Copyright © 2008 Prentice Hall All rights reserved 9-1 Capital Investment Decisions and the Time...

Capital Investment Decisions and the Time Value of Money

Chapter 9

Objective 1

Describe the importance of capital investments and the capital

budgeting process

Capital Budgeting: The Process of Making Capital Investment Decisions

• Companies make capital investments when they acquire capital assets – assets used for a long period of time

• Capital investments include buying new equipment, building new plants, automating production and developing major commercial websites

• Capital investments affect operations for many years and usually require large sums of money

Four Popular Methods of Capital Budgeting Analysis

• Payback period

• Accounting Rate of Return (ARR)

• Net Present Value (NPV)

• Internal Rate of Return (IRR)

Capital Budgeting Process

• Identify potential investments

• Project the investment’s net cash inflows

• Analyze the investments using one or more of the four methods listed previously

Typical Capital Budgeting Process1. Identify potential capital investments

2. Estimate future net cash inflows

3. Analyze potential investments:

a. Screen out undesirable investments using payback and/or ARR b. Further analyze investments using NPV and/or IRR

4. Engage in capital rationing if necessary to choose among alternative investments

5. Perform post-audits

Objective 2

Use the payback and accounting rate of return methods to make

capital investment decisions

Payback Period

Payback – the length of time it takes to recover, in net cash inflows, the cost of the capital outlay

Amount investedExpected annual net cash inflows

When the net cash inflows are equal each year, the computation of the payback period is performed by dividing the amount invested by the expected annual net cash inflows. The result is the payback period in years.

Payback with Unequal Net Cash Inflows

Accumulate net cash inflows until amount invested is recovered

Payback Period

DECISION RULE: Payback Period

Investments with shorter payback periods are more desirable, all else

being equal

E9-16: Compute Payback Period with Equal Cash Flows

Amount invested

Expected annual net cash inflow

$1,236,100

$309,025

= 4 years

Accounting Rate of Return

Average annual operating income from assetAverage amount invested in asset

Average amount invested in asset =

Original Investment + Residual Value2

• Managers compare the accounting rate of return to company’s required minimum rate of return for investments of similar risk

• If the ARR is less than the required minimum, the investment is rejected

DECISION RULE: Invest in capital

assets?

Is expected accounting rate of return > the required

rate of return?

Invest

Is expected accounting rate of return < the required

rate of return?

Do not invest

E9-19: Compute and Compare ARR

$160,000

($1,000,000 + 0)/2

240,500

(1,200,000+100,000)/2

E9-18: ARR with Unequal Cash Flows

Average annual operating income:Year 1 $310,000Year 2 280,000 Years 3-10 ($240,000 x 8) 1,920,000 Total net cash flows $2,510,000Less: Total depreciation (1,454,000) Total operating income over life $1,056,000Divided by years of life 10 Average annual operating income $105,600

E9-18: ARR with Unequal Cash Flows

Average annual operating income from assetAverage amount invested in asset

$105,600($1,454,000+0) ÷ 2

= 14.53%

Objective 3

Use the time value of money to compute the present and future values

of single lump sums and annuities

Time Value of Money

• The fact that invested money earns income over time is called the time value of money

• This is why we prefer to receive cash sooner, rather than later

Factors That Affect Time Value of Money

• Principal – amount of the investment Lump sum Annuity

• Number of periods – number of times interest is computed

• Interest rate – annual percentage Simple interest Compound interest

Present Value & Future Value

1 2 3 4 5 6

Future ValuePresent Value

Time Periods

Future Value

Interest = $1,000 x .10 $100Principal = 1,000Future value after 1 year $1,100

$1,000

10%PresentValue

FutureValue

2 yrs 3 yrs

Future Value

Future value after 1 year $1,100Plus 10% interest 110Future value after 2 years $1,210Plus 10% interest 121Future value after 3 years $1,331

$1,000

10%PresentValue

FutureValue

2 yrs 3 yrs

Future Value

Or use the Future Value of $1 tableFuture value = Present value x table factor = $1,000 x 1.331 = $1,331

