Capabilities

• 1. Discuss the difficulty encountered in finding profitable projects in competitive markets and the importance of the search.

• 2. Determine whether or not a new project should be accepted or rejected using the payback period, the net present value, the profitability index, and the internal rate of return.

• 3. Explain how the capital-budgeting decision process changes when a dollar limit is placed on the dollar size of the capital budget.

• 4. Discuss the problems encountered in project ranking.

• 5. Explain the importance of ethical considerations in capital-budgeting decisions.

• 6. Discuss the trends in the use of different capital-budgeting criteria.

●    Finding Profitable Projects

●    Capital-Budgeting Decision Criteria

●    Capital Rationing

●    Problems in Project Ranking—Capital Rationing, Mutually Exclusive Projects, and Problems with the IRR

●    Ethics in Capital Budgeting

A Glance at Actual Capital-Budgeting Practices

• Objective 1 FINDING PROFITABLE PROJECTS

• to evaluate profitable projects or investments in fixed assets, a process referred to as capital budgeting,

•  • Axiom 5: The Curse of Competitive Markets—

Why It’s Hard to Find Exceptionally Profitable Projects.

• The payback period is the number of years needed to recover the initial cash outlay.

Objective 2 CAPITAL-BUDGETING

DECISION CRITERIA A B • Initial cash outlay － $10,000 － $10,000• Annual net cash inflows • Year 1 $ 6,000 $ 5,000• 2 4,000 5,000• 3 3,000 0• 4 2,000 0• 5 1,000 0•

Net Present Value

• The net present value (NPV) of an investment proposal is equal to the present value of its annual net cash flows after taxes less the investment’s initial outlay.

n

t 1t

t

k)(1

ACF

NPV = - IO

NPV

• ACFt = the annual after-tax cash flow in tim

e period t .

• k = the appropriate discount rate; that is, the required rate of return or cost of capital

• IO = the initial cash outlay

• n = the project’s expected life

Principal

• NPV ≥ 0.0 : accept

• NPV ＜ 0.0 : reject

NPV Illustration of Investment in New Machinery

AFTER-TAX CASH FLOW Inflow year 1 15,000 2 14,000 3 13,000 4 12,000 5 11,000

Initial outlay － $40,000

Calculation for NPV Illustration of Investment in New Machinery PRESENT VALUE AFTER-TAX FACTOR AT PRESENT CASH FLOW 12 PERCENT VALUE 2 14,000 .797 11,158 3 13,000 .712 9,256 4 12,000 .636 7,632 5 11,000 .567 6,237Initial outlay － 40,000

Inflow year 1 15,000 .893 $13,395

Present value of cash flows $ 47,678

Net present value $ 7,678

Profitability Index (Benefit-Cost Ratio)

• The profitability index (PI), or benefit-cost ratio, is the ratio of the present value of the future net cash flows to the initial outlay.

IO

k

ACFn

tt

t 1 )1(PI =

• ACFt = the annual after-tax cash flow in time

period t (this can take on either positive or negative values )

• k = the appropriate discount rate; that is, the required rate of return or cost of capital

• IO = the initial cash outlay • n = the project’s expected life

Principale

• PI ≥ 1.0 : accept

• PI ＜ 1.0 : reject

PRESENT VALUE AFTER-TAX FACTOR AT PRESENT CASH FLOW 10 PERCENT VALUE Inflow year 1 15,000 0.909 13,635 2 8,000 0.826 6,608 3 10,000 0.751 7,510 4 12,000 0.683 8,196 5 14,000 0.621 8,694 6 16,000 0.564 9,024

Initial outlay － $50,000 1.000 － $50,000

IO

k

ACFn

tt

t 1 )1(

000,50$

024,9$694,8196,8$510,7$608,6$635,13$

000,50$

667,53$

= 1.0733

Internal Rate of Return

• The internal rate of return (IRR) the discount rate that equates the present value of the project’s future net cash flows with the project’s initial cash outlay.

n

t 1t

t

IRR)(1

ACF IO =

IRR

• ACFt = the annual after-tax cash flow in tim

e period t (this can take on either positive or negative values )

