mcgraw-hill /irwin copyright © 2008 by the mcgraw-hill companies, inc. all rights reserved. chapter...

McGraw-Hill /Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved.

Chapter 12

Capital Budgeting Decisions

12-2

Typical Capital Budgeting Decisions

Plant expansionPlant expansion

Equipment selectionEquipment selection Equipment replacementEquipment replacement

Lease or buyLease or buy Cost reductionCost reduction

Capital budgeting analysis can be used for any decision Capital budgeting analysis can be used for any decision that involves an outlay now in order to obtain some future that involves an outlay now in order to obtain some future return. Typical capital budgeting decisions include:return. Typical capital budgeting decisions include:

12-3

Typical Capital Budgeting Decisions

Capital budgeting tends to fall into two broad Capital budgeting tends to fall into two broad categories . . .categories . . .

Screening decisionsScreening decisions.. Does a proposed Does a proposed project meet some present standard of project meet some present standard of acceptance?acceptance?

Preference decisionsPreference decisions.. Selecting from Selecting from among several competing courses of action. among several competing courses of action.

Capital budgeting tends to fall into two broad Capital budgeting tends to fall into two broad categories . . .categories . . .

Screening decisionsScreening decisions.. Does a proposed Does a proposed project meet some present standard of project meet some present standard of acceptance?acceptance?

Preference decisionsPreference decisions.. Selecting from Selecting from among several competing courses of action. among several competing courses of action.

12-4

Time Value of Money

A dollar today is worth A dollar today is worth more than a dollar a more than a dollar a

year from now. year from now. Therefore, investments Therefore, investments

that promise earlier that promise earlier returns are preferable to returns are preferable to those that promise later those that promise later

returns. returns.

12-5

The capital budgeting techniques that best recognize the time value of money are those that involve

discounted cash flowsdiscounted cash flows.

The capital budgeting techniques that best recognize the time value of money are those that involve

discounted cash flowsdiscounted cash flows.

Time Value of Money

12-6

Learning Objective 1

Evaluate the acceptabilityof an investment project

using the net presentvalue method.

12-7

The Net Present Value Method

To determine net present value we . . .To determine net present value we . . .Calculate the present value of cash Calculate the present value of cash

inflows,inflows,Calculate the present value of cash Calculate the present value of cash

outflows,outflows,Subtract the present value of the outflows Subtract the present value of the outflows

from the present value of the inflows.from the present value of the inflows.

To determine net present value we . . .To determine net present value we . . .Calculate the present value of cash Calculate the present value of cash

inflows,inflows,Calculate the present value of cash Calculate the present value of cash

outflows,outflows,Subtract the present value of the outflows Subtract the present value of the outflows

from the present value of the inflows.from the present value of the inflows.

12-8


General decision rule . . .General decision rule . . .

12-9

Net present value analysis Net present value analysis emphasizes cash flows and not emphasizes cash flows and not

accounting net income.accounting net income.

Net present value analysis Net present value analysis emphasizes cash flows and not emphasizes cash flows and not

accounting net income.accounting net income.

The reason is that accounting net income is

based on accruals that ignore the timing of cash flows into and out of an

organization.

The reason is that accounting net income is

based on accruals that ignore the timing of cash flows into and out of an

organization.


12-10

Repairs andRepairs andmaintenancemaintenance

IncrementalIncrementaloperatingoperating

costscosts

InitialInitialinvestmentinvestment

WorkingWorkingcapitalcapital

Typical Cash Outflows

12-11

ReductionReductionof costsof costs

SalvageSalvagevaluevalue

IncrementalIncrementalrevenuesrevenues

Release ofRelease ofworkingworkingcapitalcapital

Typical Cash Inflows

12-12

Two simplifying assumptions are usually Two simplifying assumptions are usually made in net present value analysis:made in net present value analysis:

All cash flows other than the initial

investment occur at the end of periodsend of periods.

All cash flows other than the initial

investment occur at the end of periodsend of periods.

All cash flows generated by an

investment project are immediately immediately

reinvestedreinvested at a rate of return equal to the

discount rate.

