Capital Budgeting: To Invest or Not To Invest

Capital Budgeting Decision– usually involves long-term and high initial cost projects.– Invest if a project’s “value” >= “cost”.

Estimating initial costs Estimating “value”

– Estimate future cash flows: • timing (when?)• size (how much?)• risk (standard deviation, range, Min-Max?)

– Estimate discount rate• Opportunity cost of capital

– Risk of future cash flows

Mutually Exclusive vs. Independent Project

Mutual Exclusive Projects– only ONE of several potential projects can be chosen

• e.g. acquiring an accounting system.

– RANK all alternatives and select the best one.

Independent Projects– accepting or rejecting one project does not affect the

decision of the other projects.

– Must exceed a MINIMUM acceptance criteria

Net Present Value (NPV)

Net Present Value (NPV) = Total PV of future CF’s – Initial

– Reminder: PV = CFt / (1 + r)t

Reinvestment assumption– the NPV rule assumes that all cash flows can be reinvested at

the discount rate.Minimum Acceptance Criteria:

– Accept if NPV >= 0Ranking Criteria:

– Choose the highest NPV

Good Attributes of NPV Rule

1. Uses cash flows, not accounting earnings

2. Uses ALL cash flows of the project

3. Discounts ALL cash flows properly– Incorporates TVM

4. Reinvestment assumption makes economic sense

The Profitability Index (PI)

PI = Total Present Value of future CF’s / Initial Investment

Reinvestment assumption– the PI rule assumes that all cash flows can be reinvested

at the discount rate.Minimum Acceptance Criteria:

– Accept if PI >= 1Ranking Criteria:

– Select alternative with highest PI

PI (continued)

Disadvantages:– 1. May lead to incorrect decisions when comparing

mutually exclusive investments

Advantages:– 1. May be useful when available investment funds are

limited

– 2. Easy to understand and communicate

– 3. Correct decision when evaluating independent projects

Internal Rate of Return (IRR)

IRR– Defined as the discount that sets the NPV to zero

Reinvestment assumption: • the IRR calculation assumes that all future cash flows are

reinvested at the IRR

Minimum Acceptance Criteria: – Accept if the IRR >= required return

Ranking Criteria: – Select alternative with the highest IRR

IRR (continued)

Disadvantages:1. IRR may not exist or multiple IRR’s 2. May lead to incorrect decisions when comparing

mutually exclusive investments3. Reinvestment assumption may be unrealistic if project

IRR is exceptionally high Advantages:

1. Easy to understand and communicate2. Correct decision when evaluating independent projects

with conventional cash flows

NPV Profile

A graph showing the relationship between discount rate and NPV– Usually a downward sloping curve

• Negative relationship between discount rate and NPV

– A tool for computing IRR before computers– Useful for detecting multiple IRRs when project has

abnormal cash flowsCrossover Rate

– Discount rate at which 2 projects have the same NPV

Payback Period Rule

How long does it take for the project to “pay back” its initial investment?

Payback Period = # of years to recover initial costsMinimum Acceptance Criteria:

– Set by management.

Ranking Criteria: – Select alternative with the shortest payback period

Payback Rule (continued)

Disadvantages:– 1. Ignores the time value of money– 2. Ignores CF after payback period– 3. Biased against long-term projects– 4. Payback period may not exist or multiple payback periods– 5. Requires an arbitrary acceptance criteria– 6. A project accepted based on the payback criteria may not

have a positive NPV Advantages:

– 1. Easy to understand– 2. Biased toward liquidity

Discount Payback Rule

Similar to Payback except use discounted cash flow instead of cash flow to compute payback period.

