Principles of Managerial Finance 9th Edition

Principles of Managerial Finance

9th Edition

Chapter 9

Capital Budgeting

Techniques

Learning Objectives

• Understand the role of capital budgeting techniques in

the capital budgeting process.

• Calculate, interpret, and evaluate the payback period.

• Calculate, interpret, and evaluate the net present

value (NPV).

• Calculate, interpret, and evaluate the internal rate of

return (IRR).

Learning Objectives

• Use the net present value profiles to compare net

present value and internal rate of return techniques.

• Discuss NPV and IRR in terms of conflicting rankings

and the theoretical and practical strengths of each

approach.

Techniques that Ignore the Time Value of Money

• Payback. The payback method simply measures how

long (in years and/or months) it takes to recover the

initial investment.

• But payback has two major weaknesses:

• First, it fails to consider the importance of the time

value of money.

• Second, it fails to consider cash flows that occur after

the pre-set payback period.


But which is preferred?

Payback is thesame!

Cash Flow Project 1 Project 2

Initial Outlay 45000 45000

Year 1 Inflow 20000 25000


Payback 2 years 2 years

Mactool Payback Example(Failure to Recognize TVM)

• Payback Weakness: Failure to consider the time value of money (pattern of cash flows).


• Payback Weakness: Failure to consider all relevant cash flows.

But look at the total cash flows

for Project 1!

Payback sayspick Project 2!

Cash Flow Project 1 Project 2

Initial Outlay 45000 45000






Payback 2.2 years 2 years

Mactool Payback Example(Failure to Recognize ALL Cash Flows)

Time Value Techniques

• Net Present Value (NPV). Net Present Value is found

by subtracting the present value of the after-tax

outflows from the present value of the after-tax

inflows.

Decision Criteria

If NPV > 0, accept the project

If NPV < 0, reject the project

If NPV = 0, indifferent

Time Value TechniquesNet Present Value

Year Existing Hoist A Hoist B

0 -$ (37,488)$ (51,488)$

1 9,936 6,504 8,064

2 9,936 8,808 12,144

3 9,040 7,208 11,120

4 8,400 6,504 10,080

5 8,400 19,264 29,880

East Coast DrydockNet Incremental After Tax Cash Flows

Recall the Net Incremental Cash Flows for East Coast Drydock from Chapter 8


With a 15% discount rate, we would keep the existing hoist

Net Present Value

Year PVIF Existing PV Existing Hoist A PV Hoist A Hoist B PV Hoist B

0 1.0000 -$ -$ (37,488)$ (37,488)$ (51,488)$ (51,488)$

1 0.8696 9,936 8,640$ 6,504 5,656$ 8,064 7,012$

2 0.7561 9,936 7,513$ 8,808 6,660$ 12,144 9,183$

3 0.6575 9,040 5,944$ 7,208 4,739$ 11,120 7,312$

4 0.5718 8,400 4,803$ 6,504 3,719$ 10,080 5,763$

5 0.4972 8,400 4,176$ 19,264 9,578$ 29,880 14,856$

NPV = Sum of PV of CF 31,076$ (7,137)$ (7,363)$


(NPV @ 15%)i)15.01(

1


In fact, even with a discount rate of 0%, we would keep the existing hoist since it has the highest NPV.

Net Present Value


0 1.0000 -$ -$ (37,488)$ (37,488)$ (51,488)$ (51,488)$

1 1.0000 9,936 9,936$ 6,504 6,504$ 8,064 8,064$

2 1.0000 9,936 9,936$ 8,808 8,808$ 12,144 12,144$

3 1.0000 9,040 9,040$ 7,208 7,208$ 11,120 11,120$

4 1.0000 8,400 8,400$ 6,504 6,504$ 10,080 10,080$

5 1.0000 8,400 8,400$ 19,264 19,264$ 29,880 29,880$

NPV = Sum of PV of CF 45,712$ 10,800$ 19,800$


(NPV @ 0%)


Recall that the before tax operating cash inflows for Drydock in Chapter 9 were as follows:

Net Present Value

Year Hoist A Hoist B Existing

1 21,000$ 22,000$ 14,000$

2 21,000 24,000 14,000

3 21,000 26,000 14,000

4 21,000 26,000 14,000

5 21,000 26,000 14,000

Profits Before Depreciation & Taxes

East Coast Drydock


What if -- because of a measurement error -- the cash inflows for A and B were double those initially

estimated as shown below:

Net Present Value

Year Hoist A Hoist B Existing

1 42,000$ 44,000$ 14,000$

2 42,000 48,000 14,000

3 42,000 52,000 14,000

4 42,000 52,000 14,000

5 42,000 52,000 14,000

Profits Before Depreciation & Taxes

East Coast Drydock


Recalculating the NPV at a discount rate of 15%, we get:

Net Present Value


0 1.0000 -$ -$ (37,488)$ (37,488)$ (51,488)$ (51,488)$

1 0.8696 9,936 8,640$ 19,104 16,612$ 21,264 18,490$

2 0.7561 9,936 7,513$ 21,408 16,188$ 26,544 20,071$

3 0.6575 9,040 5,944$ 19,808 13,024$ 26,720 17,569$

4 0.5718 8,400 4,803$ 19,104 10,923$ 25,680 14,683$

5 0.4972 8,400 4,176$ 31,864 15,842$ 45,480 22,612$

NPV = Sum of PV of CF 31,076$ 35,101$ 41,937$


(NPV @ 15%)

The Excel function for computing NPV is

=NPV(int rate, data range)

此資料由第一期計算，財務計算機則由第零期

計算


With the new numbers, we can now see that

Hoist B should be used to replace the

existing hoist. This will maximize NPV and

ultimately, shareholder value.

