Topic 1 (Week 1): Capital Budgeting

4.2. The Three Rules of Time Travel Rule 1: Comparing and combining values Topic 1 (Week 1): Capital Budgeting It is only possible to compare or combine values at the same point in time. A dollar today and a dollar in one year are not equivalent. Rule 2: Moving cash flows forward in time To move a cash flow forward in time, you must compound it: FV = C (1 + r) (1 + r) (1 + r) (1 + r) = C (1 + r n ) Rule 3: Moving cash flows back in time To move a cash flow back in time, we must discount it: PV = C (1+r n ) 4.3. Valuing a Stream of Cash Flows Most investment opportunities have multiple cash flows that occur at different points in time. We compute the present value of this cash flow stream in two steps: 1. Compute the present value of each individual cash flow 2. Combine them C 1 (1+r) + C 2 PV = C 0 + + + (1+r) 2 FV n = PV (1 + r) n C N (1+r) N = N C n n=0 (1+r) n 4.4. Calculating the NPV NPV compares the present value of cash inflows (benefits) to the present value of cash outflows (costs): NPV = PV(benefits) PV(costs) 4.5. Perpetuities and annuities Perpetuities A perpetuity is a stream of equal cash flows that occur at regular intervals and last forever: PV = C n=1 = C (1+r) n r Annuities An annuity is a stream of N equal cash flows paid at regular intervals: Present value of an annuity: PV(annuity) = C 1 r (1 1 (1+r) N) 1

Future value of an annuity: FV(annuity) = PV (1 + r) n = C 1 r ((1 + r)n 1) Growing cash flows Growing perpetuities: A growing perpetuity is a stream of cash flows that occur at regular intervals and grow at a constant rate forever: PV (growing perpetuity) = C r g Growing annuity: A growing annuity is a stream of N growing cash flows, paid at regular intervals. It is a growing perpetuity that eventually comes to an end: PV(growing annuity) = C 1 7.1. NPV and Stand-Alone Projects r g (1 (1+g 1+r )N ) NPV investment rule: When making an investment decision, take the alternative with the highest NPV. Choosing this alternative is equivalent to receiving its NPV in cash today NPV = P + C r The NPV profile and IRR The IRR of a project provides useful information regarding the sensitivity of the project s NPV to errors in the estimate of its cost of capital. In general, the difference between the cost of capital and the IRR is the maximum estimation error in the cost of capital that can exist without altering the original decision. 7.2. The Internal Rate of Return Rule IRR investment rule: Take any investment opportunity where the IRR exceeds the opportunity cost of capital. Turn down any opportunity whose IRR is less than the opportunity cost of capital. Applying the IRR rule The IRR rule is only guaranteed to work for a stand- alone project if all of the projects negative cash flows precede its positive cash flows. If this is not the case, the IRR rule can lead to incorrect decisions. Pitfalls of the IRR rule 1. Delayed investments 2. Multiple IRRs 3. Non- existent IRR 7.3. The Payback Rule Only accept a project if its cash flows pay back its initial investment within a pre-specified period. First, calculate the amount of time it takes to pay back the initial investment (payback period). Then you accept the project if the payback period is less than a pre-specified length of time. 2

Payback rule pitfalls in practice: 1. It ignores the project s cost of capital and the time value of money 2. Ignores cash flows after the payback period 3. Relies on ad hoc decision criterion (what is the right number of years?) 7.4. Choosing Between Projects NPV rule and mutually exclusive projects When projects are mutually exclusive, we need to determine which projects have a positive NPV and then rank the projects to identify the best one: Pick the project with the highest NPV IRR and mutually exclusive projects When projects differ in their scale of investment, the timing of their cash flows, or their riskiness, then their IRRs cannot be meaningfully compared. Differences in scale: Cannot tell how much value will actually be created without knowing the scale of the investment If we double the size of a positive NPV project, then its NPV will double (Law of One Price) However, IRR is unaffected by the scale of the investment opportunity because the IRR measures the average return of the investment Differences in timing: The IRR is expressed as a return, but the dollar value of earning a given return and therefore its NPV- depends on how long the return is earned Earning a very high annual return is much more valuable if you earn it for several years Differences in risk: Project s cost of capital is determined by the project s risk, so an IRR that is attractive for a safe project may not be attractive for a risky project The incremental IRR The IRR of the incremental cash flows that would result from replacing one project with the other Tells us the discount rate at which it becomes profitable to switch from one project to the other Optimal replacement Principle: When determining the optimal replacement policy for a piece of equipment, choose the option with the lowest annual equivalent cost (highest benefit) (perpetuity value): C = PV [ 1 (1+r) N ] r 3

