M02-Capital Investment AppraisalOverview eng -270409 · Topic M02: Capital Investment Appraisal Topic Overview P.1 ... evaluating investment project with another example. PPT#8-10

Topic M02: Capital Investment Appraisal Topic Overview P.1

BAFS Learning and Teaching Example As at April 2009

Learning Objectives: 1. To determine the NPV of a project with different cash flows in a time span; 2. To determine the IRR of a project with different cash flows in a time span; 3. To find out the ARR of a given cash flow with time spans; and 4. To apply capital investment appraisal methods to evaluate the feasibility of

investing in a project. Overview of Contents: Lesson 1 Introduction of Different Capital Investment Appraisal Methods Lesson 2 Application of Capital Investment Appraisal Methods Resources:

Topic Overview, Teaching Plan and Answers to Student Worksheet PowerPoint Presentation Student Worksheet

Suggested Activities:

Group Discussion Problem Solving Case Study

Topic Overview Topic BAFS Elective Part – Business Management Module – Financial

Management M02: Capital Investment Appraisal

Level S5 / S6 Duration 2 lessons (40 minutes per lesson)



Lesson 1

Theme Introduction of Different Capital Investment Appraisal Methods Duration 40 minutes Expected Learning Outcomes: Upon completion of this lesson, students will be able to: 1. Determine the NPV of a project with different cash flows in a time span; 2. Determine the IRR of a project with different cash flows in a time span; and 3. Find out the ARR of a given cash flow with time spans. Teaching Sequence and Time Allocation:

Activities Reference Time

AllocationPart I: Introduction

Using a simple case, teacher introduces the three different capital investment appraisal methods:

Net present value (NPV) Internal rate of return (IRR) Accounting rate of return (ARR)

PPT#1-7 4 minutes

Part II: Content

Activity 1: A property investment case (Application of NPV)

Teacher explains the case to students and asks them to calculate the NPV of the project in order to decide whether the investment project is acceptable.

Students present their answers to class. Teacher comments on the answers and shows the

correct answer with workings. Teacher further explains the application of NPV in

evaluating investment project with another example.

PPT#8-10

Student Worksheet

p.1

PPT#11-14

10 minutes



Teacher demonstrates the computation and application of IRR with examples.

Activity 2: A project with equal cash flows (Application of IRR)

Teacher explains the case to students and asks them to solve it.

Students present their answer to class. Teacher comments on their answers and shows the

correct answer with workings.

PPT#15-39 Student

Worksheet pp.2-3

15 minutes

Teacher demonstrates the computation of ARR using a short case, then explains how investment decision is made with ARR.

PPT#40-50 8 minutes

Part III: Conclusion Teacher reviews the 3 investment appraisal methods

and concludes the lesson. PPT#51-53 3 minutes



Lesson 2

Theme Application of Capital Investment Appraisal Methods Duration 40 minutes Expected Learning Outcomes: Upon completion of this lesson, students will be able to apply different capital investment appraisal methods to evaluate different investment projects. Teaching Sequence and Time Allocation:

Activities Reference Time

AllocationPart I: Introduction

Teacher begins by recapping the 3 investment appraisal methods covered in Lesson 1.

PPT #54-55 2 minutes

Part II: Content

Case 1: An Investment Project Teacher explains the case and asks students to

form groups to calculate the NPV, IRR & ARR of the investment project and then decide whether to accept the project based on the results they achieved.

Teacher invites groups to present their answers. Teacher comments on students’ results and

justification, and shows the correct answer with workings.

PPT#56-66

Student Worksheet

pp.4-6

10 minutes

Case 2: Purchasing a new van or not? Teacher explains the case to students and asks

them to discuss in groups to decide whether Vincent should buy a new van.

Students are reminded to apply the 3 investment appraisal methods in making the decision.

Teacher invites groups to present and explain their answers.

Teacher gives comments on their decision and shows the correct answer with workings.

PPT#67-77

Student Worksheet

pp.7-8

12 minutes



Case 3: Two mutually exclusive projects Teacher introduces two mutually exclusively

projects to students and asks them to discuss in groups, deciding which project to invest.

Students should calculate and compare the NPV, IRR and ARR of both projects and select one for investment based on their results.

Teacher invites groups to present and explain their answer.

Teacher gives comments on their decision and shows the correct answer with workings.

PPT#78-92

Student Worksheet

pp.9-10

14 minutes

Part III: Conclusion Teacher reviews the 3 investment appraisal methods

and concludes the lesson. PPT#93-95 2 minutes



Solution to Activity 1 Given the following information: Initial outlay : $2,500,000 + $200,000 = $2,700,000 Future cash flow : $3,100,000 Required rate of return : 8% p.a. Net present value:

= $170,370.37 Since the NPV is a positive value, we can accept the property investment.

%)81(000,100,3$000,700,2$

++−=NPV



Solution to Activity 2 Given the following information: Initial outlay : $40,000 Equal annual cash flow : $16,000 for next 3 years Let r% be the required rate of return for the project If the NPV = 0, the required rate of return (r) is equal to the internal rate of return (IRR), the equation will be Using MS Excel: 1. Create the cash flow over a time span as follows. 2.

Year 0 Year 1 Year 2 Year 3

-$40,000 $16,000 $16,000 $16,000

321 %)1(000,16$

%)1(000,16$

%)1(000,16$000,40$

rrrNPV

++

++

++−=

321 %)1(000,16$

%)1(000,16$

%)1(000,16$000,40$0

IRRIRRIRR ++

++

++−=



3. In Cell C6, insert the formula “=IRR(C5:F5)” and press ENTER.

4. The program will automatically calculate the IRR for you (i.e. 10%).



In this case, the IRR for the project is equal to 10% or a more precise value of 9.701% (4 sig. fig.)