All cash flows generated by an

investment project are immediately immediately

reinvestedreinvested at a rate of return equal to the

discount rate.

Two Simplifying Assumptions

12-13

Choosing a Discount Rate

The cost of capital is the The cost of capital is the average rate of return the average rate of return the company must pay to its company must pay to its long-term creditors and long-term creditors and stockholders for the use of stockholders for the use of their funds.their funds.

The firm’s The firm’s cost of capitalcost of capital is is usually regarded as the usually regarded as the minimum required rate of minimum required rate of return.return.

The cost of capital is the The cost of capital is the average rate of return the average rate of return the company must pay to its company must pay to its long-term creditors and long-term creditors and stockholders for the use of stockholders for the use of their funds.their funds.

The firm’s The firm’s cost of capitalcost of capital is is usually regarded as the usually regarded as the minimum required rate of minimum required rate of return.return.

12-14


Let’s look at how we use the net present value

method to make business decisions.

Let’s look at how we use the net present value

method to make business decisions.

12-15


Lester Company has been offered a five year contract to provide component parts for a large

manufacturer.

12-16


At the end of five years, the working At the end of five years, the working capital will be released and may be capital will be released and may be used elsewhere by Lester.used elsewhere by Lester.

Lester Company uses a discount rate Lester Company uses a discount rate of 10%.of 10%.

Should the contract be accepted?Should the contract be accepted?

At the end of five years, the working At the end of five years, the working capital will be released and may be capital will be released and may be used elsewhere by Lester.used elsewhere by Lester.

Lester Company uses a discount rate Lester Company uses a discount rate of 10%.of 10%.

Should the contract be accepted?Should the contract be accepted?

12-17


Annual net cash inflows from operations

12-18


12-19

Present value of an annuityannuity of $1 factor for 5 years at 10%.

Present value of an annuityannuity of $1 factor for 5 years at 10%.


12-20

Present value of $1 factor for 3 years at 10%.

Present value of $1 factor for 3 years at 10%.


12-21

Present value of $1 Present value of $1 factor for 5 years at 10%.factor for 5 years at 10%.

Present value of $1 Present value of $1 factor for 5 years at 10%.factor for 5 years at 10%.


12-22

Accept the contract because the project has a positivepositive net present value.


12-23

Quick Check

Denny Associates has been offered a four-year contract to supply the computing requirements for a local bank.

The working capital is released at the end of the contract. Denny Associates requires a 14% return.

12-24

Quick Check

What is the net present value of the contract with the local bank?

a. $150,000

b. $ 28,230

c. $ 92,340

d. $132,916


a. $150,000

b. $ 28,230

c. $ 92,340

d. $132,916

12-25


a. $150,000

b. $ 28,230

c. $ 92,340

d. $132,916


a. $150,000

b. $ 28,230

c. $ 92,340

d. $132,916

Quick Check

12-26Expanding the Net Present Value Method

To compare competing investment To compare competing investment projects, we can use the following net projects, we can use the following net

present value approaches:present value approaches:Total-costTotal-cost

Incremental costIncremental cost

To compare competing investment To compare competing investment projects, we can use the following net projects, we can use the following net

present value approaches:present value approaches:Total-costTotal-cost

Incremental costIncremental cost

12-27

The Total-Cost Approach

White Co. has two alternatives:White Co. has two alternatives:(1) remodel an old car wash or, (1) remodel an old car wash or, (2) remove it and install a new one.(2) remove it and install a new one.

The company uses a discount rate of 10%.The company uses a discount rate of 10%.

White Co. has two alternatives:White Co. has two alternatives:(1) remodel an old car wash or, (1) remodel an old car wash or, (2) remove it and install a new one.(2) remove it and install a new one.


New Car Wash

Old Car Wash

Annual revenues 90,000$ 70,000$ Annual cash operating costs 30,000 25,000 Net annual cash inflows 60,000$ 45,000$

12-28


If White installs a new washer . . .If White installs a new washer . . .

Cost $300,000 Productive life 10 yearsSalvage value 7,000Replace brushes at the end of 6 years 50,000Salvage of old equip. 40,000

Let’s look at the net present Let’s look at the net present value of this alternative.value of this alternative.