7.5. Project Selection with Resource Constraint In principle, the firm should take on all positive NPV investments it can identify. In practice, there are often limitations on the number of projects the firm can undertake. Profitability index Practitioners often use the profitability index to identify the optimal combination of projects to undertake in such situations: PI = NPV resource consumed The profitability index measures the value created in terms of NPV per unit of resource consumed. Shortcomings of the profitability index: For the profitability index to be completely reliable, two conditions must be satisfied: 1. The set of projects taken following the profitability index ranking completely exhausts the available resources 2. There is only a single relevant resource constraint If more than one resource constraint is binding, then there is no simple index that can be used to rank projects. 8.1. Forecasting Earnings Capital budget- lists the projects and investments that a company plans to undertake during the coming year Capital budgeting- the process used to analyse alternative investments Incremental earnings- the amount by which the firm s earnings are expected to change as a result of the investment decision Our ultimate goal is to determine the effect of the decision on the firm s cash flows, and evaluate the NPV of these cash flows to assess the consequences of the decision for the firm s values. Incremental earnings forecast Capital expenditures and depreciation: When investments in PPE are a cash expense, they are not directly listed as expenses when calculating earnings. Instead the firm deducts a fraction of the cost as depreciation each year Interest expenses: We generally do not include interest expenses Taxes: The correct tax rate to use is the firm s marginal corporate tax rate, which is the tax rate it will pay on an incremental dollar of pre-tax income. Income tax = EBIT τ C Unlevered net income calculation: Unlevered net income = EBIT (1 τ C ) = (revenues costs depreciation) (1 τ C ) 4

Indirect effects on incremental earnings When comparing the incremental earnings of an investment decision, we should include all changes between the firm s earnings with the project versus without the project. Opportunity costs: Opportunity cost: The value it could have provided in its best alternative use Project externalities: Indirect effects of the project that may increase or decrease the profits of other business activities of the firm Cannibalisation: When sales of a new product displace sales of an existing product Side effects: When costs in another area of the firm will be reduced due to a new project (e.g. volume discounts) Sunk costs and incremental earnings Any unrecoverable cost for which the firm is already liable Sunk cost have been or will be paid regardless of the decision about whether or not to proceed with the project Exclude sunk costs from incremental earnings: Fixed overhead expenses: Past research and development expenditures: Unavoidable competitive effects Real world complexities: Sales will change from year to year The average cost per unit will change over time The average selling price will vary over time 8.2. Determining Free Cash Flow and NPV The incremental effect of a project on the firm s available cash is the project s free cash flow. Calculating free cash flow from earnings Capital expenditures and depreciation: Depreciation is not a cash flow, so we do not include it in the cash flow forecast. Instead, we include the actual cash cost of the asset when it is purchased. Net working capital (NWC): Net working capital is defined as the difference between current assets and current liabilities. The main components of NWC are cash, inventory, receivables and payables: NWC = current assets current liabilities = cash + inventory + receivables payables The difference between receivables and payables is the net amount of the firm s capital that is consumed as a result of credit transactions, known as trade credit. 5