Conclusion: Annie would be indifferent to accepting or rejecting the project.



Year 0 Year 1 Year 2 Year 3 Year 4 Year 5

Initial outlay -$200,000

Sales $100,000 $180,000 $280,000 $150,000 $100,000

Total Operating expenses

50,000 80,000 100,000 50,000 40,000

Depreciation 40,000 40,000 40,000 40,000 40,000

Earning before tax 10,000 60,000 140,000 60,000 20,000

Tax (at 15%) 1,500 9,000 21,000 9,000 3,000

Net profit 8,500 51,000 119,000 51,000 17,000

Solution to Case 1 Task (1) Net present value: = - $200,000 + $184,671.84 = - $15,328.16 Since the NPV is a negative value, Raymond should reject the project. Task (2) Internal rate of return:

54321 %)101(000,17$

%)101(000,51$

%)101(000,119$

%)101(000,51$

%)101(500,8$000,200$

++

++

++

++

++−=NPV

54321 %)1(000,17$

%)1(000,51$

%)1(000,119$

%)1(000,51$

%)1(500,8$000,200$0

rrrrr ++

++

++

++

++−=

54321 %)1(000,17$

%)1(000,51$

%)1(000,119$

%)1(000,51$

%)1(500,8$000,200$

IRRIRRIRRIRRIRR ++

++

++

++

+=



In order to determine the internal rate of return (IRR), we use MS Excel to determine the IRR.

Application of MS Excel

Step 1: Teacher inputs numbers into the Excel cells as shown in the slide.

Step 2: Set an equation into the cell C17 as =IRR(C16:H16)

Step 3: Press “enter” and the computer will automatically calculate the IRR. In this case, the IRR is 7.117%

Therefore the IRR of this project is 7.117%.

The required rate of return is 10%, which is greater than the IRR (7.117%) of this project. Therefore, Raymond should reject the project.



Task (3) Accounting rate of return: From the result, the accounting rate of return (i.e. 49.3%) is less than the target accounting rate of return (i.e. 70%). Hence, the project should be rejected. Task (4) From the results of three capital investment methods,

NPV = -$15,328.16 (negative value, rejected) IRR = 7.117% ( <required rate of return 10%, rejected) ARR = 49.3% ( < 70%, rejected)

We now conclude that the investment should be rejected by Raymond.

300495

5002465

$17,000$51,000$119,000$51,000$8,500

: is profit net average The

,$

,$

=

=

++++

0001002

$0-$200,000:is value book average The

,$=

%.349$100,000$49,300

:is project this of return of rate accounting The

=



Solution to Case 2 By NPV method: = -$155,000 + $179,024 = $24,024 The NPV value is positive, the project should be accepted. By IRR method: In order to find out the internal rate of return IRR, we use MS Excel to determine the IRR.


Step 1: Input the required numbers into the Excel cells as shown in the above figure. Step 2: Set an equation into the cell C17 as =IRR(C16:H16).

54321 %)121(000,41$

%)121(000,38$

%)121(000,60$

%)121(000,60$

%)121(000,46$000,155$

++

++

++

++

++−=NPV

0%)1(000,41$

%)1(000,38$

%)1(000,60$

%)1(000,60$

%)1(000,46$000,155$ 54321 =

++

++

++

++

++−

rrrrr

54321 %)1(000,41$

%)1(000,38$

%)1(000,60$

%)1(000,60$

%)1(000,46$000,155$

IRRIRRIRRIRRIRR ++

++

++

++

+=



Step 3: Press “enter” and the result will be generated by the computer. The IRR of the project is 18.328%. As the IRR (i.e. 18.328%) is greater than the required rate of return (i.e. 12%), the project should be accepted. By ARR method:

From the result, the ARR is 63.23% which is greater than the target rate of return 40%. Therefore the project should be accepted.

Conclusion:

As NPV > 0, IRR > required rate of return and ARR > target rate of return, the project should be accepted by Vincent and the van replaced. Based on the results achieved by using the 3 investment appraisal methods, it is concluded that Vincent should replace the van.

5$41,000$38,000$60,000$60,000$46,000

: is inflowcash net average The++++

000,49$5

000,245$

=

=

500,77$2

$0$155,000: is book value average The

=+

63.23%or 6323.0500,77$

$49,000: isreturn of rate accounting The

=



Solution to Case 3 Task (1) By NPV method: For project M: NPVM = -$400 + $449.12

= $49.12 For project N: NPVN = -$600 + $623.42

= $23.42 Task (2) By IRR method: For project M:

54321 %)101(230$

%)101(230$

%)101(60$

%)101(60$

%)101(60$400$

++

++

++

++

++−=MNPV

54321 %)101(50$

%)101(50$

%)101(50$

%)101(300$

%)101(300$600$

++

++

++

++

++−=NNPV

0%)1(

230$%)1(

230$%)1(

60$%)1(

60$%)1(

60$400$ 54321 =+

++

++

++

++

+−rrrrr

54321 %)1(230$

%)1(230$

%)1(60$

%)1(60$

%)1(60$400$

MMMMM IRRIRRIRRIRRIRR ++

++

++

++

+=




Input the required numbers into the Excel cells as shown in the following figure. And set an equation into the cell C17 as =IRR(C16:H16) Press “enter” and the result will be generated by the computer. Therefore the IRRM of project M is 13.593%. For project N:

0%)1(

50$%)1(

50$%)1(

50$%)1(

300$%)1(

300$600$ 54321 =+

++

++

++

++

+−rrrrr



Application of MS Excel:

Input the required numbers into the Excel cells as shown in the following figure. Set an equation into the cell C17 as =IRR(C16:H16) Press “enter” and the result will be generated by the computer. The IRR of project N is found as 12.276%.

