free powerpoint templates page 1 free powerpoint templates kim, gyutai department of industrial...

39
Free Powerpoint Templates Page 1 Free Powerpoint Templates Kim, Gyutai Department of Industrial Engineering Chosun University The Optimal Allocation of the Investment Capital for R&D Projects at the Commercial Stage with the Kelly Criterion

Upload: zoe-barber

Post on 05-Jan-2016

212 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: Free Powerpoint Templates Page 1 Free Powerpoint Templates Kim, Gyutai Department of Industrial Engineering Chosun University The Optimal Allocation of

Free Powerpoint TemplatesPage 1

Free Powerpoint Templates

Kim, GyutaiDepartment of Industrial Engineering

Chosun University

The Optimal Allocation of the Investment Capital for R&D Projects

at the Commercial Stage with the Kelly Criterion

Page 2: Free Powerpoint Templates Page 1 Free Powerpoint Templates Kim, Gyutai Department of Industrial Engineering Chosun University The Optimal Allocation of

Free Powerpoint TemplatesPage 2

1.Introduction

2.A Short Survey on Real Options Valuing Theories and The Kelly Criterion

The survey on the ROV theories will be talked focusing on R&D projects. In the discussion of the Kelly criterion, its basic concept will be

introduced.

3. Real Options Valuing Theories and the Kelly Criterion

The development of the optimal capital allocation of the investment fund for the R&D project will be addressed.

The Table of Contents

Page 3: Free Powerpoint Templates Page 1 Free Powerpoint Templates Kim, Gyutai Department of Industrial Engineering Chosun University The Optimal Allocation of

Free Powerpoint TemplatesPage 3

….Continued

4. A Numerical Example The methodology developed in the paper will be demonstrated

with a numerical example which was already publish in the journal.

It was modified to fit to the purpose of the paper.

Page 4: Free Powerpoint Templates Page 1 Free Powerpoint Templates Kim, Gyutai Department of Industrial Engineering Chosun University The Optimal Allocation of

Free Powerpoint TemplatesPage 4

1. Introduction

It is a main purpose of an investment project that an investor makes an effort to attain a maximum level of profit with an optimal allocation of investment capital within a minimum time horizon.

To the end, many researchers including Thorpe and Ziemba have done much work on the subject which is related with so called the Kelly criterion.

The effectiveness of the criterion has been proven by many researchers such that it now becomes so popular in the financial investing and gambling fields.

af

Page 5: Free Powerpoint Templates Page 1 Free Powerpoint Templates Kim, Gyutai Department of Industrial Engineering Chosun University The Optimal Allocation of

Free Powerpoint TemplatesPage 5

Unfortunately no work has been done on the real investment project with the application of the Kelly criterion. In this paper, we will show one small case of a real investment project for which the Kelly criterion may be applicable.

The methodology will be discussed for which the cash flows generated at the commercial stage of an R&D investment project are assumed to follow a normal probability distribution function.

Page 6: Free Powerpoint Templates Page 1 Free Powerpoint Templates Kim, Gyutai Department of Industrial Engineering Chosun University The Optimal Allocation of

Free Powerpoint TemplatesPage 6

2. A Short Survey on Real Options Valuing Theories and The Kelly Criterion

I. ROV Theories Myers first introduced a financial option pricing theory developed by

Black and Scholes used to evaluate a real investment project in 197 and coined it as a real options valuing theory (ROV).

Kester defined a R&D project as a call option and maintained that since its value was greatly affected by an interest rate, the deferral of an investing timing, and uncertainty inherent in the project, the option pricing theory played better role in economically evaluating the R&D project than traditional discounted cash flow (DCF) techniques such as a net present value (NPV) or an internal rate of return (IRR).

Nicholas described a real case study of a real options valuing theory at which Merck pharmaceutical company performed an economic appraisal of the development of a new drug.