12-29

If we install the new washer, the If we install the new washer, the investment will yield a positive net investment will yield a positive net

present value of $83,202.present value of $83,202.

If we install the new washer, the If we install the new washer, the investment will yield a positive net investment will yield a positive net

present value of $83,202.present value of $83,202.

Install the New Washer

YearCash Flows

10% Factor

Present Value

Initial investment Now (300,000)$ 1.000 (300,000)$ Replace brushes 6 (50,000) 0.564 (28,200) Net annual cash inflows 1-10 60,000 6.145 368,700 Salvage of old equipment Now 40,000 1.000 40,000 Salvage of new equipment 10 7,000 0.386 2,702 Net present value 83,202$


12-30


If White remodels the existingIf White remodels the existing washer . . .washer . . .

Remodel costs $175,000 Replace brushes at the end of 6 years 80,000

Let’s look at the present valueLet’s look at the present valueof this second alternative.of this second alternative.

12-31

If we remodel the existing washer, we will If we remodel the existing washer, we will produce a positive net present value of produce a positive net present value of

$56,405.$56,405.

If we remodel the existing washer, we will If we remodel the existing washer, we will produce a positive net present value of produce a positive net present value of

$56,405.$56,405.

Remodel the Old Washer

YearCash Flows

10% Factor

Present Value

Initial investment Now (175,000)$ 1.000 (175,000)$ Replace brushes 6 (80,000) 0.564 (45,120) Net annual cash inflows 1-10 45,000 6.145 276,525 Net present value 56,405$


12-32

Both projects yield a positive net present value.Both projects yield a positive net present value.

However, investing in the new washer will However, investing in the new washer will produce a higher net present value than produce a higher net present value than

remodeling the old washer.remodeling the old washer.

However, investing in the new washer will However, investing in the new washer will produce a higher net present value than produce a higher net present value than

remodeling the old washer.remodeling the old washer.


12-33

The Incremental-Cost Approach

Under the incremental-cost approach, Under the incremental-cost approach, only those cash flows that differ only those cash flows that differ between the two alternatives are between the two alternatives are

considered.considered.

Let’s look at an analysis of the White Co. Let’s look at an analysis of the White Co. decision using the incremental-cost decision using the incremental-cost

approach.approach.

Under the incremental-cost approach, Under the incremental-cost approach, only those cash flows that differ only those cash flows that differ between the two alternatives are between the two alternatives are

considered.considered.

Let’s look at an analysis of the White Co. Let’s look at an analysis of the White Co. decision using the incremental-cost decision using the incremental-cost

approach.approach.

12-34

YearCash Flows

10% Factor

Present Value

Incremental investment Now $(125,000) 1.000 $(125,000)Incremental cost of brushes 6 30,000$ 0.564 16,920 Increased net cash inflows 1-10 15,000 6.145 92,175 Salvage of old equipment Now 40,000 1.000 40,000 Salvage of new equipment 10 7,000 0.386 2,702 Net present value $ 26,797

We get the same answer using either theWe get the same answer using either thetotal-cost or incremental-cost approach.total-cost or incremental-cost approach.

The Incremental-Cost Approach

12-35

Quick Check

Consider the following alternative projects. Each project would last for five years.

Project A Project B Initial investment $80,000 $60,000 Annual net cash inflows 20,000 16,000 Salvage value 10,000 8,000

The company uses a discount rate of 14% to evaluate projects. Which of the following statements is true?

a. NPV of Project A > NPV of Project B by $5,230

b. NPV of Project B > NPV of Project A by $5,230

c. NPV of Project A > NPV of Project B by $2,000

d. NPV of Project B > NPV of Project A by $2,000

12-36

Consider the following alternative projects. Each project would last for five years.