• IO = the initial cash outlay

• n = the project’s expected life

• IRR = the project’s internal rate of return

1)1(

000,15$

IRR 2)1(

000,15$

IRR 3)1(

000,15$

IRR 4)1(

000,15$

IRR$45,555 =

4

1 )1(

1

ttIRR

$45,555 = 15,000

$45,555 = $15,000 (PVIFA i , 4yr )

Dividing both sides by $15,000, this becomes

3.037 = PVIFA i, 4yr

IRR for Uneven Cash Flows

Present Value

Net Cash Flows Factor at 15 Percent Present Value

Inflow year 1 $1,000 .870 $ 870

Inflow year 2 2,000 .756 1,512

Inflow year 3 3,000 .658 1,974

Present value of inflows $ 4,356

Initial outlay － $ 3,817

2. TRY i = 20 PERCENT:

Present Value

• Net Cash Flows Factor at 20 Percent Present

Value

• Inflow year 1 $1,000 .833 $ 833

• Inflow year 2 2,000 .694 1,388

• Inflow year 3 3,000 .579 1,737

• Present value of inflows $ 3,958

• Initial outlay － $ 3,817

• 3. TRY i = 22 PERCENT:

Present Value

Net Cash Flows Factor at 22 Percent Present

Value

Inflow year 1 $1,000 .820 $ 820

Inflow year 2 2,000 .672 1,344

Inflow year 3 3,000 .551 1,653

Present value of inflows $ 3,817

Initial outlay － $ 3,817

Three IRR Investment

A B C Initial outlay － $10,000 － $10,000 － $10,000

Inflow year 1 3,362 0 1,000

Inflow year 2 3,362 0 3,000

Inflow year 3 3,362 0 6,000

Inflow year 4 3,362 13,605 7,000

15%

Present Value

Net Cash Flows Factor at 15 Percent Present

Value Inflow year 1 $1,000 .870 $ 870

Inflow year 2 3,000 .756 2,268

Inflow year 3 6,000 .658 3,948

Inflow year 4 7,000 .572 4,004

Present value of inflows $11,090

Initial outlay － $ 10,000

Present Value

• Net Cash Flows Factor at 19 Percent Present Value • Inflow year 1 $1,000 .840 $ 840

• Inflow year 2 3,000 .706 2,118

• Inflow year 3 6,000 .593 3,558

• Inflow year 4 7,000 .499 3,493

• Present value of inflows $10,009

• Initial outlay － $ 10,000

-2, 000

-1, 500

-1, 000

-500

0

500

1, 000

1, 500

0 100 200 300 400 500 600

Di scount rates(%)

Net

pres

ent

valu

e($)

Objective 4

• PROBLEMS IN PROJECT RANKING-CAPITAL RATIONING, MUTUALLY EXCLUSIVE PROJECTS,

AND PROBLEMS WITH THE IRR.

• 1 Size disparity

• 2 Time disparity

• 3 Unequal live

Capital-Rationing Example of Five Indivisible Projects

Project Initial Outlay Profitability Index Net Present Value

A $200,000 2.4 $280,000

B 200,000 2.3 260,000

C 800,000 1.7 560,000

D 300,000 1.3 90,000

E 300,000 1.2 60,000

Investment Evaluation A Primary A Secondary Total Using

Methods Used: Method Method This Method

 

Payback period 24% 59% 83%

Internal rate of return 88% 11% 99%

Net present value 63% 22% 85%

Profitability index 15% 18% 33%

 

Project Size and Decision-Making Authority

Project Size Typical Boundaries Primary Decision Site

 Very small Up to $100,000 Plant

Small $100,000 to $1 million Division

Medium $1 million to $10 million Corporate investment

committee

Large Over $10 million CEO & board

KEY TERMS

Benefit-Cost Ratio (see Profitability Index)Capital Budgeting Capital Rationing Equivalent Annual Annuity (EAA)Internal Rate of Return (IRR)Mutually Exclusive Projects Net Present Value (NPV)Payback period Profitability Index (PI or Benefit-Cost Ratio)