Page 7: Free Powerpoint Templates Page 1 Free Powerpoint Templates Kim, Gyutai Department of Industrial Engineering Chosun University The Optimal Allocation of

Free Powerpoint TemplatesPage 7

II. The Kelly Criterion

The Kelly criterion provides us with the investment tool to maximize the geometric mean of return on investment played over the long period of time under the following assumptions:

to get the positive mathematical expectation, to be an independent trials process, to reinvest the returns, to play the games over the long run and to allow the fractional betting.

Page 8: Free Powerpoint Templates Page 1 Free Powerpoint Templates Kim, Gyutai Department of Industrial Engineering Chosun University The Optimal Allocation of

Free Powerpoint TemplatesPage 8

Kelly approached the criterion in two different aspects. One is the criterion widely spoken and used to calculate the optimal fixed fraction The other is one which maximizes the rate of return on investment using the Bayesian decision theory.

Page 9: Free Powerpoint Templates Page 1 Free Powerpoint Templates Kim, Gyutai Department of Industrial Engineering Chosun University The Optimal Allocation of

Free Powerpoint TemplatesPage 9

예제 9.1]

조건 ] 초기 투자비용 : 125,000( 천원 ), 잔존가액 : 40,000( 천원 )- 초기투자비용의 32%, 내용연수 : 8년 ,

감가상각방법 : 정액법 , 연간 생산량 : 2,000 개 , 단위당 가격 : 50( 천원 ), 단위당 변동비용 : 15( 천원 ),

연간 고정비용 : 10,000( 천원 ), 프로젝트 수명 : 5 년 , 법인세율 : 25%, MARR: 15%

민감도 분석예제

0)(680,59%)15( 천원NPV

Page 10: Free Powerpoint Templates Page 1 Free Powerpoint Templates Kim, Gyutai Department of Industrial Engineering Chosun University The Optimal Allocation of

Free Powerpoint TemplatesPage 10

Most of the Kelly criterion starts deriving the optimal fixed fractional bet size with the following equation .

1lim ln 0G X XNNN

where, G: an exponentially growth rate of the investment return. N: a total number of investing or a period of time of investing. X0: a total amount of the initial investment fund.

Equation (1) becomes a variety of forms depending on the structure of an odd system.

Page 11: Free Powerpoint Templates Page 1 Free Powerpoint Templates Kim, Gyutai Department of Industrial Engineering Chosun University The Optimal Allocation of

Free Powerpoint TemplatesPage 11

( ) ln 1 ln 1g f p f q f

( *) ln ln ln 2g f p p q q

The simplest form of Equation (1) is formulated with one that the odd system is of a 1 to 1 relationship, which is mathematically expressed in the following equations:

where,

f*: 2p-1. f*: an optimal betting ratio. f: a betting ratio.

g(f): a maximum geometric return when invested with f*. p: a winning probability. q: a losing probability.

Page 12: Free Powerpoint Templates Page 1 Free Powerpoint Templates Kim, Gyutai Department of Industrial Engineering Chosun University The Optimal Allocation of

Free Powerpoint TemplatesPage 12

Fig. 2. The value of g(f) as f changes at p=0.7

It was found that f*=0.4 and g(f*)=8.2%. It implies that an investor may maximize his geometric return of 8.2% per unit time if he invested only 40% of his total investment capital over a long period to time. The graph shows that as f→1-, g(f)→. Thus we can find that g(f)=0 when f=0.7165. It means that if the investor invested 71.65% of his total investment capital over a long period of time, he will certainly ruin sometime in the course of his investing activity.

An Illustrative Example of the Kelly Criterion

Page 13: Free Powerpoint Templates Page 1 Free Powerpoint Templates Kim, Gyutai Department of Industrial Engineering Chosun University The Optimal Allocation of

Free Powerpoint TemplatesPage 13

3. Real Options Valuing Theories and the Kelly Criterion

It is required to explain the implication of Vt,j at the first time to understand a binomial lattice model.

