ACST1001 Finance Fundamentals - Week 9: Firm Financial Decisions: Investment Decisions

Week 9 Learning Outcomes

  • Calculate net present value.
  • Use the NPV rule to make investment decisions.
  • Explain alternative decision rules and their drawbacks.

Week 9 Lecture Outline

  • Introduction to the firm’s investment decision
  • The NPV decision rule
  • Using the NPV rule
  • Alternative decision rules

Introduction to the Firm’s Investment Decision

  • Recall from week 1, the two key financial decisions:
    • The investment decision: Firms invest in real assets to produce goods and services. This is called the investment project.
    • The financing decision: Firms pay for these real assets by selling (issuing) financial assets (bonds, shares), which are claims on the cash flows generated by the real assets.

The Investment Decision

  • The investment decision is the most important financial decision for the following reasons:
    • Long-term impact: These decisions involve significant expenditures on long-term assets.
    • Irreversibility: Once made, investment decisions are often difficult or costly to reverse.
    • Strategic importance: Investment decisions shape the firm's future, determining capacity, capability, and competitive position.
    • Resource allocation: These decisions involve allocating limited resources among competing projects.
  • The key consideration in the investment decision is whether the proposed investment increases the value of the firm.

The Cost of Capital

  • The cost of capital is the rate of return that a company needs to earn on its investment projects to maintain its market value and satisfy its investors.
  • It is the opportunity cost of using the firm’s capital for a specific project instead of investing it elsewhere with a similar risk profile.
  • It is usually the weighted average of a firm's cost of debt (e.g., bonds) and cost of equity (e.g., shares).

Types of Projects

  • Stand-alone projects:
    • Projects are stand-alone when their cash flows are unrelated.
    • Accepting or rejecting one project does not eliminate other projects from consideration, assuming unlimited funds.
    • Example: A company can acquire a competitor and increase its manufacturing capacity simultaneously, assuming it has unlimited funds.
  • Mutually exclusive projects:
    • Acceptance of one project precludes acceptance of the others.
    • Typically, these projects perform the same function, so only one needs to be accepted.
    • Example: A company considering two locations for a new office building.

Net Present Value (NPV)

  • NPV measures the dollar change in wealth from investing in a project.
  • NPV is defined as the present value of the benefits less the present value of the costs from investing in the project:
    • NPV=PV(Benefits)−PV(Costs)NPV = PV(Benefits) - PV(Costs)
  • With this framework, the benefits are cash inflows, and the costs are cash outflows.
  • If we compute the present value of all cash flows, then NPV is the present value of all cash flows (both inflows and outflows) during the life of the project:
    • NPV=PV(all project cash flows)NPV = PV(all\ project\ cash\ flows)
  • As long as we have captured all costs and benefits of a project, decisions with a positive NPV will increase wealth.
    • As a result, the value of the firm will increase, and investors are wealthier.

The NPV Decision Rule

  • Accept a project if its NPV is positive because accepting the project increases firm value.
  • Reject a project if its NPV is negative because accepting it would decrease firm value, whereas rejecting it would cost nothing.

Introduction

  • The steps used in valuing an asset are the same whether the asset is real or financial:
    • Estimate future cash flows.
    • Determine the investor’s cost of capital or required rate of return.
    • Calculate the present value of the future cash flows.