Still has all the disadvantages of the payback rule except taking into acount TVM

Investment Rules: An Example

Rate 10%Time 0 1 2 3Project A CF -200 200 800 -800Project B CF -150 50 80 150

Capital Budgeting Example.xls

Cash Flows Estimation

Cash, CASH, CASH, CASH Incremental

– Sunk Cost

– Opportunity Costs

– Side Effects

Tax• After-tax (AT) value = Before-tax (BT) value * (1- Tax rate)

Inflation

A Simplified (Incremental) Cash Flow Statement

Revenue = Unit price x units sold- Variable Costs = Unit cost x units soldGross Profit- Cash Fixed Costs- DepreciationEBIT (Earnings Before Interest and Tax, Operating Income/Profit)- InterestEBT (Earnings Before Tax, Taxable Income)- TaxNet Income/Profit (Profit After Tax)

Two common ways to computing Operating Cash Flow (OCF)• OCF = EBIT + Depreciation – Taxes• OCF = Net Income + Depreciation + AT interest

Cash Flows for Projects (Free Cash Flows)

Net after-tax cash flow to the firm (Free Cash Flows) = Cash Flow from Operations - Addition to Fixed Assets - Addition to Net Working Capital

Net Working Capital (NWC) = Current assets – current liabilities

Additions to NWC = Ending NWC – Beginning NWC

Additions to fixed assets = Ending Net Fixed Assets (NFA) – Beginning NFA + depreciation– Or simply = the aggregate net assets purchased

Depreciation

Depreciation is a non-cash expense– Affects taxes, which is a cash expense

• Depreciation tax shield = Depreciation expense x tax rate Depreciation Methods

– IRS regulations– Accelerated method versus straight line

• Depreciable basis = Purchase cost + shipping and installation

– Depreciation Schedule• Book value = Depreciable Basis – Accumulated depreciation

Sale of Depreciated Assets• Capital Gain/loss = Resale value – Book value• Taxes on capital gain/loss = capital gain/loss x tax rate

Another Way to Compute Cash Flows

After-tax cash revenue = Before-tax cash revenue x (1 - Tax Rate) After-tax cash costs = Before-tax cash costs x (1 - Tax Rate) Tax Shield from Depreciation = Depr. Expense x Tax Rate OCF = AT revenue - AT costs + Depr tax shield Addition to Fixed Assets Addition to Net Working Capital Net AT CF = AT revenue - AT costs + Depr tax shield - addition

to assets - addition to NWC

Summary on Estimating Cash Flows

Income statement approach– Use income statement to compute tax

• OCF = Cash Revenue – Cash Expenses – taxes

Tax shield approach• OCF = (Cash Revenue – Cash Expenses) x (1- tax

rate) + tax rate x Depreciation expense

Net after-tax cash flows to firm = OCF – additions to fixed assets – additions to NWC

Two Ways to Compute NPV

Discount Net Total After-tax Increment Cash Flows– Discount all CFs at one rate

Discount Each Source of Cash Flows Individually– Allow each source of CF to be discounted at different

rate– 1. Revenue and cost: nominal risky rate– 2. Depreciation tax shield: nominal risk-free rate

Investments of Unequal Lives

Assumption: Both projects can and will be repeated

Repeat both projects until they begin and end at the same time

Compute NPV’s for the “repeated projects”

Replacement Projects

Compute NPV of New MachineCompute Equivalent Annual Cost (EAC)

– NPV - as PV– Life of New Machine - as NPER– Discount rate used in computing NPV - as RATE– Equivalent Annual Cost (EAC) - compute

PMT

Decision: Replace if EAC <= Cost of keeping the machine one more year

The Bottom Line

NPV, IRR and PI will generally give us the same decision

Exceptions– Non-conventional cash flows

• cash flow signs change more than once

– Mutually exclusive projects• Initial investments are substantially different• Timing of cash flows is substantially different

NPV directly measures the increase in value to the firm Whenever there is a conflict between NPV and another

decision rule, you should always use NPV

Capital Budgeting In Practice

We should consider several investment criteria when making decisions

NPV and IRR are the most commonly used primary investment criteria

Payback is a commonly used secondary investment criteria