Net Present Value

• The IRR is the discount rate that will equate the

present value of the outflows with the present

value of the inflows:

• The IRR is the project’s intrinsic rate of return. Decision Criteria

If IRR > k, accept the project

If IRR < k, reject the project

If IRR = k, indifferent

Time Value TechniquesInternal Rate of Return

Note that both replacement projects provide a return in excess of the cost of capital of 15%.



0 1.0000 -$ -$ (37,488)$ (37,488)$ (51,488)$ (51,488)$

1 0.7033 9,936 6,988$ 19,104 13,436$ 21,264 14,955$

2 0.4946 9,936 4,915$ 21,408 10,589$ 26,544 13,129$

3 0.3479 9,040 3,145$ 19,808 6,891$ 26,720 9,295$

4 0.2447 8,400 2,055$ 19,104 4,674$ 25,680 6,283$

5 0.1721 8,400 1,445$ 31,864 5,483$ 45,480 7,826$

Internal Rate of Return 47.63% 42.19%


IRR on Excel

Internal Rate of Return

The Excel function for computing IRR is=IRR(data range)

此資料由第零期計算，財務計算機也由第零期

計算

無法計算其 IRR

Time Value TechniquesInternal Rate of Return

What if the cost of capital were 42.19%?


0 1.0000 -$ -$ (37,488)$ (37,488)$ (51,488)$ (51,488)$

1 0.7033 9,936 6,988$ 19,104 13,436$ 21,264 14,955$

2 0.4946 9,936 4,915$ 21,408 10,589$ 26,544 13,129$

3 0.3479 9,040 3,145$ 19,808 6,891$ 26,720 9,295$

4 0.2447 8,400 2,055$ 19,104 4,674$ 25,680 6,283$

5 0.1721 8,400 1,445$ 31,864 5,483$ 45,480 7,826$

Internal Rate of Return 47.63% 42.19%

Net Present Value 18,548$ 3,584$ (0)$

Profitability Index 1.10 1.00


(NPV @ 42.19%)Notice that for Hoist B,IRR = the discount

rate and thatNPV = 0

IRR 的應用• 元智大學提供教職員優惠的年金保險，參加人員每年

將依個人服務年資由學校補助一萬五仟元（服務十年以上）、一萬元（服務六至九年）及伍仟元（服務五年以下）。根據該保險經紀人公司的試算結果，去計算該項年金保險的內部報酬率：假設現年三十九歲女性教職員，本校服務年資兩年，首欄的數字為連續十年繳納年金保險費 ( 扣除掉 5% 的單利以及學校提撥的金額 ) ，於第十八年時全數領出；次欄的數字為連續十年繳納年金保險費 ( 扣除掉 5%的單利以及學校提撥的金額 ) ，於第十九年時全數領出。兩者用 EXCEL 計算出來的內部報酬率 (IRR) 都是6% ，遠高於現行市場上任何的定存利率。

The NPV Profile shows how a project’s value changes with changes in the discount rate.

Time Value TechniquesNet Present Value Profile

Discount

Rate Existing Hoist A Hoist B

0% 45,712$ 73,800$ 94,200$

5% 39,777$ 57,918$ 72,683$

10% 34,989$ 45,287$ 55,635$

15% 31,076$ 35,101$ 41,937$

20% 27,838$ 26,780$ 30,790$

30% 22,841$ 14,162$ 13,978$

40% 19,209$ 5,196$ 2,122$

50% 16,484$ (1,399)$ (6,536)$

NPV @ Various Discount Rates

NPV Profile

Time Value TechniquesNet Present Value Profile

East Coast Drydock Net Present Value Profile

($20,000)

$0

$20,000

$40,000

$60,000

$80,000

$100,000

0% 5% 10% 15% 20% 30% 40% 50%

k (%)

NPV ($) Existing Hoist A Hoist B

47.63%

42.19%

只有當 K 大於這點時， NPV與 IRR 的決策

是一致的

• The profitability index which is also sometimes called the benefit/cost ratio, is the ratio of the present value of the inflows to the present value of the outflows.