Fig. 3. The change in the value of the project under a binomial lattice model.

Page 14: Free Powerpoint Templates Page 1 Free Powerpoint Templates Kim, Gyutai Department of Industrial Engineering Chosun University The Optimal Allocation of

Free Powerpoint TemplatesPage 14

Now we will describe the process of developing the methodology to determine an optimal allocation of the investment capital with the Kelly criterion under which the real options value follow a binomial lattice model.

If the value of the project has increased j times by time=t, then Vt,j

may be expressed in the following equation.

1 1 1 1, 0j t j

V V f u f dt j

Applying the Kelly criterion for the equation above, we obtain a geometric return on the project in the following equation.

,( ) ln ln 1,0

ln 1 1

Vt jG f j f u dt j V

t j f d

Page 15: Free Powerpoint Templates Page 1 Free Powerpoint Templates Kim, Gyutai Department of Industrial Engineering Chosun University The Optimal Allocation of

Free Powerpoint TemplatesPage 15

Since the main purpose of the Kelly criterion is to find the value of f which maximizes the expected logarithmic return on the project, we need to derive an expected value of the last equation in the previous slide.

The value of the project, Vt,j, is determined by a number of increases of the project value in a variable of j in the last equation in the previous slide, its expected value may be demonstrated in the following equation .

( ) ln 1 1,

+ ln 1 (1 )

ln 1 ( 1) =

1 (1 )

+ ln 1 (1 )

E G f E j f ut j

E t j f d

f ut p

f d

t f d

Page 16: Free Powerpoint Templates Page 1 Free Powerpoint Templates Kim, Gyutai Department of Industrial Engineering Chosun University The Optimal Allocation of

Free Powerpoint TemplatesPage 16

Since there is a high likelihood that an investor may be fully ruined as he increases his betting ratio of f, it is better to measure its risk with a traditional wisdom of variance.

The mathematical expression of variance for the case is given in the following equation .

1,

2ln 1 ( 1)

1 (1 )

Var G f t p pt j

f u

f d

(7)

12exp

12exp

1 =

u t

d t

u

exp

1 =

tp

u d

R dBu d

The following mathematical expressions have widely been used as inputs to model a binomial lattice model by researchers .

(8)

where,t: T/N.: an expected return on the

project.p:a risk-neutral probability.

Page 17: Free Powerpoint Templates Page 1 Free Powerpoint Templates Kim, Gyutai Department of Industrial Engineering Chosun University The Optimal Allocation of

Free Powerpoint TemplatesPage 17

4. A Numerical Example

The case study discussed in this section was taken from the Shockely, et.al. paper and was modified to fit for the purpose of this paper.

Wahoo (a disguised name) company wanted to perform an economic analysis for the investment project planned to develop a new drug to cure a virus-related animal disease.

The company already got admitted to receive a financial support from a Federal and State government for the development of the preclinical stage of the project.

Page 18: Free Powerpoint Templates Page 1 Free Powerpoint Templates Kim, Gyutai Department of Industrial Engineering Chosun University The Optimal Allocation of

Free Powerpoint TemplatesPage 18

The expected annual revenue was projected to be $85 million for the sale of the new drug, but not to be any change in the projected revenue.

It was estimated that the company would take up 3% and 50% of the market in 2007 and 2017, respectively. It was assumed that the annual market growth rate was of a linear function.

The company projected that a cost of goods sold, sales and general administrative expenses, and working capital would be 30%, 25%, 10% of total revenue, respectively. The company assumed that a corporate tax rate would be 12.1%.

The company assessed that building a facility to produce the drug and a logistics structure to sell it in 2007 would require $10 million, which were planned to be depreciated with a straight-line method.

Table 1 was constructed by considering the following conditions, which plays a vital role in an economic evaluation of the R&D investment project.