54321 %)1(50$

%)1(50$

%)1(50$

%)1(300$

%)1(300$600$

NNNNN IRRIRRIRRIRRIRR ++

++

++

++

+=



Task (3) By ARR method: For project M, For project N,

5$230$230$60$60$60

:isMproject ofinflowcash net average The++++

128$5

640$

=

=

200$2

$0$400:isMproject of book value average The

=+

64%or 64.0200$

$128: is Mproject ofreturn of rate accounting The

=

300$2

$0$600:isNproject of book value average The

=+

5$50$50$50$300$300

:isNproject ofinflowcash net average The++++

150$5

750$

=

=

50%or 5.0300$

$150: is Nproject ofreturn of rate accounting The

=



Task (4):

The results of three different capital investment appraisal methods are as follows: NPVM > NPVN > > $0 IRRM > IRRN > 10% (required rate of return) ARRM > ARRN > 60% (target accounting rate of return) We can conclude that project M will be accepted.

Project NPV IRR ARR

M $49.12 13.593% 64%

N $23.42 12.276% 50%

1

Topic M02: Capital Investment Appraisal

Technology Education Section Curriculum Development Institute

Education Bureau, HKSARGApril 2009

BAFS Elective PartBusiness Management Module –

Financial Management

Introduction

This lesson will enhance student understanding on 3 capital investment appraisal methods and their application in evaluating the feasibility of different investment projects.

Duration

Two 40-minute lessons

Contents

Lesson 1 - Introduction of Three Capital Investment Appraisal Methods

Lesson 2 - Application of Capital Investment Appraisal Methods

2

2Topic M02Capital Investment Appraisal

BAFS Elective PartLearning and Teaching Example

2

You are considering investing $24M now in a project with the following cash flows, (M = million)

Year Cash flows

0 - $24 M

1 $ 10 M

2 $ 10 M

3 $ 10 M

Would you take this project ?

Remarks:

Negative sign indicates cash outflow and positive sign indicates cash inflows.

Year 0 means now.

Year 1 means one year from now.

The “M” means the amount of cash flow in million.

Lesson 1

Start the lesson by asking students if they would take the investment with the cash flows shown in the table.

As the sum of the three future cash inflows are greater than the initial cash outflow, more students may answer “Yes” to the question.

Teacher should explain to students that net present value should be considered when making the decision. Then teacher introduces the 3 investment appraisal methods to be discussed in this unit.

3



Investment Appraisal Methods

To evaluate investment projects by:

1. Net present value (NPV)2. Internal rate of return (IRR)3. Accounting rate of return (ARR)

Teacher introduces three investment appraisal methods to evaluate investment projects.

4



1st Investment Appraisal Method – Net Present Value (NPV)

The NPV method directly measures how much a potential project will contribute to the owner’s wealth.

It’s also the primary investment appraisal decision criterion.

Introduce the first investment appraisal method – Net Present Value Method.

5



Net Present Value

Definition :

An investment appraisal method to rank a proposal which is equal to the sum of the ‘present value’ of ‘future cash flows’discounted at the required ‘rate of return’.

Explain that the NPV is an investment appraisal method.

NPV = the sum of the present value of future cash flows (include the initial cash flow)

The required rate of return is the cost of capital.To calculate NPV of an investment, we need to sum up all the discounted future cash flows at present with the required rate of return minus the initial cash outflow.

6



Net Present Value

The NPV equation as follows :

∑= +

=

+++

++

++=

n

tt

t

nn

rCFNPV

rCF

rCF

rCFCFNPV

0

22

11

0

)1(

)1(...

)1()1(

The equation of the NPV is introduced.

Remarks :

CFt is the cash flow at time t where t = 0, 1, 2 ….., nr = required rate of return

7



Net Present Value

Decision criteria :

If the project NPV is: >0 or positive value, then accept the project<0 or negative value, then reject the project=0, neither accept or reject a project, more

information is required for further decision

State the decision criteria for acceptance or rejection of a project.

NPV may have the following three possible values.If NPV > 0, accept the project.If NPV < 0, reject the project.If NPV = 0, normally we may accept the project but it does not increase the wealth of the owner. Of course, we may reject the project as it has the same reason. Therefore, more information is needed for making the decision.

8



Read the case in Student Worksheet P.1, then calculate the NPV of the investment and solve the problem.

Activity 1: A property investment case

Activity 1

Referring to the Student Worksheet P.1, teacher explains the information about the case, then asks students to calculate the NPV of the investment and decide whether to accept it or not.

9



Initial outlay : $2,500,000 + $200,000 = $2,700,000

One year laterFuture cash flow : $3,100,000 Required rate of return : 8% p.a.

Accept this investment project or not?

Solution for Activity 1:

To help students calculate the NPV, teacher may summarise the information about the project as shown in the slide.

Remarks:

Initial outlay (cash flow) = property investment + decoration

10



Solution for Activity 1

Net present value :

= $170,370.37

Since the NPV is a positive value, we can accept the property investment.

%)81(000,100,3$000,700,2$

++−=NPV

Apply the equation to find the NPV.

Judging the value of the NPV (which is > 0), the suggested property investment is acceptable.

11



Net Present Value

Now you are considering to invest your $24M in a project with the following cash flows, (M = million)

Year Cash flows0 - $24 M1 $ 10 M2 $ 10 M3 $ 10 M

Return to the investment project introduced in the beginning of the lesson (Slide 2) and remind students of the following:

- Initial cash outflow is $24 M.- Cash inflows in the next 3 years are equal to $10 M each year.- The required rate of return is 8% per year.

12



Net Present Value (Cont’d)

Assume the required rate of return is also 8%, is this project acceptable?