Project A Project B Initial investment $80,000 $60,000 Annual net cash inflows 20,000 16,000 Salvage value 10,000 8,000

The company uses a discount rate of 14% to evaluate projects. Which of the following statements is true?

a. NPV of Project A > NPV of Project B by $5,230

b. NPV of Project B > NPV of Project A by $5,230

c. NPV of Project A > NPV of Project B by $2,000

d. NPV of Project B > NPV of Project A by $2,000

Quick Check

12-37

Least Cost Decisions

In decisions where revenues are not In decisions where revenues are not directly involved, managers should directly involved, managers should

choose the alternative that has the least choose the alternative that has the least total cost from a present value total cost from a present value

perspective.perspective.

Let’s look at the Home Furniture CompanyLet’s look at the Home Furniture Company..

In decisions where revenues are not In decisions where revenues are not directly involved, managers should directly involved, managers should

choose the alternative that has the least choose the alternative that has the least total cost from a present value total cost from a present value

perspective.perspective.

Let’s look at the Home Furniture CompanyLet’s look at the Home Furniture Company..

12-38


Home Furniture Company is trying to Home Furniture Company is trying to decide whether to overhaul an old delivery decide whether to overhaul an old delivery truck now or purchase a new one.truck now or purchase a new one.


Home Furniture Company is trying to Home Furniture Company is trying to decide whether to overhaul an old delivery decide whether to overhaul an old delivery truck now or purchase a new one.truck now or purchase a new one.


12-39

Old TruckOverhaul cost now 4,500$ Annual operating costs 10,000 Salvage value in 5 years 250 Salvage value now 9,000

Here is information about the trucks . . .Here is information about the trucks . . .


12-40

Buy the New Truck

YearCash Flows

10% Factor

Present Value

Purchase price Now $ (21,000) 1.000 $ (21,000)Annual operating costs 1-5 (6,000) 3.791 (22,746)Salvage value of old truck Now 9,000 1.000 9,000 Salvage value of new truck 5 3,000 0.621 1,863

Net present value (32,883)

Keep the Old Truck

YearCash Flows

10% Factor

Present Value

Overhaul cost Now $ (4,500) 1.000 $ (4,500)Annual operating costs 1-5 (10,000) 3.791 (37,910)Salvage value of old truck 5 250 0.621 155

Net present value (42,255)


12-41


Home Furniture should purchase the newnew truck.

Net present value of costs associated with purchase of new truck (32,883)$ Net present value of costs associated with remodeling existing truck (42,255) Net present value in favor of purchasing the new truck 9,372$

12-42

Quick Check

Bay Architects is considering a drafting machine Bay Architects is considering a drafting machine that would cost $100,000, last four years, and that would cost $100,000, last four years, and provide annual cash savings of $10,000 and provide annual cash savings of $10,000 and considerable intangible benefits each year. How considerable intangible benefits each year. How large (in cash terms) would the intangible large (in cash terms) would the intangible benefits have to be per year to justify investing benefits have to be per year to justify investing in the machine if the discount rate is 14%?in the machine if the discount rate is 14%?

a. $15,000a. $15,000b. $90,000b. $90,000c. $24,317c. $24,317d. $60,000d. $60,000


a. $15,000a. $15,000b. $90,000b. $90,000c. $24,317c. $24,317d. $60,000d. $60,000

12-43


a. $15,000a. $15,000b. $90,000b. $90,000c. $24,317c. $24,317d. $60,000d. $60,000


a. $15,000a. $15,000b. $90,000b. $90,000c. $24,317c. $24,317d. $60,000d. $60,000

Quick Check

$70,860$70,860//2.914 = $24,3172.914 = $24,317$70,860$70,860//2.914 = $24,3172.914 = $24,317

12-44


Rank investment projectsin order of preference.

12-45

Screening Decisions

Pertain to whether or not some proposed

investment is acceptable; these

decisions come first.

Preference Decisions

Attempt to rank acceptable

alternatives from the most to least

appealing.

Preference Decision – The Ranking of Investment Projects

12-46

The net present value of one project cannot be directly compared to the net present

value of another project unless the investments are equal.

Net Present Value Method

12-47

Ranking Investment Projects

Profitability Net present value of the project index Investment required=

A BNet present value (a) $800 $1,000Investment required (b) $80,000 $5,000Profitability index (a) ÷ (b) 0.01 0.20

Investment

The higher the profitability index, theThe higher the profitability index, themore desirable the project. Therefore, investment B is more desirable the project. Therefore, investment B is

more desirable than investment A. more desirable than investment A.

