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Issues in Capital Budgeting II. FINA 4463 (Chapter 12 in text). Capital Rationing. 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?

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Issues in capital budgeting ii l.jpg

Issues in Capital Budgeting II

FINA 4463

(Chapter 12 in text)

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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

    • Simply choosing highest NPV means choose A

      • Uses up total budget

      • NPV = 21.4

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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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    Problems with Profitability Index

    • If projects chosen via PI do not exhaust the budget, you may not get the optimal solution


    • Required return = 10%, budget constraint = $100

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    Problems with Profitability Index

    • PI says take first two projects for total NPV = 2.27 + 1.36 = 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

    • 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


    • 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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    • 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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    (example continued)

    • To solve, compare 3 projects of unequal lives: replace in year 1

      vs. replace in year 2

      vs. replace in year 3