1. Capital Budgeting

2. Capital budgeting: Defined as the analysis of
investment alternatives involving cash flows
received or paid over time.
Capital budgeting is used for decisions about
replacing equipment, leasing or buying, and
plant acquisitions.
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3. A euro today is worth more than a euro tomorrow, because
you could invest the euro today and have your euro plus
interest tomorrow.
Value at end
Alternative of one year
A. Invest €1,000 in bank account earning
5 percent per year €1,050
B. Invest €1,000 in project
returning €1,000 in one year
€1,000
Alternative B forgoes the €50 of interest that could have been
earned from the bank account.
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4. Because investment decisions are made at the
beginning of the investment period, all future cash
flows must be converted to their equivalent value
now.
Beginning-of-year amount (1 Interest rate) =
End-of-year amount
Beginning-of-year amount = End-of-year
amount (1 Interest rate)
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5. FV = Future Value
PV = Present Value
r = Interest rate per period
n = Periods from now
Future Value of a single amount:
FV = PV (1 + r)n
Present Value of a single flow:
PV = FV (1 + r)n
Discount factor = 1 (1 + r)n
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6. Present value of an annuity (a stream of equal
periodic payments for a fixed number of
years)
PV = (PMT r) { 1 – [1 (1 + r)n]}
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7. Procedure
1. Identify after-tax cash flows for each period
2. Determine discount rate
3. Multiply by appropriate present-value factor
for each cash flow. PV factor is 1.0 for cash
invested today.
4. Sum of the present values of cash flows =
net present value (NPV)
5. If NPV 0, then accept project
6. If NPV < 0, then reject project
NPV is also known as discounted cash flow (DCF).
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8. 1. Discount after-tax cash flows, not accounting
earnings
Cash can be invested and earn interest. Accounting
earnings include accruals that estimate future cash
flows.
2. Include working capital requirements
Consider cash needed for additional inventory and
accounts receivable.
3. Include opportunity costs but not sunk costs
Sunk costs are not relevant to decisions about future
alternatives.
4. Exclude financing costs
The firm’s opportunity cost of capital is included in the
discount rate.
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9. Determine cash flows after taxes:
Time Cash flow
Beginning of project Cash to acquire assets
Future years Depreciation deduction
return reduces future tax payments
(depreciation tax shield)
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10. t = Tax rate (tax refund if negative income)
R = Revenue in one year (assume all cash)
E = All cash expenses in one year (excludes
depreciation)
D = Depreciation in one year on income tax return
Tax expense for one year:
TAX= (R - E - D) t
After-tax cash flow for year:
ATCF = R - E - Tax
= R - E - (R - E - D) t = (R - E)(1 - t) + Dt
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11. Methods that consider time value of money:
1. Discounted cash flow (DCF), also known as
net present value (NPV) method
2. Internal rate of return (IRR)
Methods that do not consider time value of
money:
3. Payback method
4. Accounting rate of return on investment
(ROI)
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12. Payback = the time required until cash inflows from
a project equal the initial cash investment.
Advantages of payback method:
 Simple to explain and compute
Disadvantages of payback method:
 Ignores time value of money
 Ignores cash flows beyond end of payback period
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13. Average annual accounting income from
project Average annual investment in the
project
= Return on investment (ROI)
Average annual investment = (Initial investment
+ Salvage value at end) 2
Advantages of ROI method:
 Simple to explain and compute using financial
statements
Disadvantages of payback method:
 Ignores time value of money
 Accounting income is not equal to cash flow
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14. Internal rate of return (IRR) is the interest rate that
equates the present value of future cash flows to
the cash outflows.
By definition: PV = FV (1 + irr)^n
Comparison of IRR and DCF/NPV methods
 Both consider time value of cash flows
 IRR indicates relative return on investment
 DCF/NPV indicates magnitude of investment’s
return
 IRR can produce multiple rates of return
 IRR assumes all cash flows are reinvested at
project’s constant IRR
 DCF/NPV discounts all cash flows with specified
discount rate
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15. DCF/NPV has become the most commonly
used capital budgeting method for
evaluating new and replacement projects in
business enterprises.
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