$1,000

10%PresentValue

FutureValue

2 yrs 3 yrs

Future Value of an Annuity

0 $1,000

10%PresentValue

FutureValue

$1,000

Year 3 $1,000Year 2 Future value of $1,000 in 1 year ($1,000 + ($1,000 x 10%) 1,100Year 1 Future value of $1,000 in 2 years ($1,100 + ($1,100 x 10%) 1,210

$3,310

Future Value of an Annuity

0 $1,000

10%PresentValue

FutureValue

$1,000

Future value = Payment x table factor

= $1,000 x 3.310

= $3,310

E9-20: Compare Retirement Savings Plans Using Future Value Concepts

Plan 1Future value = Payment x table factor

= $3,000 x 164.494= $493,482

Plan 2Future value = Payment x table factor

= $7,500 x 21.384= $160,380

E9-20: Compare Retirement Savings Plans Using Future Value Concepts

Plan 1Future value of $1 = present value x table factor

= $493,482 x 2.594= $1,280,092

Plan 2Future value of $1 = present value x table factor

= $160,380 x 2.594= $416,026

Present Value

? $1,100

Present value x 1.10 = $1,100Present value = $1,100/1.10Present value = $1,000

PresentValue

FutureValue

Present Value

? $1,100

Present value x 1.10 = $1,100Present value = $1,100/1.10Present value = $1,000

PresentValue

FutureValue

Present value x 1.10 = $1,000Present value = $1,000/1.10Present value = $909

Present Value of $1 Table

?$1,100

10%PresentValue

FutureValue

Present Value = Future Value x Table Factor = $1,100 x 0.826 = $909

Present Value of an Annuity

?$1,100

10%PresentValue

FutureValue

Present Value of $1,100 in one year:$1,100 x 0.909 = $1,000

$1,100

Present Value of $1,100 in two years:$1,100 x 0.826 = $909

$1,000 + $909 = $1,909

Present Value of an Annuity Table

?$1,100

10%PresentValue

FutureValue

$1,100

Present Value of Annuity = Payments x Table Factor = $1,100 x 1.736 = $1,909.60

E9-22: Fund Future Cash Flows

Req. 1Present value of annuity = Payment x table factor

= $30,000 x ?= ?

Req. 2Present value of annuity = Payment x table factor

= $30,000 x ?= ?

E9-23: Choosing a Lottery Payout Option Using Present Value

Option 1:

Present value of $1 = $12,000,000 x ?

Option 2:

Present value annuity = $2,250,000 x ?

E9-23: Choosing a Lottery Payout Option

Option 3:

Present value of $1 = $10,000,000 x ?

Objective 4

Use discounted cash flow models to make capital investment

decisions

Discounted Cash Flow Models

• Recognize time value of money

• Two methods Net present value Internal rate of return

• Compare amount of investment with its expected net cash inflows

Net Present Value Method

• Discount cash inflows to their present value and then compare with capital outlay required by the investment

• Discount rate (hurdle rate or required rate of return) – required minimum rate of return given riskiness of investment

• Proposal is acceptable when NPV is ≥ zero• The higher the NPV, the more attractive the

investment

Net Present Value

assets?

Is NPV positive?

Invest

Is NPV negative?

Do not invest

E9-25: Calculate NPV – Equal Annual Cash Flows

Cash Flow

When? Type of cash flow

PV factor

Project A

(272,000) (272,000)Now

60,000 Yrs 1-8 Annuity 4.639 278,340

$6,340

Cash Flow

PV factor

Project B

(380,000) (380,000)Now

70,000 Yrs 1-9 Annuity 5.328 372,960

$(7,040)

Net Present Value for Unequal Cash Inflows

When annual cash inflows are unequal, you must use the present value of one table applied to each annual cash inflow

E9-27: Calculate NPV – Unequal Cash Flows

Cash Flow

PV factor

(900,000) (900,000)Now

260,000 Yr 1 Lump sum .877 228,020

$(19,935)

