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**Issues in Capital Budgeting II**

FINA 4463 (Chapter 12 in text)

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Capital Rationing

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Capital Rationing Usual assumption is that firm should accept all NPV>0- projects What if firm has a number of NPV>0 projects, but doe not have resources to take on all of them? This is situation of capital rationing Limited amount of capital to invest Must decide how to best invest the limited resources

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**Sources of Rationing Two types of capital rationing:**

Soft rationing: capital constraint imposed internally by the firm Head office may assign a budget to each division If soft rationing is leading to a division foregoing many NPV>0 projects, then the budget should be changed

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**Hard rationing: capital constraint imposed on firm by the capital markets**

Firm has limited internal cash, cannot borrow and cannot (or will not) issue new equity In a perfect world, there would never be externally imposed capital constraints In perfect world, firm could simply announce it had a good project to invest in, show investors the risk and return projections, and then investors would be willing to invest equity in/lend to the project

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**However, the world is not perfect.**

There are several reasons that firms may be unable or unwilling to bring in external financing for a good projects: Firm and investors may disagree on value of project Management may lack creditability Especially true for smaller, newer firms, or firms with poor records Flotation Costs It costs money to issue new shares/bonds The additional cost may make raising money to finance a project not worthwhile Flotation costs are higher for smaller issues, so small firms are affected the most (also higher for equity issues compared to debt).

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3. Underpriced shares Firms shares may be trading below their true value Management knows that the shares are undervalued (management has better info about firm than market = asymmetric information) Selling shares to raise funds to finance a project means that shareholders get a good project, but are selling part of the firm at a discount In some cases the project will not be worthwhile and firm will skip project Biggest effect on firms with high degree of asymmetric information (complicated firms, new firms, firms with few analysts following them)

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**Note: firms can benefit from having cash on hand available.**

Can fund NPV>0 projects that without accessing markets Do not have to skip a good projects because of reasons above Assuming a firm is subject to capital rationing, how should it solve for the optimal investment strategy, given the constraint?

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**Firm has $10 million available for investment, 3 potential projects**

Example: Firm has $10 million available for investment, 3 potential projects Simply choosing highest NPV means choose A Uses up total budget NPV = 21.4 Cashflows (millions) Project Year 0 Year 1 Year 2 10% A -10 30 5 21.4 B -5 20 16.1 C 15 11.9

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**However you could take B and C instead**

Uses up entire budget Total NPV = 28 B and C is the better choice Best combination of projects is fairly obvious in this case, but may not be in more complicated situations

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**Solving for Optimal Decision in Capital Rationing Problems**

Common way to approach capital rationing problem is to use the profitability index PI shows which projects give “most value for your money” PI = value of project per dollar invested Choose project with highest PI, and keep choosing projects until your budget runs out

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**From previous example:**

Solution by PI: choose B and C Project PI A 3.1 B 4.2 C 3.4

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**Problems with Profitability Index**

If projects chosen via PI do not exhaust the budget, you may not get the optimal solution Example Required return = 10%, budget constraint = $100 Cashflows Year 0 Year 1 P.I. NPV -5 8 1.454 2.27 7 1.272 1.36 -100 120 1.091 9.09

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**Problems with Profitability Index**

PI says take first two projects for total NPV = = 3.63 This leaves $90 of budget unspent Better to take third project by itself, for total NPV = 9.09 Reason: PI has difficulty in comparing projects of different sizes Note: As long as your answer using PI uses up entire budget the NPV should be the maximum possible

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**Problems with Profitability Index**

PI also runs into problems if there is more than one constraint faced by firm Projects are mutually exclusive (if you take one you cannot take the other) Projects are dependant (you can only take on one project, if you have already taken another) Budget constraints in more than one period Etc. The usual approach to capital rationing situations is to solve for the optimal investment using optimization software on a computer Maximize an objective function subject to certain constraints Can use “Solver” on Excel

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**Investments of Unequal Lives**

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**Investments of Unequal Lives**

When comparing mutually exclusive alternatives, NPV does not always give correct choice as to the best alternative if they are of different lengths e.g. comparing Machine A to Machine B where B costs more but lasts longer NPV does not take into account the different lifespans of the projects

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**Investments of Unequal Lives**

Example Machine A costs $10,000 and increase profits by $5000/year. It lasts 6 years. Machine B costs $5,500 and increases profits by $5000/year. It lasts 3 years Discount rate = 10%

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A has highest NPV A is best choice if this is a “one time deal” If you will only buy a machine once and never replace it More commonly, machines have to be replaced as they wear out If replacement of machines as they wear out is relevant, there are two methods to correctly compare the alternatives Project Replication Equivalent Annuities

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Project Replication Find a common multiple of the two life lengths Use this as total project length for both alternatives, where each alternative is repeated the appropriate number of times Calculate NPV over this common time frame and compare Equivalent Annuities Equate the NPV of each alternative to an annuity The length of the annuity equals the life of the project Solve for annuity payment that would give the same NPV The annuity payment represents the value per year created by the project Since projects are now on a common time frame (per year), can simply compare

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**Optimal Replacement Time**

It may sometimes pay to replace a machine before the end of its “natural” life May happen if: Better machine becomes available Salvage value is decreasing as machine ages Machine becomes more expensive to operate or less efficient overtime Optimal time to replace a machine is just a special case of comparing projects of unequal lives

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Example: A machine you always need for your production process Lasts a maximum of three years before replacement needed It becomes less efficient over time When replaced, you will replace with an identical (but new) machine How often should you replace? Discount rate=10%

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**Salvage value if sold this year**

(example continued) To solve, compare 3 projects of unequal lives: replace in year 1 vs. replace in year 2 vs. replace in year 3 Year 1 2 3 Cashflow -60000 40000 35000 25000 Salvage value if sold this year 30000 15000

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