The increase in net working capital is defined as: NWC t = NWC t NWC t 1 Calculating free cash flow directly: FCF = (revenues costs depreciation) (1 τ C ) + depreciation CapEx NWC FCF = unlevered net income + depreciation CapEx NWC The depreciation tax shield is the tax savings that results from the ability to deduct depreciation. As a consequence, depreciation expenses have a positive effect on free cash flow. Calculating the NPV: NPV = FCF t (1+r) t = FCF 1 (1+r) t The NPV of a project is the sum of the present values of each free cash flow. 8.3. Choosing Among Alternatives When evaluating an alternative production method or distribution channel (or any other alternative project) what matters is the incremental cash flows. Consider only those cash flows that differ from your base case All rules/ caveats regarding choice between mutually exclusive alternatives apply 8.4. Further Adjustments to Free Cash Flow Other non- cash items: E.g. Add back any amortisation of intangible assets Timing of cash flows: Cash flows are often spread throughout the year Salvage or liquidation value: Gain on sale = sale price book value Book value = purchase price accumulated depreciation After tax cash flow from asset sale = sale price (gain on sale τ C ) Terminal or continuation value: Represents the market value of the free cash flow from the project at all future dates. Frequently modelled as a growing perpetuity Tax carry forwards: Allows companies to take losses during its current year and offset them against gains in future years 8.5. Analysing the Project Break- even analysis The break-even level is the level for which the investment has an NPV of zero. E.g. IRR 6

Sensitivity analysis Sensitivity analysis shows how the NPV varies with a change in one of the assumptions, holding the other assumptions constant. By conducting a sensitivity analysis, we learn which assumptions are most important; we can then invest further resources and effort to refine these assumptions. Such an analysis also reveals which aspects of the project are most critical when we are actually managing the project. Scenario analysis Scenario analysis considers the effect on the NPV of changing multiple project parameters. 22.5. Applications to Multiple Projects In this section, we describe two important specific applications: how to decide between investing in two mutually exclusive projects of different lengths, and how to determine the order of investment for a staged investment opportunity. Comparing mutually exclusive investments with different lives Calculating the NPV on a standalone basis ignores the differences in the project s lifespans To truly compare two options, we must consider what will happen once the shorter- lived equipment wears out- consider the following three possibilities 1. The technology is not replaced: If the shorter- lived technology is not replaced (and the firm reverts to its old production process), there will be no additional benefits Therefore, the original comparison is correct 2. Replacement at the same terms: Suppose that we expect the costs and benefits of the shorter-lived design to be the same in five years In that case, it will be optimal to replace the machine with a new equivalent machine, as we will again earn its NPV 3. Technological advances allow us to replace it at improved terms: In reality, the future cost of a machine is uncertain Suppose we expect the cost of the new technology to fall The NPV will rise by the decline in cost Staging mutually dependent investments The advantage of staging is that it allows us to postpone investment until after we learn important new information. We can avoid making the investment unless the new information suggests it is worthwhile. In some situations, we can choose the order of the development stages. Mutually dependent investments: The value of one project depends upon the outcome of others 7

Investment scale: Other things being equal, it is beneficial to make the least costly investments first, delaying more expensive investments until it is clear they are warranted Investment time and risk: Other things being equal, it is beneficial to invest in riskier and lengthier projects first, delaying future investments until the greatest amount of information can be learned A general rule: By making smaller, riskier investments first, we gain the most additional information at the lowest cost In general, we can find the optimal order to stage mutually dependent projects by ranking each project from highest to lowest 22.6. Rules of Thumb The profitability index rule Some firms use the following rule of thumb: invest whenever the profitability index exceeds a specified level Profitability index = NPV initial investment It is often better to wait too long (use a profitability index criterion that is too high) than to invest too soon (use a profitability index criterion that is too low). The hurdle rate rule The profitability index rule raises the bar on the NPV to take into account the option to wait. The hurdle rate rule raises the discount rate. The hurdle rate rule uses a higher discount rate (hurdle rate) than the cost of capital to compute the NPV, but then applies the regular NPV rule: invest whenever the NPV calculated using this higher discount rate is positive. When the source of uncertainty that created a motive to wait is interest rate uncertainty, there is a natural way to approximate the optimal hurdle rate. In this case, the rule of thumb is to multiply the cost of capital by the ratio of the callable annuity rate, which is the rate on a risk-free annuity that can be repaid at any time, to the risk-free rate: Hurdle rate = cost of capital callable annuity rate risk free rate We should then invest whenever the NPV of the project is positive using this hurdle rate. 8