Agency Problem and Payback Period

Agency Problem

• A principal-agent conflict between the owner/shareholder and the manager is the classic agency problem.
• Managers tend to focus on short-term results, causing conflicts.
• Agents apply for funding, which gives principals authority to provide capital.
• Agents are focused on short-term liquidity goals.
• Principals consider longer-term projects to add more value to the company.
• Managers prioritize near-term performance to keep their jobs and avoid risks, which sacrifices long-term profits.
• Using the payback period instead of more advanced methods stems from the principal-agent conflict.

Payback Period (PB)

• PB is the time needed to recover the initial investment outlay.
• Utilize a project if its PB is less than a cutoff.
• Strengths include ease of understanding and indication of a project's risk/liquidity.
• Weaknesses include ignoring the time value of money, CFs after the payback period, and subjectivity.
• Payback (PB) = Years before cost recovery + (Remaining cost to recover)/(CF during the next period)

Discounted Payback (DPB)

• DPB is the length of time until the sum of an investment’s discounted cash flows equals its cost.
• Utilize an investment if the discounted PB is less than the cutoff.
• DPB uses the same method to determine the time needed to recover costs as in PB: PB methodology applied to DCFs.
• DPB can be defined as the amount of time needed for a project to have a net present value (NPV) of zero.
• A project has a NPV of zero and the discount rate equals the internal rate of return (IRR) if the DPB equals the project length.

IRR: Scale and Timing Effects

• IRR is the discount rate that sets NPV to zero.
• The reinvestment rate problem is the inability to reinvest intermediate cash flows at the IRR.
• The actual profit generates a return much different from IRR because of this inability to have intermediate cash flows appreciate at the IRR until the end of the project or investment
• IRR selects projects based on a higher IRR.
• NPV selects projects based on a higher NPV > 0.
• Timing and scale issues of IRR arise when IRR is inconsistent with NPV.
• Practitioners favor IRR because it measures rate of return, per surveys, despite academics preferring NPV.
• Literature considers schemes for resolving the inconsistency between IRR and NPV, including the reinvestment rate problem.

Classification of Investment Projects

• Classification of Investment Projects are divided by dependent and purpose perspective
• Types under dependent perspective are:
  • Independent
  • Mutually exclusive
  • Contingent
• Independent projects are judged regardless of other projects.
• Mutually exclusive projects involve choosing one project over another.
• The decision to accept one project depends on the acceptance of another project for contingent projects.

IRR vs. NPV

• IRR and NPV will agree if projects are independent and cash flows are conventional.
• If a project has unconventional cash flows, IRR and NPV methods can produce different accept/reject decisions.
• The IRR and NPV methods can produce different accept/reject decisions if projects are mutually exclusive

Reinvestment Rates

• The reinvestment rate problem stems from not being able to invest intermediate cash flows at the IRR until project end.
• The resolution to the reinvestment issue within an NPV analysis is that the company can reinvest intermediate cash flows in future projects of similar risk.
• IRR is the discount rate that sets NPV to zero, therefore not precisely interpreted as the actual return generated by the project
• The firm's cost of capital is also called the modified internal rate of return (MIRR), per Solomon's suggestion of the opportunity cost being the reinvestment rate.

Modified Internal Rate of Return (MIRR)

• MIRR assumes that interim positive cash flows are reinvested at the same rate of return as the project that generated them, resolving two IRR problems.
• The weighted average cost of capital should be used for reinvesting the interim cash flows.
• Only one MIRR can be found for projects with alternating positive and negative cash flows
• The formula:
  • Adds the negative cash flows after discounting them to time zero using the external cost of capital.
  • Adds the positive cash flows including the proceeds of reinvestment at the external reinvestment rate to the final period.
  • Finds the rate of return that equates the magnitude of the discounted negative cash flows at time zero to the future value of the positive cash flows at the final time period.

Multiple IRRs

• Multiple IRRs can occur when cash flows alternate from being inflows to outflows more than once.
• The NPV calculation is unaffected by having alternating cash inflows and outflows through time.
• IRR is affected because mathematically each time the cash flows alternate from inflow to outflow a new discount rate that sets NPV to zero may emerge.

Profitability Index (PI)

• PI is the discounted sum of the cash inflows divided by the discounted sum of the cash outflows, and is a ratio version of NPV.
• PI > 1 is equivalent to an NPV > 0.
• PI = 1 is equivalent to an NPV = 0.
• PI < 1 is equivalent to an NPV < 0.
• PI is not as useful as NPV.
• Both MIRR and PI metrics require calculating a ratio of benefits over costs, but benefit/cost ratios differ as PI discounts benefits rather than appreciating them as in the MIRR.
• MIRR relation to PI: MIRR = (PI(1 + k)N)1/N − 1
• (1 + MIRR)N/(1 + k)N = PI
• If PI > 1, NPV > 0, then MIRR > k.
• If PI = 1, NPV = 0, then MIRR = k.
• If PI < 1, NPV < 0, then MIRR < k.
• Since the NPV, through the PI, is integrated into the MIRR, MIRR must always agree with the associated NPV analysis.