The higher the profitability index, theThe higher the profitability index, themore desirable the project. Therefore, investment B is more desirable the project. Therefore, investment B is

more desirable than investment A. more desirable than investment A.

12-48

The higher the internal The higher the internal rate of return, the rate of return, the

more desirable the more desirable the project.project.

The higher the internal The higher the internal rate of return, the rate of return, the

more desirable the more desirable the project.project.

When using the internal rate of return method to rank competing investment

projects, the preference rule is:

Internal Rate of Return Method

12-49Other Approaches toCapital Budgeting Decisions

Other methods of making capital budgeting Other methods of making capital budgeting decisions include . . .decisions include . . .The Payback Method.The Payback Method.Simple Rate of Return.Simple Rate of Return.

Other methods of making capital budgeting Other methods of making capital budgeting decisions include . . .decisions include . . .The Payback Method.The Payback Method.Simple Rate of Return.Simple Rate of Return.

12-50


Determine thepayback period

for an investment.

12-51

The Payback Method

The The payback periodpayback period is the length of time that it is the length of time that it takes for a project to recover its initial cost out takes for a project to recover its initial cost out

of the cash receipts that it generates.of the cash receipts that it generates.

When the net annual cash inflow is the same When the net annual cash inflow is the same each year, this formula can be used to each year, this formula can be used to

compute the payback period:compute the payback period:

The The payback periodpayback period is the length of time that it is the length of time that it takes for a project to recover its initial cost out takes for a project to recover its initial cost out

of the cash receipts that it generates.of the cash receipts that it generates.

When the net annual cash inflow is the same When the net annual cash inflow is the same each year, this formula can be used to each year, this formula can be used to

compute the payback period:compute the payback period:

Payback period = Investment required Net annual cash inflow

12-52

The Payback Method

The management at the Daily Grind wants to install The management at the Daily Grind wants to install an espresso bar in its restaurant.an espresso bar in its restaurant.

The espresso bar:The espresso bar:

1.1. Costs $140,000 and has a 10-year life.Costs $140,000 and has a 10-year life.

2.2. Will generate net annual cash inflows of Will generate net annual cash inflows of $35,000.$35,000.

Management requires a payback period of 5 years or Management requires a payback period of 5 years or less on all investments.less on all investments.

What is the payback period for the espresso bar?What is the payback period for the espresso bar?

The management at the Daily Grind wants to install The management at the Daily Grind wants to install an espresso bar in its restaurant.an espresso bar in its restaurant.

The espresso bar:The espresso bar:

1.1. Costs $140,000 and has a 10-year life.Costs $140,000 and has a 10-year life.

2.2. Will generate net annual cash inflows of Will generate net annual cash inflows of $35,000.$35,000.

Management requires a payback period of 5 years or Management requires a payback period of 5 years or less on all investments.less on all investments.

What is the payback period for the espresso bar?What is the payback period for the espresso bar?

12-53

Payback period = Payback period = Investment required Investment required Net annual cash inflowNet annual cash inflow

Payback period = Payback period = $140,000 $140,000 $35,000$35,000

Payback period = Payback period = 4.0 years4.0 years

According to the company’s criterion, According to the company’s criterion, management would invest in the management would invest in the

espresso bar because its payback espresso bar because its payback period is less than 5 years.period is less than 5 years.

According to the company’s criterion, According to the company’s criterion, management would invest in the management would invest in the

espresso bar because its payback espresso bar because its payback period is less than 5 years.period is less than 5 years.

The Payback Method

12-54

Quick Check

Consider the following two investments:

Project X Project YInitial investment $100,000 $100,000Year 1 cash inflow $60,000 $60,000Year 2 cash inflow $40,000 $35,000Year 3-10 cash inflows $0 $25,000

Which project has the shortest payback period?

a. Project X

b. Project Y

c. Cannot be determined




a. Project X

b. Project Y


12-55




a. Project X

b. Project Y





a. Project X

b. Project Y


Quick Check

•Project X has a payback period of 2 years.Project X has a payback period of 2 years.•Project Y has a payback period of slightly more than 2 years.Project Y has a payback period of slightly more than 2 years.•Which project do you think is better?Which project do you think is better?