250,000 Yr 2 Lump sum .769 192,250

225,000 Yr 3 Lump sum .675 151,875210,000 Yr 4 Lump sum .592 124,320

200,000 Yr 5 Lump sum .519 103,800

175,000 Yr 6 Lump sum .456 79,800

E9-27 2.Cash Flow

PV factor

75,000 Yr 7 .400 30,000Lump sum

50,000 Yr 7 .400 20,000Lump sum

(100,000) (45,600)Yr 6 Lump sum .456

$4,400

Profitability Index

Number of dollars returned for every dollar invested

Present value of net cash inflows

Investment

E9-29: Capital Rationing Decision

Present value of net cash inflows

Investment

A: $1,695,000 ÷ $1,500,000 = 1.13

B: $1,960,000 ÷ $1,750,000 = 1.12

C: $2,200,000 ÷ $2,000,000 = 1.10

Internal Rate of Return

• Rate of return a company can expect to earn by investing in the project

• The interest rate that will cause the present value to equal zero

Step 1: Identify the expected net cash receipts

Step 2: Find the discount rate that makes total present value of net cash receipts = present value of cash outflows

Annuity PV factor = Investment ÷ Annual Net Cash Receipts

Step 3: On the present value of an annuity of $1 table, scan the row corresponding to the expected life

Choose column closest to annuity factor you calculated in Step 2

assets?

Does the IRR exceed required rate of return?

Invest

Is the IRR less than required rate of return?

Do not invest

E9-26: Calculate IRR of Equal Cash Flows

Project A:

PVA = Payment x Table Factor

272,000 = 60,000 x Factor

4.533 = Factor

Between 14% and 16%

E9-26: Calculate IRR of Equal Cash Flows

Project B:

PVA = Payment X Table Factor

380,000 = 70,000 x Factor

5.429 = Factor

Between 10% and 12%

IRR with Unequal Periodic Cash Flows

Trial and error procedure is needed to determine the discount rate making the project’s NPV equal to zero

E9-28: Compute IRR for Unequal Cash Flows

Compute net present value at 10%:Cash Flow

PV factor

$60,200

(950,000) (950,000)Now

500,000 Yr 1 .909 454,500

400,000 Yr 2

Lump sum

.826 330,400Lump sum300,000 Yr 3 .751 225,300Lump sumSince the NPV is positive, the IRR must be higher

than 10%. Try 12% next.

E9-28: Compute IRR – Unequal Cash Flows

PV factor

(950,000) (950,000)Now

500,000 Yr 1 .893 446,500

400,000 Yr 2

Lump sum

.797 318,800Lump sum

$28,900

300,000 Yr 3 .712 213,600Lump sumSince the NPV is positive, the IRR must be higher

than 12%. Try 14% next.

E9-28: Compute IRR – Unequal Cash Flows

PV factor

(950,000) (950,000)Now

500,000 Yr 1 .877 438,500

400,000 Yr 2

Lump sum

.769 307,600Lump sum

$(1,400)

300,000 Yr 3 .675 202,500Lump sum

Objective 5

Compare and contrast the four capital budgeting methods

Comparison of CapitalBudgeting Models

Payback Period

• Simple

• Focus is the time it takes to recover cash

• Ignores cash flows after payback period

• Highlights risks of investments with longer cash recovery periods

• Ignores time value of money

• Only method that uses accrual accounting

• Shows how investment will affect operating income

• Measures profitability of asset over its entire life

• Ignores time value of money

Net Present Value• Incorporates time value of money and net

cash flows• Indicates if asset will earn minimum

required rate of return• Shows excess (deficiency) of present

value of cash inflows over cost• Profitability index can be computed for

capital rationing decisions

• Incorporates time value of money and net cash flows

• Computes unique rate of return

• No additional steps needed for capital rationing decisions

End of Chapter 9

Copyright © 2008 Prentice Hall All rights reserved 9-1 Capital Investment Decisions and the Time...

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