Page 19: Free Powerpoint Templates Page 1 Free Powerpoint Templates Kim, Gyutai Department of Industrial Engineering Chosun University The Optimal Allocation of

Free Powerpoint TemplatesPage 19

The company guesstimated that the market share of the drug would decrease by 20% annually after 2017. It assumed that a minimum attractive rate of return and a risk-free discount rate would be 11% and 5%, respectively.

It was assumed that an investment capital would be always constant.It was also assumed that only one-fourth of the total investment capital

for commercialization would be invested in the first commercialization stage in 2007, and depending on the result of the first commercialization stage, the rest of the investment capital would be invested in the following stage.

Page 20: Free Powerpoint Templates Page 1 Free Powerpoint Templates Kim, Gyutai Department of Industrial Engineering Chosun University The Optimal Allocation of

Free Powerpoint TemplatesPage 20

Page 21: Free Powerpoint Templates Page 1 Free Powerpoint Templates Kim, Gyutai Department of Industrial Engineering Chosun University The Optimal Allocation of

Free Powerpoint TemplatesPage 21

A binomial lattice model for the project of Wahoo Company

In the first time, we derived the optimal betting ratio considering a general binomial lattice model with the following findings and assumptions.

First, a risk-free interest rate for 3-year Koran government bonds came up with around 4%.

It was assumed that a probability that the value of the project increased was 60%. Then, we could find the values of u and d as followings:

Using the values above, we could determine the values of u1 and d1.

654.7 1.63379

400.4

224.9 0.56169400.4

u

d

1 ( 1) (1.63511 1) 0.63511

1 (1 ) (1 0.56169) 0.48310

u u

d d

Page 22: Free Powerpoint Templates Page 1 Free Powerpoint Templates Kim, Gyutai Department of Industrial Engineering Chosun University The Optimal Allocation of

Free Powerpoint TemplatesPage 22

Now, we need to calculate f* using the following equation whose explanation was omitted due to the limited page. It is noted that when putting the value of d1 into the following equation, we need to have a minus sign for it.

1 11* 1 1

1 0.04 0.04 (0.6)(0.63511) (0.4)( 0.56169)

(0.04 0.63511)(0.04 0.56169)

=0.33806

R R pu qdB Bf

R u R dB B

The term of f*=0.33806 implies that the company should invest only 33.8% of the total investment capital in the commercialization stage.

If the company invests such portion, then it would obtain

( * 0.33806) ln 0.05827170

WNG fn W

This number provides a rate of return of 1.2% per unit time.

Page 23: Free Powerpoint Templates Page 1 Free Powerpoint Templates Kim, Gyutai Department of Industrial Engineering Chosun University The Optimal Allocation of

Free Powerpoint TemplatesPage 23

Fig. 5 shows change in the value of G(f) as the probability varies. Looking the graph in Fig. 5, we can detect that the value of G(f) rapidly decreases and finally approach negative infinity as f→1” and p→0. On the other around, G(f) goes up to a maximum value. In this case, if the company invests 87.7% of its total investment capital, it would absolutely be ruined.

Fig. 5. The value of G(f) with changes in the value of f and p

Page 24: Free Powerpoint Templates Page 1 Free Powerpoint Templates Kim, Gyutai Department of Industrial Engineering Chosun University The Optimal Allocation of

Free Powerpoint TemplatesPage 24

Now we would analyze the betting ratio applying the Kelly criterion to the binomial lattice model referring to the discussion in Section III.