Organising the Cash Flows and Computing the NPV

  • By undertaking a single, stand-alone project, a firm does not constrain its ability to take other projects.
  • In the utilization of a ‘take it or leave it’ approach, we simply either accept or reject a project.
  • A fertiliser company, Frederick’s Feed and Farm, can create a new environmentally friendly fertiliser at a large savings over the company’s existing fertiliser.
  • The fertiliser will require a new factory that can be built at a cost of 81.681.6 million.
  • The estimated benefits from the new fertiliser will be 2828 million per year for four years.
  • Given a discount rate of rr, the NPV is:
    • NPV=−81.6+281+r+28(1+r)2+28(1+r)3+28(1+r)4NPV = -81.6 + \frac{28}{1 + r} + \frac{28}{(1 + r)^2} + \frac{28}{(1 + r)^3} + \frac{28}{(1 + r)^4}
  • We can also use the annuity formula for the cash flows of 2828 from year 1 to year 4:
    • NPV=−81.6+28×1r×[1−1(1+r)4]NPV = -81.6 + 28 \times \frac{1}{r} \times [1 - \frac{1}{(1 + r)^4}]
  • If the firm’s management estimates the cost of capital to be 10% per year (r = 0.10), the NPV is:
    • NPV = -81.6 + \frac{28}{1.1} + \frac{28}{1.1^2} + \frac{28}{1.1^3} + \frac{28}{1.1^4} = $7.2\ million
  • In this case, the NPV is positive – the present value of the benefits exceeds the present value of the costs.
  • The NPV investment rule indicates that by making the investment, Fredrick’s will increase its value today by 7.27.2 million, so the firm should undertake this project.

The NPV Profile

  • The NPV of the project depends on its appropriate cost of capital.
  • Often, there may be some uncertainty regarding the project’s cost of capital.
  • In that case, it is helpful to compute an NPV profile, which graphs the project’s NPV over a range of discount rates.
  • The discount rate that sets the NPV of the cash flows equal to zero is an investment’s internal rate of return (IRR). Thus, by constructing the NPV profile, we have determined that Fredrick’s project has an IRR of 14%.

Measuring Sensitivity with the Internal Rate of Return

  • The firm’s managers provided the cost of capital.
  • If you are unsure of your cost of capital estimate, it is important to determine how sensitive your analysis is to errors in this estimate. The IRR can provide this information.
  • For Fredrick’s, if the cost of capital estimate is more than the 14% IRR, the NPV will be negative.
  • Therefore, provided our estimate of the cost of capital of 10% is within 4% of the true cost of capital, our decision to accept the project is correct.
  • The difference between the cost of capital and the IRR tells us the amount of estimation error in the cost of capital estimate that can exist without altering the original decision.

Summary of the NPV Rule

  • Decision Rule:
    • NPV > 0: Accept the project.
    • NPV < 0: Reject the project.
  • Key Advantages:
    • Accounts for the time value of money.
    • Considers the entire lifespan of the project, including all expected cash flows.
    • A direct measure of how much an investment will increase the value of the firm.
    • The discount rate in NPV can be adjusted to reflect the risk of the project or the cost of capital.
  • Key Disadvantages:
    • Relies on estimates of future cash flows and the discount rate, both of which can be difficult to predict accurately.
    • Calculations can be complex and less accessible to individuals without a strong financial background.

The Payback Rule

  • The payback rule is based on the notion that an opportunity that pays back the initial investment quickly is the best idea.
  • Calculate the amount of time in years it takes to pay back the initial investment, called the ‘payback period’.
    • Accept if the payback period is less than a pre-specified length of time.
    • Reject if the payback period is greater than a pre-specified length of time.

The Payback Rule Example

  • Assume Frederick’s requires all projects to have a payback period of two years or less. In this case, would the firm undertake the fertiliser project under this rule?
  • Recall, the cash flows for this project are:
  • The payback period in years can be calculated as follows:
    • Year 0: Cash flow -81.6, Cumulative cash flow -81.6
    • Year 1: Cash flow 28, Cumulative cash flow -53.6
    • Year 2: Cash flow 28, Cumulative cash flow -25.6
    • Year 3: Cash flow 28, Cumulative cash flow 2.4
    • Year 4: Cash flow 28, Cumulative cash flow 20.4
    • Payback period=year before full recovery+unrecovered cost at start of yearcash flow during yearPayback\ period = year\ before\ full\ recovery + \frac{unrecovered\ cost\ at\ start\ of\ year}{cash\ flow\ during\ year}
    • Payback period=2+25.628=2.91 yearsPayback\ period = 2 + \frac{25.6}{28} = 2.91\ years
  • While simple to compute, the payback rule requires us to use an arbitrary cut-off period in summing the cash flows.
  • 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.

