Chapter 5: Investment Rules & Net Present Value

Mutual exclusion and differences in projet size

- Sometimes projects can have contrasting IRRs and NPVs ---> Regardless of the IRR, the project with the larger NPV is preferable - IRR calculation assumes that interim cash flows can be reinvested at the IRR, - While the NPV assumes the cash flows can be reinvested at the cost of capital. -The latter assumption is more reasonable. This is because a competitive market will bid away positive returns and investors will be left with the required return, which is the project'scost of capital.

Most Large firms group projects into categories based on perceived risk:

1) Maintenance 2) Cost-saving/revenue enhancing 3) Capacity expansion 4) New products and business 5) Projects required by government regulation or firm policy

Unconventional Cash Flows

Inverse Annuities: - One big positive cash flow followed by a number of negative cash flows. The pattern of payments is simply a standard annuity, but from an insurance company's perspective - With this type of CF, small IRRs are better.AKA if IRR < cost of capital, accept the project in this case Multiple IRRs: - Multiple IRRS occur when CF fluctuate between positive (inflows) and negative (outflows) through time. - i.e. more than one root (solutions) to IRR polynomial - the # of roots is equal to the # sign reversals in the stream of CF - *In this case, IRR use completely inappropriate (ONLY RELY ON NPV)

Net Present Value

Measure of the difference between the MARKET VALUE of an investment and ITS COST -->NPV often refer to as "discountned cash flow" valuation NPV Rule: 1) ACCEPT if NPV > 0 2) REJECT if NPV < 0 - NPV is a measure of economic profit and positive value, which is difficult to find in a competitive market, means that investors are earning more than the rate they require for the risk they bare for taking the project *NOTE: if NPV = 0 then project is generating apporpriate cost of capital for the firm.

NPV profile can be used to investigate problem with mutually exclusive projects

NPV Profile: A graph of NPV of a project against various costs of capital (r) - r is depicted on horizontal axis - NPV on vertical axis Crossover point (rate): the discount rate that makes the NPV of two projects the same (Assuming they cross). - Find the CR by taking the difference in the project's cash flows, and calculate the IRR

NPV and IRR

NPV and IRR will agree when projects are both CONVENTIONAL and INDEPENDENT 1) Conventional cash flows: an initial cash outflow followed by one or more expected future cash inflows 2) Independent projects are accepted or rejected without affecting the decision regarding another project *When accepting one project prevents investing in another, these projects are MUTUALLY EXCLUSIVE --> Use NPV profile in this case

Internal Rate of Return (IRR)

Project's expected return; calculated as the discount rate that gives a project a 0 NPV 0 = Initial investment + CF1/(1+IRR)^1 + CF2/(1+IRR)^2 + ... + CFn/ (1+IRR)^N IRR Rule: 1) ACCEPT if IRR > cost of capital (i.e. the required rate of return) 2) REJECT: if IRR < cost of capital

Profitability Index (or benefit/cost ratio)

The present value of the future cash flows DIVIDED by the Initial Investment PI = [PV (all future cash flows)] / Initial Investment RULE: if the PI > 1, do the project. - If a project has a positive NPV, then the PI will be GREATER THAN 1 - The PI gives a measure of VALUE PER $ Invested *This method has ranking problems similar to IRR when dealing with mutually exclusive projects, i.e. (we care more about project that adds greatest value, not necessarily biggest return per dollar) *a good method for firms w/ limited capital and looking for projects that offer biggest bang for buck

Modified IRR

The rate that equates the PV of all cash outflows and the future value of all cash inflows. The Method converts project valuation problem into a lump sum. MIRR rule: Accept the project if MIRR > cost of capital PV(outflows) = [FV(inflows at period N)] / [(1+MIRR)^N] *NOTE: ignore the negative sign on the outflows - The PV side of equation is the PV(Costs of Project discounted at cost of capital) - The FV cash flow is the compounded value of all Future inflows using the cost of capital and compounding to period N (the last period of the project) - Essentially comparing the 2 end points (value of costs today vs. value of cash flows in future) *MIRR avoids some of IRR pitfalls (e.g. multiple solutions) *MIRR and IRR will generate different rates. Bc MIRR assumes CF discounted and reinvested at cost of capital, while IRR assumers reinvest occurs at IRR

Project Cost of Capital:

The rate used to evaluate, or discount project cash flows. - The cost of capital reflects the riskiness of project cash flows, NOT the rate the firm currently pays for its assets or this riskiness of firm's assets. - Cost of capital reflects the return the firm's investors will require for the prospective project that is under consideration