To perform the analysis, we need to calculate E[Gt,j(f)] and Var[Gt,j(f)] and

the expected value and standard deviation of the value of the project. Then, those values were estimated to be as followings:

16%, 60% 1.822, 0.549, 0.500u d p

(1 0.822 )5 (0.5) ln5, (1 0.45 )

+5 ln 1 0.451

fE G fj f

f

5 0.5 0.55,

21 0.822

ln1 0.45

Var G fj

f

f

We selected G5,j(f) to calculate E[G5,j(f)] and Var[G5,j(f), which are as followings:

Page 25: Free Powerpoint Templates Page 1 Free Powerpoint Templates Kim, Gyutai Department of Industrial Engineering Chosun University The Optimal Allocation of

Free Powerpoint TemplatesPage 25

Fig. 6. The expected value and variance of the projectFig. 6 shows the sensitivity analysis on the value of E[G5,j(f)]

and Var[G5,j(f) with changes in the values of f and p. Investigating the graph in Fig. 6, we might find the optimal

betting ratio of 93%, which was derived by MATHEMATICA. This optimal betting ratio yields a rate of return on the project

of 13% per unit time.

Page 26: Free Powerpoint Templates Page 1 Free Powerpoint Templates Kim, Gyutai Department of Industrial Engineering Chosun University The Optimal Allocation of

Free Powerpoint TemplatesPage 26

Fig. 7. The sensitivity analysis on the expected value with change in the value of f

Looking at the graph in Fig. 6 and 7, it can be easily recognized that a variance of the project geometrically increases at which f >0.4 and the expected value rapidly decreases at which f >0.93.

If the company borrows more money from the outside and invests it, then we can see that it would completely be ruined at f =1.7

Page 27: Free Powerpoint Templates Page 1 Free Powerpoint Templates Kim, Gyutai Department of Industrial Engineering Chosun University The Optimal Allocation of

Free Powerpoint TemplatesPage 27

Most of research on the Kelly criterion has been focused on a financial investment project solely and it has been reported that the Kelly criterion plays a key role in a successful financial investing activity.

However, not much work has been done on a real investment project. So this paper was concerned with doing a little research on the application of the Kelly criterion to an economic analysis of a real investment project

And we found some interesting results from this research, but we believe that we need further research on this topic to refine the work and investigate the reason why the rates of return found in this paper are so much different.

Page 28: Free Powerpoint Templates Page 1 Free Powerpoint Templates Kim, Gyutai Department of Industrial Engineering Chosun University The Optimal Allocation of

Free Powerpoint TemplatesPage 28

Thank you so much!!!

And Wish you have a

merry Christmas and

seasoning greetings!!!

Page 29: Free Powerpoint Templates Page 1 Free Powerpoint Templates Kim, Gyutai Department of Industrial Engineering Chosun University The Optimal Allocation of

Free Powerpoint TemplatesPage 29

투자프로젝트의 NPV(6%) 의 분포

단위 : 천원

Page 30: Free Powerpoint Templates Page 1 Free Powerpoint Templates Kim, Gyutai Department of Industrial Engineering Chosun University The Optimal Allocation of

Free Powerpoint TemplatesPage 30

- 의사결정나무분석법 (Decision Tree Analysis: DTA)

불확실한 미래에 일어날 일을 도식화하여 보여주는 대표적인 방법 의사결정마디 (decision node) : 투자프로젝트의 대안들을 표시 선택마디 (chance node) : 의사결정마디의 대안들에 영향을 미치는 임의의 사건에 관한 확률 청산 값 : 화폐가치로 표시된 숫자

역방향으로 계산 청산 값인 화폐가치를 극대화하는 대안을 최선의 대안으로 선정

예제 9.9] DTA 를 이용한 투자프로젝트의 위험성 분석

조건 ] 3 가지 대안 : (1) 이 투자프로젝트를 지금 당장 포기하는 것 - 2,000 만원 처분비용 발생 ,

(2) 현재 발생하고 있는 비용수준에서 현 투자프로젝트를 지속적으로 실행하는 것 - 5,000 만원 비용 발생 ,

(3) 현재 실행 중인 투자프로젝트의 성공 가능성을 향상시키기 위하여 현재의 발생 비용을 증가시키는 것 - 1 억원 비용 발생 1 년 후 수익 : 3 억원 , 현 수준 노력에 의한 투자프로젝트의 성공 / 실패 확률 : 40%/60%,