Ask students to apply the NPV investment appraisal method to evaluate this project. Solution will be given in the next slide.



Net Present Value

Apply the NPV equation

Therefore the NPV of the project is $1.77M.

MMMNPV

MMMMNPV

77.1$77.25$24$

%)81(10$

%)81(10$

%8110$24$ 32

=+−=

++

++

++−=

Apply the equation and substitute the required information to find the NPV.

Remarks:

Teacher may change the required rate of return for students to determine the NPV and to show how NPV is affected by the required rate of return.

13



Net Present Value

Since the NPV is positive, we accept the project.

Draw the conclusion based on the findings – i.e. Accept the project as the NPV is positive.

14



2nd Investment Appraisal Method – Internal Rate of Return

Internal rate of return (IRR)

This method determines the rate of return for a given project with future cash flows.

Teacher introduces the 2nd Investment Appraisal Method – Internal Rate of Return (IRR).

15



Internal Rate of Return

Definition :

The discount rate that brings the NPV of the project to zero.

It is simply the discount rate at which the NPV = 0.

Teacher explains that IRR is the discount rate that brings the NPV of a project to zero.

16




The equation for determining the IRR

where IRR is the internal rate of return

).........()(

)......()(

...)()(

2 0 1

1 111

0

22

11

0

=+

=

+++

++

++=

∑=

n

tt

t

nn

IRRCFNPV

rCF

rCF

rCFCFNPV

The equation is similar to that of NPV and derived from NPV with the discount rate of the project to be determined when NPV = 0.

Teacher may elaborate the NPV equation and extend to the equation for determining the IRR.The r in the first equation is the required rate of return for calculating the NPV of a series of future cash flows.The IRR in the second equation is the internal rate of return when NPV is zero.

17




Project decision criteria IRR Vs r :

Accept the project if IRR > r, Reject the project if IRR < r .

To decide whether to accept a project or not, we should compare the internal rate of return (IRR) with the required rate of return (r).

18




To determine the IRR of one period of cash flow. For example :Suppose a corporate project will generate a one year future cash flow of $23.5M, with initial investment of $20M and the corporate required rate of return is 9% per year.What is the IRR ?

Teacher illustrates how the IRR of one period of cash flow can be determined using the above example.

19




Year Cash flow

0 -$20 million1 $23.5 million

The internal rate of return of this corporate project is

Where m = million

0)1(

5.23$20$ 1 =++−

IRRmm

This is a simple case for determining the IRR with only one future cash inflow.

The IRR can be worked out easily by substituting the cash inflow and outflow to the equation introduced in slide 17.

20




Solve the equation :

The internal rate of return (IRR) of this corporate project is 17.5%.

17.5% or 0.175 IRR =∴=

=+

175.120$

5.23$1mmIRR

Teacher asks volunteer(s) to demonstrate their calculation before showing the answer to the class.

21




Since the IRR (17.5%) is greater than the required rate of return (9%), this corporate project is acceptable.

Teacher reminds students that if the IRR is less than the corporation required rate of return, the project should be rejected.

22




Now we return to the first example of the lesson (suggested in slide 2) and find the IRR of the investment given that the required rate of return is 8%.

Year Cash flows0 - $24 M1 $ 10 M2 $ 10 M3 $ 10 M

Teacher may re-visit the case established in the beginning of this lesson. (i.e. slide 2).

Ask students to find the IRR for this investment.




What is the IRR for this investment ?

Set up the equation: (M=million)

0)1(

10$)1(

10$1

10$24$ 32 =+

++

++

+−IRR

MIRR

MIRRMM

Teacher may set up the equation for the students in order to direct their workings or ask someone to demonstrate it.




Solving the equation:You may get the following equation

It is obviously an equation with IRR3 which cannot be solved easily.

32 )1(10

)1(10

11024

IRRIRRIRR ++

++

+=

After eliminating the “millions” in all the terms, and re-arranging the equation, students will get the equation as shown in the slide.

An equation having a (1+IRR)3 term is hard to solve. Hence, teacher may introduce other methods for students to solve the equation and find the IRR.

Go to the next slide for other methods.




To solve the IRR in the equation, we may use MS Excel software if a computer is available.

With Excel software, the IRR can be solved easily.

Teacher suggests that students use MS Excel to solve the IRR.Teacher demonstrates the steps of using the software to solve the IRR with the help of the following slides.

Other solving tools include :1. Scientific calculator plus mathematical skills2. A financial calculator




Set up the equation and input the numbers into cells as shown in next slide.

Steps :1. Set up the equation at cell C5.2. Press enter and the computer will

calculate the internal rate of return.

Teacher starts Excel and sets up the table as shown in the next slide.

Teaching tools :A ScreenA ProjectorA computer with MS Excel application program.




Teacher sets up the table and fills in the date as shown in the slide.Write the equation in the Cell C5 as “=IRR(C4:F4)”.Press enter and the IRR will be generated.Formatting of IRR may be needed to show the number of decimal places required.




IRR = 12.044%

The IRR of the investment will be 12.044%.




Since the IRR (12.044%) is greater than the required rate of return (8%), we accept the investment.

Comparing the IRR with the required rate of return, a decision on whether to accept the investment can be made.



Activity 2:A project with equal cash flows

Read the case in Student Worksheet P.2, then solve the problem.

Activity 2

Ask students to complete Activity 2 of Student Worksheet P.2 to consolidate students’ understanding on the concept of internal rate of return (IRR).

Teacher explains that to decide “between accepting or rejecting the project” means setting the equation “NPV=0”. [Hence: internal rate of return (IRR) = required rate of return (r)]

Students are suggested to use MS Excel to help solve the equation.

