Key Concepts and Skills • Be able to compute payback and discounted payback and understand their shortcomings • Be able to compute the internal rate of return and profitability index, understanding the strengths and weaknesses of both approaches • Be able to compute net present value and understand why it is the best decision criterion
1.Net Present Value • NPV is the difference between the market value of a project and its cost or how much value is created from undertaking an investment. • 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, which is the NPV.
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
n CFt ∑ PV = (1 + R)t t = 0 Net Present Value Sum of the PVs of all cash flows NOTE: t = 0 Initial cost often is CF0 and is an outflow. n CFt ∑ - CF0 NPV = (1 + R)t t = 1 Initial Outlay
NPV – Decision Rule If the NPV is positive, accept the project. Reject if negative. • A positive NPV means that the project is expected to add value to the firm and will therefore increase the wealth of the owners. • Since our goal is to increase owner wealth, NPV is a direct measure of how well this project will meet our goal.
Calculating NPV with Spreadsheets • Spreadsheets are an excellent way to compute NPVs, especially when you have to compute the cash flows as well. • Using the NPV function: • The first component is the required return entered as a decimal. • The second component is the range of cash flows beginning with year 1. • Add the initial investment after computing the NPV.
2. Payback Period • How long does it take to get the initial cost back in a nominal sense? • Computation • Estimate the cash flows • Subtract the future cash flows from the initial cost until the initial investment has been recovered • Decision Rule – Accept if the payback period is less than some preset limit
The Payback Period Method • Disadvantages: • Ignores the time value of money • 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
The Payback Period Method • Disadvantages: • Ignores the time value of money • 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
3.Discounted Payback Period • Compute the present value of each cash flow and then determine how long it takes to pay back on a discounted basis • Compare to a specified required period • Decision Rule - Accept the project if it pays back on a discounted basis withinthe specified time
4. Profitability Index • For conventional CF Projects: PV(Cash Inflows) Absolute Value of Initial Investment • PI is essentially a Benefit/Cost Ratio • Minimum Acceptance Criteria: • Accept if PI > 1
Advantages and Disadvantages of the Profitability Index • Advantages • Closely related to NPV, generally leading to identical decisions • Easy to understand and communicate • May be useful when available investment funds are limited • Disadvantages • May lead to incorrect decisions in comparisons of mutually exclusive investments PI = PV(future CF) | Initial Outlay |
4 Internal Rate of Return • IRRis the most important alternative to NPV • It is often used in practice and is intuitively appealing • It is based entirely on the estimated cash flows and is independent of interest rates found elsewhere
The Internal Rate of Return • 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
Similarity Between NPV & IRR Formulas NPV: Enter R and solve for NPV IRR: Enter NPV = 0, solve for IRR.
5.5 Problems with IRR • Multiple IRRs • The Scale Problem • Mutually Exclusive Projects
$200 $800 0 1 2 3 100% = IRR2 - $800 -$200 0% = IRR1 Multiple IRRs There are two IRRs for this project: Which one should we use?
ModifiedInternal Rate of Return (MIRR) • Controls for some problems with IRR Three Methods: • DiscountingApproach • Reinvestment Approach • 3. Combination Approach • MIRRwill be different number for each method • For this reason, some of us call it the Meaningless IRR rather than the Modified IRR.
Best Method for MIRR MIRR Method 1DiscountingApproach Step 1: Discount future outflows (negative cash flows) to present and add to CF0 Step 2: Zero out negative cash flows which have been added to CF0. Step 3: Compute IRR normally
MIRR Method 2ReinvestmentApproach Step 1: Compound ALL cash flows (except CF0) to end of project’s life Step 2: Zero out all cash flows which have been added to the last year of the project’s life. Step 3: Compute IRR normally
MIRR Method 3CombinationApproach Step 1: Discount all outflows (except CF0) to present and add to CF0. Step 2: Compound all cash inflows to end of project’s life Step 3: Compute IRR normally
The Scale Problem How to deal with this issue? - Calculate incremental IRR or NPV of incremental cash flows
Dealing with The Scale Problem How to justify the large budget using the IRR approach?
Dealing with The Scale Problem • Formula for Calculating the Incremental IRR: • IRR=66.67% • NPV of Incremental Cash Flows:
IRR and Mutually Exclusive Projects • Mutually exclusive projects • If you choose one, you can’t choose the other • Example: You can choose pursue an MBA at • either the UWM or Marquette, but not both • Intuitively you would use the following decision rules: • NPV – choose the project with the higher NPV • IRR – choose the project with the higher IRR
Example With Mutually Exclusive Projects The required return for both projects is 10%. Which project should you accept and why?
NPV Profiles IRR for A = 19.43% IRR for B = 22.17% Crossover Point = 11.8%
With the cross– over in the NPV profiles, we find that the better project depends critically on the required return. When the required return is low (less than 11.8%), pick project A. When the required return is high (greater than 11.8%), pick project B. Mutually Exclusive
NPV vs. IRR • NPV and IRR will generally give us the same decision With Two Exceptions: • Non-conventional cash flows – cash flow signs change more than once • There can be multiple IRRs for the same project • Mutually exclusive projects • Initial investments are substantially different • Timing of cash flows is substantially different
5.7 The Practice of Capital Budgeting • Varies by industry: • Some firms may use payback, while others choose an alternative approach. • The most frequently used technique for large corporations is either IRR or NPV.