현 수준의 노력보다 두 배의 노력을 할 경우 투자프로젝트의 성공 / 실패 확률 : 80%/20%

의사결정나무분석법

Page 31: Free Powerpoint Templates Page 1 Free Powerpoint Templates Kim, Gyutai Department of Industrial Engineering Chosun University The Optimal Allocation of

Free Powerpoint TemplatesPage 31

풀이 ] DTA 기법을 이용한 투자의사결정 - 평균수익 포기대안 = -20,0001.0 = -20,000( 천원 )

유지대안 = 250,0000.4+(-50,000) 0.6

=70,000( 천원 )

증가대안 = 200,0000.8+(-100,000) 0.2

=140,000( 천원 )

- 증가대안의 청산 값이 가장 크므로 증가대안 선택

의사결정나무분석법

-20,000

250,000

-50,000

200,000

포기대안

유지대안

증가대안

p=1

p=40%

q=60%

P=80%

Q=20%-100,000

청산 값확률정보대안종류

p= 유지대안 성공확률q= 유지대안 실패확률P= 증가대안 성공확률Q= 증가대안 실패확률

p= 유지대안 성공확률q= 유지대안 실패확률P= 증가대안 성공확률Q= 증가대안 실패확률

투자프로젝트에 관한 의사결정나무

Page 32: Free Powerpoint Templates Page 1 Free Powerpoint Templates Kim, Gyutai Department of Industrial Engineering Chosun University The Optimal Allocation of

Free Powerpoint TemplatesPage 32

- 옵션 (Option) 특정의 투자자산을 특정한 기일 내에 특정한 가격으로 매입하든지 혹은 처분할 수 있는 권리 콜옵션 (call option), 풋옵션 (put option)

유럽피언옵션 (European option), 아메리칸옵션 (American option)

- 실물옵션 (real option) 실물투자자산에 관한 투자의사결정문제에서 미래에 발생할 더 바람직한 선택을 할 수 있는 권리

- 실물옵션의 대표적 사례 실물투자프로젝트의 투자시점을 연기할 수 있는 유연성 현재 실행 중인 투자프로젝트를 축소하거나 증가하거나 혹은 포기할 수 있는 유연성

- DCF 기법과의 차이점 DCF 기법 실물옵션의 사례들을 투자평가 과정에 적절하게 반영하지 못함 투자프로젝트에 내재된 불확실성으로부터 초래되는 투자프로젝트의 가치를 향상시킬 수 있는

기 회를 투자평가과정에서 무시 실물옵션 기법 투자프로젝트의 투자시점을 다양한 측면에서 분석가능

실물옵션가치론

Page 33: Free Powerpoint Templates Page 1 Free Powerpoint Templates Kim, Gyutai Department of Industrial Engineering Chosun University The Optimal Allocation of

Free Powerpoint TemplatesPage 33

- 1 단계 BLOPM 으로 주식옵션 (stock option) 가치 구하기

조건 ]

- “SS” 회사 주식 현재가치 : 43 만원- 행사가격 (exercise price): 45 만원- 주가가 48 만원이 될 확률 : 60%

- 주가가 38 만원이 될 확률 : 40%

- 무위험 이자율 : 5%

- 유럽피언 옵션

풀이 ] 주식옵션의 가치 계산

- 주식과 옵션으로 구성된 복제포트폴리오 (replicating portfolio) 구성 - 옵션은 공매도- 무위험차익거래는 없음- 불확실성을 완전히 소멸시키도록 주식 매입 수 () 를 결정

이항격자옵션가치모델(binomial lattice option pricing model : BLOPM)

주가 : 48 만원옵션가치 : 3 만원

주가 : 38 만원옵션가치 : 0

주가 : 43 만원옵션가치 : ?

t=0

상승확률 =60%

하락확률 =40%

t=1

Page 34: Free Powerpoint Templates Page 1 Free Powerpoint Templates Kim, Gyutai Department of Industrial Engineering Chosun University The Optimal Allocation of