•Project X has a payback period of 2 years.Project X has a payback period of 2 years.•Project Y has a payback period of slightly more than 2 years.Project Y has a payback period of slightly more than 2 years.•Which project do you think is better?Which project do you think is better?

12-56

Ignores the Ignores the time valuetime valueof money.of money.

Ignores cashIgnores cashflows after flows after the paybackthe payback

period.period.

CriticismsCriticismsof the paybackof the payback

period.period.

Evaluation of the Payback Method

12-57

Serves as Serves as screening screening

tool.tool.

Identifies Identifies investments that investments that

recoup cash recoup cash investments investments

quickly.quickly.Identifies Identifies

products that products that recoup initial recoup initial investment investment

quickly.quickly.

StrengthsStrengthsof the paybackof the payback

period.period.

Evaluation of the Payback Method

12-58

11 22 33 44 55

$1,000$1,000 $0$0 $2,000$2,000 $1,000$1,000 $500$500

When the cash flows associated with an investment project change from year to year,

the payback formula introduced earlier cannot be used.

Instead, the un-recovered investment must be tracked year by year.

When the cash flows associated with an investment project change from year to year,

the payback formula introduced earlier cannot be used.

Instead, the un-recovered investment must be tracked year by year.

Payback and Uneven Cash Flows

12-59

11 22 33 44 55

$1,000$1,000 $0$0 $2,000$2,000 $1,000$1,000 $500$500

For example, if a project requires an For example, if a project requires an initial investment of $4,000 and initial investment of $4,000 and

provides uneven net cash inflows in provides uneven net cash inflows in years 1-5, as shown, the investment years 1-5, as shown, the investment would be fully recovered in year 4.would be fully recovered in year 4.

For example, if a project requires an For example, if a project requires an initial investment of $4,000 and initial investment of $4,000 and

provides uneven net cash inflows in provides uneven net cash inflows in years 1-5, as shown, the investment years 1-5, as shown, the investment would be fully recovered in year 4.would be fully recovered in year 4.

Payback and Uneven Cash Flows

12-60


Compute thesimple rate of returnfor an investment.

12-61

Simple Rate of Return Method

Does not focus on cash flows -- rather it focuses on accounting net operating accounting net operating incomeincome.

The following formula is used to calculate the simple rate of return:

Simple rateSimple rateof returnof return ==

Annual IncrementalAnnual IncrementalNet Operating IncomeNet Operating Income

Initial investmentInitial investment**

**Should be reduced by any salvage from the sale of the old equipment

12-62


The Management of the Daily Grind wants to The Management of the Daily Grind wants to install an espresso bar in its restaurant.install an espresso bar in its restaurant.

The espresso bar:The espresso bar:1.1. Cost $140,000 and has a 10-year life.Cost $140,000 and has a 10-year life.2.2. Will generate incremental revenues of Will generate incremental revenues of

$100,000 and incremental expenses of $100,000 and incremental expenses of $65,000, including depreciation.$65,000, including depreciation.

What is the simple rate of return on the What is the simple rate of return on the investment project?investment project?

The Management of the Daily Grind wants to The Management of the Daily Grind wants to install an espresso bar in its restaurant.install an espresso bar in its restaurant.

The espresso bar:The espresso bar:1.1. Cost $140,000 and has a 10-year life.Cost $140,000 and has a 10-year life.2.2. Will generate incremental revenues of Will generate incremental revenues of

$100,000 and incremental expenses of $100,000 and incremental expenses of $65,000, including depreciation.$65,000, including depreciation.

What is the simple rate of return on the What is the simple rate of return on the investment project?investment project?

12-63

Simple rateSimple rateof returnof return

$100,000 - $65,000 $100,000 - $65,000 $140,000$140,000 = 25%= 25%==

Criticisms of the simple rate of return Criticisms of the simple rate of return include that this method ignores the time include that this method ignores the time value of money and it can fluctuate from value of money and it can fluctuate from

year to year.year to year.