31



Internal Rate of Return –Activity 2 (Solution)


-$40,000 $16,000 $16,000 $16,000

Initial outlay : $40,000Equal annual cash flow : $16,000 for 3 years

321 %)1(000,16$

%)1(000,16$

%)1(000,16$000,40$

rrrNPV

++

++

++−=

Teacher helps students to set up the equation by summarising the information in the problem as shown in the slide.

32




If the NPV = 0, the required rate of return (r) is equal to the internal rate of return (IRR)

The equation will be

321 %)1(000,16$

%)1(000,16$

%)1(000,16$000,40$0

IRRIRRIRR ++

++

++−=

If NPV = 0, the required rate of return (r) is equal to internal rate of return (IRR).

Ask students to solve the above equation by using MS Excel or a financial calculator.

33




The steps are as follows :create the cash flow in a time span

If needed, teacher may demonstrate the steps of using MS Excel again to help students solve the equation with slides 34-36.




In the Cell C6, insert the formula “=IRR(C5:F5)” and press ENTER.




The program will automatically calculate the IRR (i.e. 10%).

For weaker students, teacher may demonstrate the input of data to the cells one by one in MS Excel table.

36




In this case, the IRR for the project is equal to 10% or a more precise value of 9.701% (4 sig. fig.)

The MS Excel will work out the IRR with the given cash flows.

37




Students may change the format of the IRR to more decimal places.

38




Conclusion :

Annie would be indifferent to accepting or rejecting the project if the required rate of return (=IRR) = 9.701%.

Teacher can draw a conclusion on Activity 2 with the answer achieved.

39



3rd Investment Appraisal Method - Accounting Rate of Return (ARR)

A ratio of accounting profit to average accounting value.

In other words, it is a “benefit to cost” ratio.

Teacher introduces the third investment appraisal method – Accounting Rate of Return (ARR) to the class.



Accounting Rate of Return

The equation of ARR is:

book value averageincomenet average

=ARR

Teacher explains to students that ARR can be calculated by using the above equation.




Accounting rate of return decision rule :

Project is acceptable if ARR > target return.

Project is rejected if ARR < target return.

Teacher further explains how decision is made with ARR.




For example :

This project generates the following cash flows and has no salvage value at the end of year 4:

Year Cash Flows0 -$201 $252 $303 $154 $50

Teacher explains to students the calculation of ARR with the example shown in this slide.




If the target rate of return is 1.2, find the ARR of the project and determine the feasibility of this investment.

Ask students to determine the ARR and compare that with the target rate of return.




30 4

50153025 :is income net Average =+++

102

020 :is value book Average =+

31030 :is return of rate Accounting =

Teacher demonstrates how to apply the ARR equation to determine the result.

The accounting rate of return in this case is equal to 3.

The average book value is the average of initial cash outflow and the salvage value.




The accounting rate of return is 3.

Since the ARR > target rate of return (1.2), the investment is acceptable.

A conclusion is drawn based on the results.




Now return to the investment project introduced in slide 2, and assume the project has no salvage value at the end of year 3.

Year Cash flows

0 - $24 M

1 $ 10 M

2 $ 10 M

3 $ 10 M

Teacher may use the investment project introduced in the beginning of the lesson to reinforce students’ understanding on the use of ARR for decision making.

It is assumed that the salvage value of the investment project is 0 at the end of year 3.




What is the ARR of this investment?

If the target rate of return of this project is 1.09, shall we accept this project ?

Ask students to calculate the ARR of the investment and decide by comparing the result with the given target rate of return. The solution will be given in the following slides.



Solution

103

101010income net Average =++=

122

024value book Average =+

=

83301210return of rate Accounting .==

Show the calculation step by step as shown in the slide.



Solution

The accounting rate of return is 0.833.

Since the ARR is less than the target rate of return (1.09), the project should be rejected.

Teacher explains how the conclusion is made based on the findings.



Summary

Three investment appraisal methods were introduced in the lesson, including: NPV, IRR and ARR.

The decision criteria of these three investment methods helps us decide whether to accept or reject an investment project.

Teacher concludes the lesson by recapping the three investment appraisal methods introduced in the lesson.



Summary

Investment project summary:Method Value Accept or reject

projectNPV 1.77M Accepted

IRR 12.044% Accepted

ARR 0.833 Rejected

Although the 3 investment appraisal methods introduced can help to decide whether to accept or reject an investment project, the final decision depends highly on the required/target rate of return set by the investor(s). This can be explained by the application of three different investment appraisal methods on the investment project introduced in slide 2. As summarised in the slide, different decisions will be made with different investment appraisal methods.

Remarks:

Decision on acceptance of an investment will be different if the rate of return, target rate of return or required rate of return in different appraisal methods change accordingly.



End of Lesson One

End of Lesson 1



To evaluate the feasibility of the capital investment projects in different cases.

Application of Capital Investment Appraisal Methods

Lesson 2

Teacher starts the lesson by briefing students on the learning objective of this lesson.



1. Net present value (NPV)

2. Internal rate of return (IRR)

3. Accounting rate of return (ARR)

Investment Appraisal Methods

Recap the three investment appraisal methods learnt in lesson 1 before moving on to the discussion of the cases prepared for this lesson.

To speed up the activities, teacher may distribute the Student Worksheet pp.4-10 at the end of lesson one and ask students to read through the cases before the lesson.



Case 1 – An Investment Project

Refer to Student Worksheet P.4 for the details of the case and complete the tasks that follow.

Instruction

1. Divide the class into groups of 4-5 students.2. Ask the students to read through the case carefully and underline

the crucial information for completing tasks (1)-(4).

