Alternative Investment Rules and Capital Budgeting Analysis Capital budgeting is the planning for...

Alternative Investment Rules and Capital Budgeting Analysis

Capital budgeting is the planning for purchases of assets whose returns

are expected to continue beyond one year.

Common Models

• There are several common models used in evaluating capital budgeting decisions:– Net present value – Payback period– Average accounting return– Internal rate of return– Profitability index

Defining Project Type

• Mutually 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.

The Net Present Value (NPV) Rule

• Net Present Value (NPV) = Total PV of future CF’s + Initial Investment

• Estimating NPV:– 1. Estimate future cash flows: how much? and when?

– 2. Estimate discount rate

– 3. Estimate initial costs

• Minimum Acceptance Criteria: Accept if NPV > 0• Ranking Criteria: Choose the highest NPV

Good Attributes of the NPV Rule

• 1. Uses cash flows

• 2. Uses ALL cash flows of the project

• 3. Discounts ALL cash flows properly

The Payback Period Rule

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

• Payback Period = # of years to recover initial costs.

• Minimum Acceptance Criteria: set by management. Project must “pay back” within a certain period.

• Ranking Criteria: set by management.

Disadvantages of Payback Rule

• Ignores the time value of money.• Ignores CF after payback period.• Biased against long-term projects.• Payback period may not exist or there may

be multiple payback periods.• Requires an arbitrary acceptance criteria.• A project accepted based on the payback

criteria may not have a positive NPV.

Advantages of Payback Rule

• Easy to understand

• Biased toward liquidity

The Average Accounting Return (AAR) Rule

• AAR = Average NI / Average Book Value of Investment

• Minimum Acceptance Criteria: set by management.

• Ranking Criteria: set by management.

Disadvantages of AAR Rule

• Ignores the time value of money

• Uses an arbitrary benchmark cutoff rate

• Based on book values, not cash flows and market values

Advantages of AAR Rule

• The accounting information is usually available

• Easy to calculate

The Internal Rate of Return (IRR) Rule

• The IRR is the discount rate that sets the NPV to zero.

• Minimum Acceptance Criteria: Accept if the IRR > required return.

• Ranking Criteria: Select alternative with the highest IRR.

Disadvantages of IRR Rule

• Does not distinguish between investing and financing.

• IRR may not exist, or there may be multiple IRR’s

• Problems with mutually exclusive investments– borrowing or lending?– multiple (or no) rates of return– mutually exclusive projects: scale and timing

Advantages of IRR Rule

• Easy to understand and communicate

Problem # 1: Borrowing or LendingCf(0) Cf(1) Cf(2) Cf(3) IRR NPV @ 10%

+1000 -500 -500 -500 23.4% -243.43

This project represents the borrower’s side of a loan. Thus, as the discount rate increases, the NPV of the project increases.

23% r

NPV

Problem # 2: Multiple Rates of Return

NPV @

Cf(0) Cf(1) Cf(2) IRR 10%

-4,000 25,000 -25,000 25% -1,934

& 400%

NPV

r400%25%

Note: It is alsopossible there isno IRR.

Mutually Exclusive Projects: Problem # 1-- The Scale Problem

NPV

Cf(0) Cf(1) IRR @ 10%

Project 1 -100 200 100% $82

Project 2 -1000 1500 50% $323.6

Do not compare the IRR’s of mutually exclusive projects.

Mutually Exclusive Projects: Problem #2-- Timing Problem

Cf(0) Cf(1) Cf(2) Cf(3)

A: -$10,000 $10,000 $1,000 $1,000

B: -$10,000 $1,000 $1,000 $12,000

NPV NPV NPV

@ 0% @10% @15% IRR

A: $2,000 $669 $109 16.04%

B: $4,000 $751 -$484 12.94%

NPV & IRR for Timing Problem

-4000

-3000

-2000

-1000

0

1000

2000

3000

4000

5000

0 10 20 30 40

rNP

V

When interest rates are low, Project B has the higher NPV. When interest rates are high,Project A has the higher NPV.

Project B

Project ACrossoverRate

The Profitability Index (PI) Rule

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

• Minimum Acceptance Criteria: Accept if PI > 1

• Ranking Criteria: Select alternative with highest PI

Disadvantages of PI Rule

• Problems with mutually exclusive investments

Advantages of PI Rule

• May be useful when available investment funds are limited

• Easy to understand and communicate

• Correct decision when evaluating independent projects

Example: Investment Rules

Compute the IRR, NPV, PI, and payback period for the following two projects. Assume the required return is 10%.

Year Project A Project B

0 -$200 -$150

1 $200 $50

2 $800 $100

3 -$800 $150

Example of Investment Rules: NPV, IRR, PI

Project A Project B

CF0 -$200.00 -$150.00

PV0 of CF1-3 $241.92 $240.80

NPV = $41.92 $90.80

IRR = 0%, 100% 36.19%

PI = 1.2096 1.6053

Example of Investment Rules: Payback Period

Payback Period:

Project A Project B

Time CF Cum. CF CF Cum. CF

0 -200 -200 -150 -150

1 200 0 50 -100

2 800 800 100 0

3 -800 0 150 150

Payback Period (cont’d)

Payback period for project B = 2 years

Payback period for project A = 1 or 3 years?

Relationship Between NPV and IRR

Discount rate NPV for A NPV for B-10% -87.52 234.77

0% 0.00 150.0020% 59.26 47.9240% 59.48 -8.6060% 42.19 -43.0780% 20.85 -65.64

100% 0.00 -81.25

120% -18.93 -92.52

NPV Profiles

-150

-100

-50

0

50

100

150

200

250

300

-10 0 20 40 60 80 100 120

r

NP

V

Project A

Project B

CrossoverRate

NPV & Capital Budgeting

Four basic steps for project valuation:1. Generate proposals.