Time Value TechniquesProfitability Index

Decision Criteria

If PI > 1, accept the project

If PI < 1, reject the project

If PI = 1, indifferent

PI = PV Inflows PV Outflows

Time Value TechniquesProfitability Index

Returning to the last East Coast Drydock example, we get:


0 1.0000 -$ -$ (37,488)$ (37,488)$ (51,488)$ (51,488)$

1 0.8696 9,936 8,640$ 19,104 16,612$ 21,264 18,490$

2 0.7561 9,936 7,513$ 21,408 16,188$ 26,544 20,071$

3 0.6575 9,040 5,944$ 19,808 13,024$ 26,720 17,569$

4 0.5718 8,400 4,803$ 19,104 10,923$ 25,680 14,683$

5 0.4972 8,400 4,176$ 31,864 15,842$ 45,480 22,612$

Profitability Index 1.94 1.81


(NPV @ 15%)

Choose Hoist A since PIA > PIB

Double A 和 B的 cash flow 後

Problems with Discounted Cash Flow Techniques

Mutually exclusive projects compete in some way with the same resources. A firm can pick one, or the other, but not

both.

Year A B

Acquisition Cost 0 (100,000) (60,000)

Cash Inflow s 1 60,000 36,000

2 60,000 36,000

3 60,000 36,000

NPV (@14%) $39,300.00 $23,580.00

IRR 36% 36%

(Mutually Exclusive Projects)Dyer, Inc., Project Analysis

Project

Conflicting Rankings for Mutually Exclusive Projects

rate NPV(A) NPV(B)

0% 80,000$ 48,000$

10% 49,211$ 29,527$

20% 26,389$ 15,833$

30% 8,967$ 5,380$

40% (4,665)$ (2,799)$

50% (15,556)$ (9,333)$

Project

Dyer, IncNPV Profile

Mutually exclusive projects compete in some way with the same resources. A firm can pick one, or the other, but not

both.



NPV Profile(Mutually Exclusive Projects)

Project A

Project B

$(40,000)

$(20,000)

$-

$20,000

$40,000

$60,000

$80,000

$100,000

0% 10% 20% 30% 40% 50% 60%



36%

兩個 project 的 IRR 皆為 36%亦即 NPV=0 時的 K 皆為 36%

若 AB 為 mutually exclusive ，則當 k<36% 時，選 A 當 k>36% 時，都不要若 AB 為 Independent ，當 k<36% ， 2 者都選當 k>36% ，都不要

e f g

NPV

AB

If k<eIf e<k<fIf k>f

k(%)

• Interdependent projects are those that influence the value of others.

• In general terms, if there are two interdependent projects, then three appraisals are required:– Project A

– Project B

– And Project A plus B



如：兩家鄰近的購物中心

Summary

• If projects are mutually exclusive and not subject

to capital rationing, the project with the higher NPV

should be selected.

• If the projects are independent, and there is no

capital restriction, both should be chosen if they

have positive NPVs.

• In the presence of capital restrictions, the project

with the higher NPV should be selected.


Table 9.7 Reinvestment Rate Comparisons for a Projecta

Year FVIF10%,t FVIF15%,t

(1) (2) (3) (4) (5) (6) (7)

1 $52,000 2 1.210 $62,920 1.323 $68,7962 78,000 1 1.100 $85,800 1.150 $89,7003 100,000 0 1.000 $100,000 1.000 $100,000

Future Value end of year 3 $248,720 $258,496NPV @ 10%=$16,867 > 0 ∴ accept IRR=15% > 10% ∴ accept

aInitial investment in this project is $170,000.

Cashinflows

Future value[(2)×(4)]

Future Value[(2)×(6)]

Reinvestment rateNumber of

years earninginterest (t)

[3-(1)]

10% 15%

0 1 2 3

-170,000 +52,000 +78,000 +100,000

%15)1(

000,100

)1(

000,78

)1(

000,52000,170:

867,16)1.1(

000,100

)1.1(

000,78

)1.1(

000,52000,170

321

321

rrrr

IRR

NPV

Table 9.8 Project Cash Flows After Reinvestment

10% 15%

1 $0 $02 0 03 248,720 258,496

NPV@10% $16,867 $24,213 IRR 13.5% 15.0%

Year Operating cash inflows

Reinvestment rate

Initial investment $170,000

0 1 2 3

-170,000 +52,000 +78,000 +100,000

248,720

和上頁相同和上頁相同

%5.13000,170)1(

720,248:

867,16000,170)1.1(

720,248

3

3

rr

IRR

NPV

%15000,170)1(

496,258

213,24000,170)1.1(

496,258

3

3

rr

NPV

Table 9.9 Preferences Associated with ExtreamDiscount Rates and Dissimialr CashInflow Patterns

Discount rate LowHigh Not preferred Preferred

Not preferred

Cash inflow Pattern

Higher early year cashinflows

Lower early year cashinflows

Preferred

基本上： greater the difference between the magnitude and timing of cash inflows, the greater the likelihood of conflicting rankings between NPV and IRR.

理論上：用 NPV ，不要用 IRR 。因為 (1)NPV 假設 intermediate cash flows are reinvested at cost of capital ， IRR 則假設intermediate cash flows are reinvested at IRR 。 NPV 法的假設較為合理且保守。 (2)non-conventional cash flow 常會有多重或零個 IRR 的解

實務上：業界仍偏好 IRR

若期初投資一樣的話

WHY? 因為晚期的 Cash flow會被高折現率 severely penalized in present value terms.

Principles of Managerial Finance 9th Edition

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