56



Case 1 – An Investment ProjectYear 0 Year 1 Year 2 Year 3 Year 4 Year 5


Sales $100,000 $180,000 $280,000 $150,000 $100,000

Total Operating expenses

50,000 80,000 100,000 50,000 40,000

Depreciation 40,000 40,000 40,000 40,000 40,000

Earning before tax

10,000 60,000 140,000 60,000 20,000

Tax (at 15%) 1,500 9,000 21,000 9,000 3,000

Net profit 8,500 51,000 119,000 51,000 17,000

Teacher should remind students of the following :- The net cash flows (net profit) should be determined first before

applying the three investment appraisal methods.- Depreciation is under straight-line method.- The tax rate is adopted as a Hong Kong case.



Case 1 – An Investment Project

Tasks(1) Determine the NPV of this project.(2) Determine the IRR of this project.(3) Calculate the accounting rate of return

for this project.(4) Decide whether Raymond should accept

the project or not based on the results of Tasks (1) – (3)

Explain the tasks to students and give them 10 minutes to complete Student Worksheet pp.5-6.

Then ask each group to present their work before revealing the answers to the class with the following slides.



Case 1 – An Investment ProjectTask (1) (Solution)

NPV:

= - $200,000 + $184,671.84= - $15,328.16

Since the NPV is negative, Raymond should reject the project.

54321 %)101(000,17$

%)101(000,51$

%)101(000,119$

%)101(000,51$

%)101(500,8$000,200$

++

++

++

++

++−=NPV

Reveal the answer of Task (1) to the class.

Hints:

Students should formulate the equation, then substitute the appropriate figures to the equation and calculate the result, to make a conclusion.

If NPV > 0, Raymond should accept the project.If NPV < 0, he should reject it.

In this case, NPV is -$15,328.16 (negative), so Raymond should reject the project.




Internal rate of return

In order determine the IRR, we need the application of MS Excel to help.

54321 %)1(000,17$

%)1(000,51$

%)1(000,119$

%)1(000,51$

%)1(500,8$000,200$0

rrrrr ++

++

++

++

++−=

54321 %)1(000,17$

%)1(000,51$

%)1(000,119$

%)1(000,51$

%)1(500,8$000,200$

IRRIRRIRRIRRIRR ++

++

++

++

+=

Teacher reveals the answer of Task (2) and explains with the notes below:

1. Set up the IRR equation.2. Use MS excel to determine the IRR. Teacher may demonstrate the

steps with the help of the following slides.





Use of MS Excel :

Step 1 :Input the necessary numbers into the Excel cells as shown in the slide.

Step 2 :Set an equation into the cell C5 as =IRR(C4:H4).





Use of MS Excel (cont’d) :

Step 3:Press “enter” and the computer will automatically calculate the IRR.In this case the IRR is 7.117%.




The IRR of this project is 7.117%.

Since the required 10% rate of return is greater than the IRR (7.117%), Raymond should reject the project.

Comparing the IRR and required rate of return, teacher concludes that the project should be rejected.



Case 1 – An Investment ProjectTask (3) (Solution) Accounting rate of return

300495

$17,000$51,000$119,000$51,000$8,500: is profit net average The

,$=++++

0001002

$0-$200,000 :is value book average The ,$=

%.349$100,000$49,300 : is return of rate accounting The =

Explain the answer of Task (3) with the following guidelines :

– Students should first calculate the average net profits of the future five years.

– Find the average book value by taking the average of the initial and salvage value.

– Then the accounting rate of return can be determined simply by applying the equation.




The accounting rate of return (i.e. 49.3%) is less than the target accounting rate of return (i.e. 70%).

Hence, the project should be rejected.

By comparing the ARR and the target accounting rate of return, teacher concludes that the project should be rejected.




Results of three capital investment methods:

NPV = -$15,328.16 (negative value rejected)

IRR = 7.117% (<required rate of return 10%, rejected)

ARR = 49.3% ( < 70%, rejected)

We can conclude that the investment should be rejected by Raymond.

Conclude the case by summarising all the findings achieved in Task (1) to Task (3).



Case 2 – Purchase a new van or not ?

Refer to Student Worksheet P.7 for the case details and complete the tasks that follow.

Ask students to remain in the same group and read Case 2 carefully, then underline the crucial information for completing task.



Case 2 – Purchasing a new van or not ?

Task

Based the information, decide whether Vincent should purchase the new van.

Explain the case to students and give them 10 minutes to complete the task in Student Worksheet P.8.

Ask each group to complete their work before revealing the answers to the class with the following slides.




By NPV method :NPV =

= -$155,000 + $179,024= $24,024

The NPV value is positive, the project is acceptable.

54321 %)121(000,41$

%)121(000,38$

%)121(000,60$

%)121(000,60$

%)121(000,46$000,155$

++

++

++

++

++−

As in case 1, the three investment appraisal methods can be applied in deciding whether the project should be accepted or not.

Teacher explains the application of NPV method :- Set up the net present value equation and calculate the NPV of the

future cash flows from the new van.- A conclusion is drawn based on the NPV value.- Accept the project if NPV > 0; reject it if NPV < 0.

In this case, NPV (=$24,024) is > 0, so the project is acceptable.




By IRR method :

Solve the IRR using MS Excel.

0%)1(000,41$

%)1(000,38$

%)1(000,60$

%)1(000,60$

%)1(000,46$000,155$ 54321 =

++

++

++

++

++−

rrrrr

54321 %)1(000,41$

%)1(000,38$

%)1(000,60$

%)1(000,60$

%)1(000,46$000,155$

IRRIRRIRRIRRIRR ++

++

++

++

+=

Explain the IRR method with the following :- Set up the IRR equation and find out the IRR of investing a new van.- Substitute the cash flows into the equation.- Solve the IRR using MS Excel.




- Input the numbers into the Excel cells as shown in the figure.- Set an equation into the cell C17 as =IRR(C16:H16).