Criticisms of the simple rate of return Criticisms of the simple rate of return include that this method ignores the time include that this method ignores the time value of money and it can fluctuate from value of money and it can fluctuate from

year to year.year to year.


12-64

Postaudit of Investment Projects

A postaudit is a follow-up after the A postaudit is a follow-up after the project has been completed to see project has been completed to see

whether or not expected results were whether or not expected results were actually realized.actually realized.

A postaudit is a follow-up after the A postaudit is a follow-up after the project has been completed to see project has been completed to see

whether or not expected results were whether or not expected results were actually realized.actually realized.

12-65

The Concept of Present Value

Appendix 12AAppendix 12AAppendix 12AAppendix 12A

12-66


Understand presentvalue concepts and the

use of present value tables.

12-67

A dollar received today is worth more

than a dollar received a year from now

because you can put it in the bank today

and have more than a dollar a year from

now.

The Mathematics of Interest

12-68

Assume a bank pays 8% interest on a $100 deposit made today. How much

will the $100 be worth in one year?

FFnn = P(1 + r) = P(1 + r)nn


Helen Roybark

Notes to Slide 68F: Changed the word "the" to read "one." Changed "F" to read "F1" to agree with the Lecture Notes.Deleted "n" to agree with the Lecture Notes.Variables: Changed the words "is" to "=" to agree with the Lecture Notes.

12-69

Assume a bank pays 8% interest on a $100 deposit made today. How much

will the $100 be worth in one year?

FFnn = P(1 + r) = P(1 + r)nn

FF11 = $100(1 + .08) = $100(1 + .08)11

FF11 = $108.00 = $108.00


12-70

Compound Interest

FFnn = P(1 + r) = P(1 + r)nn

What if the $108 was left in the bank for a What if the $108 was left in the bank for a second year? How much would the second year? How much would the

original $100 be worth at the end of the original $100 be worth at the end of the second year? second year?

12-71

Compound Interest

The interest that is paid in the second year on the interest earned in the first year is

known as compound interest.

FF22 = $100(1 + .08) = $100(1 + .08)22

FF22 = $116.64 = $116.64

12-72

Present Value

Future Value

An investment can be viewed in two ways—its future value or its present

value.

Let’s look at a situation where the future value is known and the present

value is the unknown.

Computation of Present Value

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Present Value

If a bond will pay $100 in two years, If a bond will pay $100 in two years, what is the what is the present value of the $100present value of the $100 if if an investor can earn a return of 12% on an investor can earn a return of 12% on

investments?investments?

(1 + r)(1 + r)nnP =P =FFnn

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Present Value

This process is called discounting. We have discounted the $100 to its present value of $79.72. The interest rate used to find the present value is called the discount rate.

(1 + .12)(1 + .12)22P =P =$100$100

P =P = $79.72$79.72

12-75

Present Value

Let’s verify that if we put $79.72 in the bank today Let’s verify that if we put $79.72 in the bank today at 12% interest that it would grow to $100 at the at 12% interest that it would grow to $100 at the

end of two years.end of two years.

Year 1 Year 2Beginning balance 79.72$ 89.29$ Interest @ 12% 9.57$ 10.71$ Ending balance 89.29$ 100.00$

Year 1 Year 2Beginning balance 79.72$ 89.29$ Interest @ 12% 9.57$ 10.71$ Ending balance 89.29$ 100.00$

If $79.72 is put in the bank today and earns If $79.72 is put in the bank today and earns 12%, it will be worth $100 in two years.12%, it will be worth $100 in two years.

If $79.72 is put in the bank today and earns If $79.72 is put in the bank today and earns 12%, it will be worth $100 in two years.12%, it will be worth $100 in two years.

