Capital Budgeting Topics Investments of Unequal Lives

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Capital Budgeting Topics Investments of Unequal
Lives

• There are times when application of the NPV rule
  can lead to the wrong decision. Consider an
  investment in equipment required in the
  production process
• There are two choices
• The Auto Machine costs 40,000 today, has
  annual operating costs of 1,000 and lasts for 10
  years.
• The Manual Machine costs 10,000 today, has
  annual operating costs of 5,000 and lasts for 5
  years.
• Which one should we choose?

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Investments of Unequal Lives

• At first glance, the Manual has the lower NPV
  (r 10)

This overlooks the fact that the Auto Machine
lasts twice as long. When we incorporate that,
the Auto Machine is actually cheaper.
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Investments of Unequal Lives - Replacement Chain

• The Manual Machine time line of cash flows over
  ten years with a replacement at the end of its
  life

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Investments of Unequal Lives

• Replacement Chain - Matching Cycle
• Repeat the projects forever, find the PV of that
  perpetuity.
• Assumption Both projects can and will be
  repeated.
• Repeat projects until they begin and end at the
  same timelike we just did with the air cleaners.
• Compute NPV for the repeated projects.
• The Equivalent Annual Cost Method

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Investments of Unequal Lives EAC

• The Equivalent Annual Cost Method
• Applicable to a much more robust set of
  circumstances than replacement chain.
• The Equivalent Annual Cost is the value of the
  level payment annuity that has the same PV as our
  original set of cash flows.
• NPV EAC annuity factor

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Investments of Unequal Lives EAC

• For example, the EAC for the Auto Machine is
• Using the annuity factor

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Financial Leverage and Beta

• Financial leverage is the sensitivity of a firms
  fixed costs of financing.
• The relationship between the betas of the firms
  debt, equity, and assets is given by

• Financial leverage always increases the equity
  beta relative to the asset beta.

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Financial Leverage and Beta Example

• The XYZ, Inc., is currently all-equity and it has
  a beta of 1.10.
• The firm has decided to lever up to a capital
  structure of 25 debt and 75 equity.
• Since the firm will remain in the same industry,
  its asset beta should remain 0.90.
• However, assuming a zero beta for its debt, its
  equity beta would become twice as large

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The Project versus the Firm

• Any projects cost of capital depends on the use
  (the project) to which the capital is being
  putnot the source of capital.
• Therefore, it depends on the risk of the project
  and not the risk of the firm.

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Capital Budgeting Project Risk
Project IRR
Hurdle rate
Firms risk (beta)

• A firm that uses one discount rate for all
  projects may over time increase the risk of the
  firm while decreasing its value.

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Capital Budgeting Project Risk

• Suppose a firm is made of three equal size
  departments. The companys cost of equity capital
  is based on the CAPM. The risk-free rate is 4
  the market risk premium is 10
• The breakdown of the companys departments.

Electronic parts dep. b 1.1Electric
equipment dep. b 1.4Computer parts dep. b
2.0
Average b of assets 1.5
Cost of Equity 4 1.5 14 4 19 When
evaluating a new computer parts project, which
cost of capital should be used?
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Capital Budgeting Project Risk

• Suppose a computer part project with an IRR of
  20 is accepted.
• It will change the firm division into 50
  computer parts and 25 for each other department.
  

New Average b of assets 1.725
The firm required return 4 1.72510
21.25 Which is definitely above the firm actual
return
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The Cost of Capital with Debt

• The Weighted Average Cost of Capital is given by

• It is because interest expense is tax-deductible
  that we multiply the last term by (1- tC) making
  the true cost of debt rD(1- tC)

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Estimating Widget Inc. Cost of Capital

• First, we estimate the cost of equity and the
  cost of debt.
• We estimate an equity beta to estimate the cost
  of equity.
• We can often estimate the cost of debt by
  observing the YTM of the firms debt.
• Second, we determine the WACC by weighting these
  two costs.

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Estimating Widgets Cost of Capital

• The industry average beta is 1.30 the risk free
  rate is 4 and the market risk premium is 5.6.
• Thus the cost of equity capital is

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Estimating Widgets Cost of Capital

• The yield on the companys debt is 7.2
  (relative to similar maturity treasury bonds and
  credit risk) and the firm is in the 36 marginal
  tax rate.
• The debt is 26 of the total firm value

9.55 percent is Widgets cost of capital. It
should be used to discount any project where the
projects risk is equal to the risk of the firm
as a whole, and the project is financed with the
same leverage as the whole firm.