- Press ‘enter’ and the result will be generated by the computer (i.e.18.328%).

- The IRR will be displayed in the screen.




IRR (18.328%) > required rate of return (12%)

Acceptable!

A conclusion is drawn by comparing the IRR with the required rate of return.The proposal is accepted as the IRR is higher than the required rate of return.




By ARR method :

5$41,000$38,000$60,000$60,000$46,000

: is inflowcash net average The++++

000495

000245

,$

,$

=

=

Teacher now demonstrates how ARR is used to evaluate the case.




500,77$2

$0$155,000: is book value average The

=+

63.23%or 6323.0500,77$

$49,000: isreturn of rate accounting The

=

After calculating the average net profit and the average book value of the project, the ARR can be determined by $49000 / $77500 = 0.6323 or 63.23%




ARR (i.e.63.23%) > target rate of return (i.e.40%)

Acceptable!

Teacher explains how a conclusion is drawn by comparing the ARR with the target rate of return.




NPV > 0, IRR > required rate of return and,ARR > target rate of return.

The project is acceptable to Vincent and the van could be replaced.

Based on the results achieved by using the 3 investment appraisal methods, it is concluded that Vincent could replace the van.



Case 3 – Two mutually exclusive projects

Refer to Student Worksheet P.9 for the case details and complete the tasks that follow.

In this case, investment appraisal methods are applied to evaluate two mutually exclusive projects.



The project cash flows are :

Project 0 1 2 3 4 5

M -$400 $60 $60 $60 $230 $230

N -$600 $300 $300 $50 $50 $50


The project cash flows are summarised in tabular form.



Tasks(1) Determine the NPV of Project M & N.(2) Determine the IRR of the 2 projects.(3) Calculate the ARR for the 2 projects.(4) Decide whether the project M or N should be

accepted based on the results of Tasks (1) –(3).


Briefly explain the case, then ask students to remain in the same group and complete the above 4 tasks in 10 minutes. Solutions are given in the following slides.



Case 3 – Two mutually exclusive projects (Solution)

Task (1)By NPV method :NPVM =

NPVM = -$400 + $449.12 = $49.12

54321 %)101(230$

%)101(230$

%)101(60$

%)101(60$

%)101(60$400$

++

++

++

++

++−

Explain how the NPV of Project M is calculated:- Set up the NPV equation.- Substitute appropriate figures in the equation.- Calculate project ‘M’ NPV by using scientific calculator.- Draw conclusion: The NPV of project M is $49.12.




Task (1)

By NPV method :NPVN =

NPVN = -$600 + $623.42 = $23.42

54321 %)101(50$

%)101(50$

%)101(50$

%)101(300$

%)101(300$600$

++

++

++

++

++−

Repeat the steps to find out the NPV of Project M. The NPV of project M is $23.42.

Remarks:

As project M and N are mutually exclusive, only one of the projects can be selected.Comparison of the 2 projects based on their NPVs are be discussed in Task (4).




Task (2)

By IRR method – Project M :

Using MS Excel to solve the IRRM.

0%)1(

230$%)1(

230$%)1(

60$%)1(

60$%)1(

60$400$ 54321 =+

++

++

++

++

+−rrrrr

54321 %)1(230$

%)1(230$

%)1(60$

%)1(60$

%)1(60$400$

MMMMM IRRIRRIRRIRRIRR ++

++

++

++

+=

Explain the IRR calculation of project M as follows: - Set up the IRR equation- Substitute the cash flows of project M into the equation- Solve the IRR of project M using MS Excel




Task (2)

- Input numbers into the Excel cells as shown.- Set an equation into the cell C17 as =IRR(C16:H16).



Case 3 – Two mutually exclusive projects (Solution) Task (2)

- Press “enter” and the result is generated by the computer. - The IRR of project M will be displayed on the screen.- The IRR of project M is 13.593%.



By IRR method – Project N :

Using MS Excel to solve the IRRN.

0%)1(

50$%)1(

50$%)1(

50$%)1(

300$%)1(

300$600$ 54321 =+

++

++

++

++

+−rrrrr

54321 %)1(50$

%)1(50$

%)1(50$

%)1(300$

%)1(300$600$

NNNNN IRRIRRIRRIRRIRR ++

++

++

++

+=


Repeat the steps to work out the IRR of project N:- Set up the IRR equation.- Substitute the cash flows (of project N) into the equation.- Solve the IRR using MS Excel.




Task (2)

- Input the numbers into the Excel cells as shown in the figure.- Set an equation into the cell C17 as =IRR(C16:H16).



Task (2)


- Press “enter” and the result is generated by the computer. - Hence, the IRR of project N is found to be 12.276%.

Comparison of the 2 projects based on their IRRs will be discussed in Task (4).



By ARR method :

5$230$230$60$60$60

: isMproject of inflowcash net average The++++

1285

640

$

$

=

=


Explain the steps of calculating ARR of project M:Steps: 1. Calculate the average net cash inflow.



200$2

$0$400: is Mproject of book value average The

=+

64%or 64.0200$

$128: is Mproject ofreturn of rate accounting The

=


Task (3)

Steps (Cont’d): 2. Determine the book value of project M.3. Substitute the answers in Steps 1 & 2 to the ARR equation.4. Solve the equation. The ARR of project M is 64%.



By ARR method :

5$50$50$50$300$300

:isNproject of inflowcash net average The++++

1505

750

$

$

=

=


Repeat the steps to determine the ARR of project N.



300$2

$0$600: is Nproject of book value average The

=+

50%or 5.0300$

$150: is Nproject ofreturn of rate accounting The

=


Task (3)

As shown in the slide, the ARR of project N is 50%.