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RatePeriods 10% 12% 14%

1 0.909 0.893 0.877 2 0.826 0.797 0.769 3 0.751 0.712 0.675 4 0.683 0.636 0.592 5 0.621 0.567 0.519

RatePeriods 10% 12% 14%

1 0.909 0.893 0.877 2 0.826 0.797 0.769 3 0.751 0.712 0.675 4 0.683 0.636 0.592 5 0.621 0.567 0.519

$100 $100 ×× 0.797 = $79.72 present value 0.797 = $79.72 present value (rounded)(rounded)

Present value factor of $1 for 2 periods at 12%.Present value factor of $1 for 2 periods at 12%.Present value factor of $1 for 2 periods at 12%.Present value factor of $1 for 2 periods at 12%.

Present Value – An Example

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Quick Check

How much would you have to put in the How much would you have to put in the bank today to have $100 at the end of five bank today to have $100 at the end of five years if the interest rate is 10%?years if the interest rate is 10%?

a. $62.10a. $62.10

b. $56.70b. $56.70

c. $90.90c. $90.90

d. $51.90d. $51.90


a. $62.10a. $62.10

b. $56.70b. $56.70

c. $90.90c. $90.90

d. $51.90d. $51.90

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a. $62.10a. $62.10

b. $56.70b. $56.70

c. $90.90c. $90.90

d. $51.90d. $51.90


a. $62.10a. $62.10

b. $56.70b. $56.70

c. $90.90c. $90.90

d. $51.90d. $51.90

Quick Check

$100 $100 0.621 = $62.10 0.621 = $62.10$100 $100 0.621 = $62.10 0.621 = $62.10

12-79

11 22 33 44 55 66

$100$100 $100$100 $100$100 $100$100 $100$100 $100$100

Present Value of a Series of Cash Flows

An investment that involves a series of identical cash flows at the end of

each year is called an annuityannuity.

12-80


Lacey Inc. purchased a tract of land on which a $60,000 payment will be due each

year for the next five years. What is the present value of this stream of cash

payments when the discount rate is 12%?

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We could solve the problem like this . . .

Periods 10% 12% 14%1 0.909 0.893 0.877 2 1.736 1.690 1.647 3 2.487 2.402 2.322 4 3.170 3.037 2.914 5 3.791 3.605 3.433

Present Value of an Annuity of $1

$60,000 × 3.605 = $216,300$60,000 × 3.605 = $216,300

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Quick Check

If the interest rate is 14%, how much If the interest rate is 14%, how much would you have to put in the bank today so would you have to put in the bank today so as to be able to withdraw $100 at the end as to be able to withdraw $100 at the end of each of the next five years?of each of the next five years?

a. $34.33a. $34.33b. $500.00b. $500.00c. $343.30c. $343.30d. $360.50d. $360.50


a. $34.33a. $34.33b. $500.00b. $500.00c. $343.30c. $343.30d. $360.50d. $360.50

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a. $34.33a. $34.33b. $500.00b. $500.00c. $343.30c. $343.30d. $360.50d. $360.50


a. $34.33a. $34.33b. $500.00b. $500.00c. $343.30c. $343.30d. $360.50d. $360.50

Quick Check

$100 $100 3.433 = $343.30 3.433 = $343.30

12-84

Quick Check

If the interest rate is 14%, what is the If the interest rate is 14%, what is the present value of $100 to be received at present value of $100 to be received at the end of the 3rd, 4th, and 5th years?the end of the 3rd, 4th, and 5th years?

a. $866.90a. $866.90

b. $178.60b. $178.60

c. $ 86.90c. $ 86.90

d. $300.00d. $300.00


a. $866.90a. $866.90

b. $178.60b. $178.60

c. $ 86.90c. $ 86.90

d. $300.00d. $300.00

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a. $866.90a. $866.90

b. $178.60b. $178.60

c. $ 86.90c. $ 86.90

d. $300.00d. $300.00


a. $866.90a. $866.90

b. $178.60b. $178.60

c. $ 86.90c. $ 86.90

d. $300.00d. $300.00

Quick Check

$100 (3.433 - 1.647) = $100 1.786 = $178.60or

$100 (0.675 + 0.592 + 0.519) = $100 1.786 = $178.60

$100 (3.433 - 1.647) = $100 1.786 = $178.60or

$100 (0.675 + 0.592 + 0.519) = $100 1.786 = $178.60

12-86

End of Chapter 12