payback period of two years or less. • Would the firm undertake the project under this rule? Solution: • 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 period is >2 years, the project will be rejected.Problems with the Payback Rule • Payback rule is simple to compute, BUT — Requires us to use an arbitrary cutoff period — Ignores cash-flows after the payback period — Does not discount future cash flows, i.e. ignores the time value of money • Can therefore lead to rejection of a project that would have increased the value of the firmChoosing Between Projects • If you can’t pick every project with a positive NPV (e.g. if there are mutually exclusive projects): — Pick the project(s) with the highest NPV! • Ranking projects based on IRR or Payback Period can lead to the wrong answer: — Sometimes IRR and Payback Period rank projects in the same order as NPV, but at other times they disagreeExample: Choosing Between ProjectsSolutionSummary of decision rules • NPV — Definition: Difference between present value of project’s benefits and present value of its costs — NPV Rule: Take projects that have a positive NPV; don’t take projects with a negative NPV • IRR — Definition: The discount rate that sets NPV of cash flows equal to zero — IRR Rule: Take projects where IRR>Cost of capital — Often gives the same answer as the NPV Rule, but there are exceptions • Payback Period — Definition: Amount of time to pay back initial investment — Payback Rule: Take a project where payback period is less than a set cutoff — Is simple to compute but has several