Summary of Payback Rule

  • Decision Rule:
    • Payback period ≤ Threshold: Accept the project.
    • Payback period > Threshold: Reject the project.
  • Key Advantages:
    • Easy to calculate and understand for people without strong finance backgrounds.
    • A simple measure of a project’s recovery of the initial cost of the investment project.
  • Key Disadvantages:
    • Doesn't explicitly take the time value of money or risk into account.
    • Does not indicate the effects of the project on firm value.
    • Lacks a decision criterion grounded in economics.
    • Does not consider cash flows past the payback period.
    • Bias against long-term projects such as research and development and new products.

The Internal Rate of Return (IRR) Rule

  • The internal rate of return (IRR) is the discount rate that makes the NPV of the investment project equal to zero.
  • The IRR decision rule:
    • Accept a project if the IRR > Cost of capital
    • Reject a project if the IRR < Cost of capital
  • The IRR rule will give the same answer as the NPV rule in many, but not all, situations. For instance, it gives the correct answer for Fredrick’s fertiliser opportunity.
  • Whenever the cost of capital is below the IRR of 14%, the project has a positive NPV, and you should undertake the investment.
  • The NPV and IRR rules agree, but using the payback rule with a required payback period of two years or less would cause Fredrick’s to reject the project.

Weakness in IRR

  • In most cases, the IRR rule agrees with NPV for stand-alone projects if all negative cash flows precede positive cash flows.
  • But the decision rule will need to be modified when positive cash flows precede negative cash flows.
  • For projects involving both positive and negative future cash flows, multiple internal rates of return can exist.

IRR Rule Example

  • The example below has a cash inflow at the beginning, followed by cash outflows:
  • The NPV profile indicates that the decision rule changes in this case. We would only accept the project if the IRR < cost of capital.
  • Consider a project with the following cash outflows:
    • Year 0: Cash flow -$1,000
    • Year 1: Cash flow $2,500
    • Year 2: Cash flow -$1,540
  • This project has both positive and negative future cash flows. Hence, it will have multiple IRRs.
  • The project should be accepted only if the cost of capital is between 10% and 40%.

Summary of Internal Rate of Return (IRR)

  • Decision Rule:
    • IRR > Cost of capital: Accept the project.
    • IRR < Cost of capital: Reject the project.
  • Key Advantages:
    • IRR is expressed as a percentage, which is easy for decision-makers to interpret.
    • Like NPV, IRR takes into account the time value of money.
    • IRR is useful for comparing multiple projects of different sizes, durations, or cash flow structures.
  • Key Disadvantages:
    • The decision rule will need to be modified when positive cash flows precede negative cash flows.
    • For projects involving both positive and negative future cash flows, multiple internal rates of return can exist.
    • When comparing two mutually exclusive projects, IRR may not always give the correct decision.

Summary

  • Introduction to the firm’s investment decision
    • Long-term investment decisions, cost of capital, stand-alone projects, mutually exclusive projects
  • The NPV decision rule
    • A good project is one with a positive NPV. The NPV measures the increase in wealth from investing in the project
  • Using the NPV rule
    • If your objective is to maximise wealth, the NPV rule always gives the right answer
    • The difference between the cost of capital and the IRR is the maximum amount of estimation error that can exist in the cost of capital estimate without altering the original decision
  • Alternative decision rules
    • Payback rule and IRR rule
    • Understand their advantages and disadvantages

Formula Summary

  • NPV: NPV=PV(Benefits)−PV(Costs)NPV = PV(Benefits) - PV(Costs)
    • The benefits are cash inflows, and the costs are cash outflows. Hence, the NPV is the present value of all cash flows (both inflows and outflows) during the project's life.
    • NPV=PV(all project cash flows)NPV = PV(all\ project\ cash\ flows)
  • Payback period: =year before full recovery+unrecovered cost at start of yearcash flow during year= year\ before\ full\ recovery + \frac{unrecovered\ cost\ at\ start\ of\ year}{cash\ flow\ during\ year}
  • IRR: = the discount rate that makes the NPV zero