Summary of results:

Project NPV IRR ARR

M $49.12 13.593% 64%

N $23.42 12.276% 50%


The results achieved in Tasks (1) – (3) are summarised in tabular form.

Before revealing the answer of Task (4) in the next slide, ask students to compare the above results to decide which project should be accepted.



The results of three different capital investment appraisal methods are as follows:

NPVM > NPVN > $0IRRM > IRRN > 10% (required rate of return)ARRM > ARRN > 60% (target accounting rate of return)

We can conclude that project M is acceptable.


Task (4)

Based on the results achieved by the three capital investment appraisal methods, project M is more favourable than project N.

Remarks:

By using NPV method, the project with positive NPV is normally accepted. However, for 2 mutually exclusive projects both with positive NPVs, the one with higher NPV is more preferable and should be selected.By the same token, higher IRR/ARR of 2 mutually exclusive projects are also more preferable and should be selected.



The End

End of the Lesson 2

Topic M02: Capital Investment Appraisal Student Worksheet P.1


BAFS Elective Part – Business Management Module – Financial Management Topic M02: Capital Investment Appraisal

Activity 1:

A property investment case Suppose buying a Kowloon flat costs $2,500,000 and it requires $200,000 for painters, plumbers and renovation. One year later, when placing the flat back on the market, it is found worth $3,100,000. Assume the required rate of return is 8% per year, calculate the net present value (NPV) of the property investment, and decide whether to accept the property investment.

Initial outlay: ____________________ Future cash flow: ____________________ Required rate of return: ____________________ Net present value: Since the NPV is a _______________ value, we can __________ the property investment.



Activity 2:

A project with equal cash flows

Annie begins a project with the initial cash outlay of $40,000. The project will provide equal annual cash flows of $16,000 for the next three years. At what required rate of return would Annie be indifferent between accepting or rejecting the project?


Initial outlay: __________ Equal annual cash flow: ___________ for next _____ years Let r be the required rate of return for the project.

NPV = If the NPV = 0, the required rate of return (r) is equal to the internal rate of return (IRR). The equation will be:

0 =



Using MS Excel:

1. Create the cash flows over the following time span:

2. In the Cell C6, insert the formula of IRR. 3. Once the result is generated, draw your conclusion:

Annie would be indifferent between accepting or rejecting the

project of the required rate of return IRR = ____________



Case 1:

An investment project

Raymond invests $200,000 in a project that depreciates constantly over five years to zero salvage value. The annual tax rate on profit from this project is 15%. The required rate of return is 10%. The target accounting rate of return is 70%. The following table shows the sales and total operating expenses for the five years and the net profit for the project. Year 0 Year 1 Year 2 Year 3 Year 4 Year 5


Sales $100,000 $180,000 $280,000 $150,000 $100,000

Total Operating

expenses

50,000 80,000 100,000 50,000 40,000

Depreciation 40,000 40,000 40,000 40,000 40,000

Earning before tax 10,000 60,000 140,000 60,000 20,000

Tax (at 15%) 1,500 9,000 21,000 9,000 3,000

Net profit 8,500 51,000 119,000 51,000 17,000

Tasks: (1) Determine the net present value of this project. (2) Determine the internal rate of return of this project. (3) Calculate the accounting rate of return for this project. (4) Decide whether Raymond should accept the project or not based on

each of the above results.



Show your workings below :

Task (1): Determine the NPV of the project. NPV = Task (2): Determine the IRR of the project. IRR =



Task (3) : Determine the ARR of the project. ARR = Task (4): Conclusions • Should Raymond invest in the project?

Yes / No (Circle the correct answer) • Reasons:



Case 2:

Purchasing a new van or not?

Vincent is the manager of a logistics company. He wants to buy a new van that costs $155,000. The required annual rate of return of this van is expected to be 12% per year. The estimated life of the new van is 5 years and will have no salvage value (i.e. the net book value is zero) at the end of the 5th year. The estimated future net cash inflows contributed by the new van for the next five years are as follows: Year 1 2 3 4 5 Net cash flows $46,000 $60,000 $60,000 $38,000 $41,000

When making the investment decision, Vincent also takes the following into consideration: - The required rate of return is 12% per year. - The target accounting rate of return is 40%. Task: Based on the information, determine whether Vincent should purchase the new van. [Hints: You should apply the 3 investment appraisal methods introduced in this session to justify your decision.]



Workings: By NPV Method: By IRR Method: By ARR Method: Conclusion: • Should Vincent purchase the new van?

Yes / No (Circle the correct answer)

• Reasons:



Case 3 :

Two mutually exclusive projects A public corporation is considering the following two mutually exclusive projects, Project M and Project N. They both have the required rate of return of 10% and the target accounting rate of return of 60%. The cash flows of these two projects are:

Project 0 1 2 3 4 5

M -$400 $60 $60 $60 $230 $230

N -$600 $300 $300 $50 $50 $50

Based on the given information, complete the 4 tasks below and decide whether project M or N should be accepted: Tasks (1) Determine the net present value of Project M & Project N. (2) Determine the internal rate of return of the 2 projects. (3) Calculate the accounting rate of return for the 2 projects. (4) Decide whether the project M or N should be accepted based on the

results of Tasks (1) – (3)

Task (1) : Determine the net present value of Project M & Project N. NPV of Project M: NPV of Project N:



Task (2): Determine the internal rate of return of the 2 projects. IRR of Project M: IRR of Project N: Task (3): Calculate the accounting rate of return for the 2 projects. ARR of Project M: ARR of Project N: Task (4): Decide whether the project M or N should be accepted.

Documents

M02-Capital Investment AppraisalOverview eng -270409 · Topic M02: Capital Investment Appraisal Topic Overview P.1 ... evaluating investment project with another example. PPT#8-10