2. Estimate cash flows.

3. Evaluate and select projects.

4. Review decisions.

Generating Proposals

• Projects may come from growth opportunities.

• Projects may come from cost reduction opportunities.

• Projects may be required to meet legal requirements or health and safety standards.

Estimating Cash Flows

• Cash Flows should be estimated on an incremental basis. Compare the cash flows with the project to cash flows without the project.

• Cash flows should be measured on an after-tax basis, except for government projects.

• Use cash flows - not accounting income.

Estimating Cash Flows

• “Let bygones be bygones” - ignore sunk costs.

• Remember opportunity costs of resources used.

• Consider side effects - are cash flows from other projects affected? Either up or down?

Example: Project Valuation

• Suppose a steel company is thinking of adding a new blast furnace to its operations. You have just completed a $1 million feasibility study and have found the following:

• Adding the blast furnace will result in $50 million in new sales each year and will save $100 million per year in expenses. However, the furnace will cost $10 million per year to operate.

Example - Continued• Suppose the furnace costs $1,000 million and uses

some parts from a (fully depreciated) retired furnace that could be sold for $30 million. The new furnace will last 10 years and has a salvage value of $200 million. The project will require $20 million of working capital over its 10-year life.

• The firm uses straight-line depreciation for tax purposes and pays 40% in corporate income taxes.

• Assume the cost of capital is 10%.

Example - Continued• Step One (“No Rules, Just Right”, i.e., it works

for me...): Initial Cash Flow.• $1,000 million capital expenditure• $20 million working capital• $30 million lost gain on sale of old furnace• But, would have paid taxes on gain of (.40*$30

million) = $12 million. Net gain if sold old furnace = $18 million

• Total initial cash flow = -$1,038 million• (Negative sign reflects cash outflow.)

Example - Continued• Step Two: Operating Cash Flows.• Change in Depreciation each year =

$1,000 million ÷ 10 = $100 million• Change in Revenue = $50 million • Change in Expenses = $10 million - $100 million

(savings) = -$90 • Change in Taxes = ($50 - (-$90) - $100) * .40 =

$16 million• CFi = ($50 - (-$90) - $100) - $16 + $100 = $124

million

Example - Continued• In Cash Flow Statement Format:

Revenues $50- Expenses -(-90)- Depreciation -100= EBT = $40- Taxes (.40) -16= EAT = $24+ Depreciation +100= Cash Flow = $124

Example - Continued

• Step Three: Project Termination Cash Flows.

• Salvage Value = $200 million

• Owe taxes of (.40 * $200 million) = $80 million

• Release of Working Capital = $20 million

• Total = $200 - $80 + $20 = $140 million

Example - Continued

• Step Four: Find NPV

• NPV = -$1,038 million + $124 million * (PVIFA10%, 9) + ($124 million + $140 million) * PVIF10%, 10)

• CF0 = -1,038, C01 = 124, F01 = 9, C02 = 264, F02 = 1, I% =10%

• NPV = -$222 million, IRR = 5.10%

Example - Continued

• Step Five: Make decision.

• Reject project since NPV is less than zero.

Additional Considerations

• Inflation

• Comparing Projects with Different Lives

Cash Flows and Inflation

• It is important to recognize the effects of inflation on cash flows.

• The Fisher equation says:• (1 + nominal rate of interest) = (1 + real

interest rate) * (1 + inflation rate)• Example: If the real interest rate is 5% and

inflation is 4%, the nominal rate of interest is 9.2% (1.05 x 1.04 = 1.092, or 9.2%)

Consistency

• The most important lesson in choosing the appropriate discount rate is to be consistent.

• Nominal cash flows must be discounted with the nominal interest rate.

• Real cash flows must be discounted with the real interest rate.

Projects with Different Lives - Replacement Chain Analysis

• Replacement chain analysis assumes that alternative projects can and will be repeated.

• Matching-cycle analysis finds a common multiple of both projects and finds NPV for project string, i.e., if one project last 2 years and the other lasts 3 years, compare NPVs if invest in the first project 3 times consecutively and the second project 2 times consecutively.

• Huh?

Projects with Different Lives - Replacement Chain Analysis

• Equivalent annual cost analysis finds the equal annual payments over the life of the project that have the same NPV as the true cash flows.

• Generally, easier to compute than matching-cycle analysis.

Example: Equivalent Annual Cost

Suppose we’re looking at the cost of two machines, A and B, r = 5%. (All cash outflows.)

Machine A Machine B

t=0 $15 million $20 million

t=1 $2 million $1 million

t=2 $2 million $1 million

t=3 $1 million

Example - Continued

• Project A lasts two years.

• Find the NPV of A = -$18.72 million.

• Find the equal annual amount that gives an NPV of -$18.72 million over 2 years.

• N=2, I=5, PV=-$18.72, FV=0 ==> PMT= $10.07 million

• Payments of $10.07 million gives same NPV as Machine A’s Cash Flows

Example - Continued

• Project B lasts 3 years and has NPV=-22.72• Find the equal annual amount that gives an

NPV of -$22.72 million over 3 years.• N=3, I=5, PV=-$22.72, FV=0 ==> PMT=

$8.34 million• Payments of $8.34 million gives same NPV

as Machine B’s Cash Flows• Choose Machine B - Lowest Cost