1. Investment Decision Rules: NPV Chap 8

Investment Decision Rules

• This chapter discusses the NPV decision rule, its application, alternative decision rules, project selection, projects with varying lifespans, projects with resource constraints, and overall decision-making.

The NPV Decision Rule

• Net Present Value is used by most firms to measure value
• NPV is measured in terms of cash today
• NPV = PV (Benefits) – PV (Costs)
• If a firm receives $550 in one year for $500 today with an 8% interest rate:
  • PV(Benefit) = ($550 in one year) / ($1.08 in one year/$ today) = $509.26 today
  • NPV = $509.26 - $500 = $9.26 today
• As long as NPV is positive, the decision increases the firm's value, regardless of current cash needs or preferences
• When making an investment decision, the alternative with the highest NPV should be selected
• Selecting the highest NPV is equivalent to receiving its NPV in cash today

Application of the NPV Decision Rule

• Accept positive-NPV projects, as accepting them is equivalent to receiving their NPV in cash today
• Reject negative-NPV projects, as accepting them would reduce the firm's value (NPV = 0)

Utilizing the NPV Rule

• A fertilizer company can create a new environmentally friendly fertilizer with large savings
• The fertilizer factory costs $81.6 million to build and generates an estimated $28 million return after the first year for four years
• NPV can be computed with a discount rate r using individual terms for each year

Calculating NPV Using Annuity Formula

• NPV can be calculated as: NPV = -81.6 + (28 / r) * [1 - (1 / (1+r)^4)]
• If the company's cost of capital is 10%, the NPV is $7.2 million, indicating the investment should be undertaken

NPV Profile

• The NPV depends on the cost of capital, including uncertainty
• The NPV profile graphically represents the NPV over a range of discount rates, which can be created in Excel
• Based on the data, the NPV is positive only when discount rates are less than 14%
• If unsure of the cost of capital estimate, determine how sensitive the analysis to errors in this estimate
• Internal Rate of Return measures the return of the project and the discount rate that makes NPV = 0
• When the rules conflict, base the decision on the NPV rule

Alternative Decision Rules: The Payback Rule

• The payback rule is based on the principle that an opportunity that quickly returns the initial investment is favorable
• The payback period is accepted if less than a prespecified length of time
• The payback period is rejected if greater than a prespecified length of time

Payback Rule Applied

• A firm requiring projects to have a payback period of two years or less may reject a fertilizer project
  • The project has inflows of $28 million per year and an initial investment of $81.6 million
  • The sum of the cash flows for years 1 and 2 is $28 × 2 = $56 million
• The $56 million will not cover the initial investment of $81.6 million.
• The cash inflows don't exceed the initial until year 3 ($28 × 3 = $84 million)
• The payback period exceeds two years, and the firm will reject the project

Using The Payback Rule

• With a simple computation, the payback rule requires an arbitrary cutoff in summing cash flows
• The payback rule sums the cash flows and compares them to a cash outflow today
• A project that would have increased the company's value may be rejected

Disadvantages of the Payback Rule

• Ignores the time value of money
• Ignores cash flows after the payback period
• Lacks a decision criterion grounded in economics

IRR and NPV Rule Agreement

• The IRR rule agrees with NPV for stand-alone projects in most cases if negative cash flows precede positive cash flows
• In other cases the IRR may disagree with NPV
• Any investment opportunity can be taken when IRR exceeds the opportunity cost of capital, known as the IRR rule

Delayed Investments

• Offer A involves a one-time payment of $1 million upfront; Offer B involves yearly payments of $500,000 at the end of the next three years
• The estimated cost of capital is 10%
• NPV can be set to zero, and solve for r to get IRR, or IRR = 23.38%
• Based on IRR, Option A is best, where 23.38% is > the 10% opportunity cost of capital
• However, NPV shows that Option B is best with NPV = -$243,426

NPV and IRR Conflicts

• The IRR can be reversed for projects when expenses are upfront and cash is received in the future
• With delayed investments the project with a low rate is best
• If the firm makes an additional payment of $600,000 in 10 years, this results in multiple IRRs
• The general equation to determine the NPV of the new investment opportunity as: NPV =1,000,000 - [500,000/(1+r)] - [500,000/(1+r)^2] - [500,000/(1+r)^3] + [600,000/(1+r)^10]

Mutually Exclusive Projects

• Can't just pick the project with a positive NPV
• Projects must be ranked and the best one chosen
• Pick the project with the highest NPV with a series of projects

NPV and Mutually Exclusive Projects

• With mutually exclusive projects rank them by NPV to find the most valuable project
• The present value of the inflows are the formula: CF1 / r –g
• The coffee shop should be chosen with the highest value

Differences in Scale

• A 10% IRR can have very different value implications for an initial investment of $1 million vs. an initial investment of $100 million
• NPV of Maria's investment in her boyfriend's business is: NPV = -$10,000 + (6000 / 1.12) + (6000 / 1.12^2) + (6000 / 1.12^3) = $4,411
• NPV of Maria's investment in the delivery business is: NPV = -$10,000 + (5000 / 1.12) + (5000 / 1.12^2) + (5000 / 1.12^3) = $2,009
• IRR is unaffected by scale (still 36.3%)

Crossover Point

• The crossover point is the discount rate that makes the NPV of the two alternatives equal
• Project A over Project B can be computed as the difference of the NPVs
• General Equation for Projects’ value: NPV = -$2,000 + ( 900 / 1+r )+ ( 900 / (1+r)^2 ) + ( 900 / (1+r)^3) =0
• The crossover occurs at a discount rate of 16.65%
• The crossover point is the discount rate at which we would be indifferent between the two projects
• Incremental impact is when zero chooses one project over another

Shortcomings of The IRR

• Always rely on NPV
• In general, it is dangerous to use the IRR in choosing between projects
• The dollar value of earning depends on how long it takes to earn this return
• Picking the investment opportunity with the largest IRR can lead to a mistake

Evaluating Projects With Different Lives

• Often, a company will need to choose between two solutions to the same problem
• In order to compare a new option to server A, Server C needs to compute its annual cost.
  • Compute Server C’s NPV
  • Compute the equivalent four-year annuity value
• Server C's annual cost of $5620 is greater than the annual cost of server A ($5020)
• The additional cost associated with purchasing and maintaining server C is not worth the extra year
• The equivalent annual annuity tool allows us to see put costs into an equivalent annuity

Equivalent Annual Annuity

• To compare options with different lives Vendor Y charges yearly and upfront, Vendor Z charges two years
• Compute its NPV and EAA
• NPV : NPVY = −$100,000 − $12,000 [(1 / 0.08) − (1 / 0.08(1.08)3] = −$130,925

Important Considerations

• Required life
• The replacement cost

Choosing Projects When Resources Are Limited

• If there is a fixed supply of the resource so that you cannot undertake all possible opportunities, simply picking the highest-NPV opportunity might not lead to the best decision
• Value Created or NPV is the Profitability Index Formula divided by Resource Consumed

Profitability Index Applied

• Project proposal to develop a new home networking router is put forward
• The project will require 50 software engineers, and expected NPV is $17.7 million
• 190 engineers are available but no additional hires
• Determine the profitability index for each project with engineering headcount with engineering headcount

Maximizing Total NPV

• To maximize NPV within the constraint of 190 engineers, select the first four projects on the list
• 3 otherwise valuable projects, C, D, and B, are forgone
• A resource constraint forces NetIt to forgo with a total NPV of $33.6 million

Shortcomings

• With multiple resource constraints, the usefulness of the profitability index breaks down
• Resource constraints must be increased
• In some situations it does not give an accurate answer if some resources are not fully utilized