Free Powerpoint TemplatesPage 34

- 1 단계 : 주가가 상승할 경우의 복제포트폴리오의 가치

- 2 단계 : 주가가 하락할 경우의 복제포트폴리오의 가치

- 3 단계 : 1 단계와 2 단계의 복제포트폴리오 가치가 같도록 연립방정식 구성하여 구하기

- 4 단계 : 값을 이용하여 복제포트폴리오의 가치를 계산 ( 상승 또는 하락의 경우 모두 결과 동일 )

주식옵션의 가치를 계산하는 과정

348

38

3.0

38348

)(1.143)3.0(48348 만원

Page 35: Free Powerpoint Templates Page 1 Free Powerpoint Templates Kim, Gyutai Department of Industrial Engineering Chosun University The Optimal Allocation of

Free Powerpoint TemplatesPage 35

- 5 단계 : 복제포트폴리오의 현재가치 구하기 ( 무위험 이자율 =5%)

- 6 단계 : 5 단계에서 구한 복제포트폴리오 가치는 현재의 포트폴리오 가치와 동일

- “SS” 회사의 주식 콜옵션의 현재가치는 20,430 원

주식옵션의 가치를 계산하는 과정

)(857.10)1%,5,/(4.11 만원FP

)(043.2

857.10)3.0(43

857.1043

만원

f

f

f

Page 36: Free Powerpoint Templates Page 1 Free Powerpoint Templates Kim, Gyutai Department of Industrial Engineering Chosun University The Optimal Allocation of

Free Powerpoint TemplatesPage 36

예제 9.10] 실물옵션가치 결정하기

조건 ] 초기투자자본 =2,000,000( 천원 ), 투자프로젝트 현재가치 =1,900,000( 천원 ), 상승가치=2,834,450( 천원 ),

하락가치 = 1,273,610( 천원 ), 무위험할인율 =8%, 실물옵션만기 =1 년

실물옵션가치 결정

38V1u: 28 억 3,445 만원

V1d: 12 억 7,361 만원

V0:19 억원옵션가치 : ?

t=1t=0

상승확률 =60%

하락확률 =40%

Page 37: Free Powerpoint Templates Page 1 Free Powerpoint Templates Kim, Gyutai Department of Industrial Engineering Chosun University The Optimal Allocation of

Free Powerpoint TemplatesPage 37

풀이 ]

(1) 전통적인 DCF 을 토대로 한 투자의사결정

- 이 투자프로젝트의 NPV= -1 억원이기 때문에 DCF 의사결정 기법에 의해서는 투자프로젝트 기각

(2) 실물옵션가치론을 토대로 한 투자의사결정

- 1 단계 : 투자프로젝트가 상승할 경우의 복제포트폴리오의 가치

상승할 경우의 1 년 후 옵션의 가치 = 투자프로젝트 – 초기투자자본 = 28 억 3,445 만원 – 20 억원 = 8 억 3,445 만원

- 2 단계 : 투자프로젝트가 하락할 경우의 복제포트폴리오의 가치

하락할 경우의 1 년 후 옵션의 가치 = 0

실물옵션가치 결정

)(12019 억원초기투자자본투자프로젝트의

PVNPV

3445.83445.28

7361.12

Page 38: Free Powerpoint Templates Page 1 Free Powerpoint Templates Kim, Gyutai Department of Industrial Engineering Chosun University The Optimal Allocation of

Free Powerpoint TemplatesPage 38

- 3 단계 : 1 단계와 2 단계의 복제포트폴리오 가치가 같도록 연립방정식 구성하여 구하기

- 4 단계 : 값을 이용하여 복제포트폴리오의 가치를 계산

-5 단계 : 복제포트폴리오의 현재가치 구하기 ( 무위험 이자율 =8%)

- 6 단계 : 5 단계에서 구한 복제포트폴리오 가치는 현재의 포트폴리오 가치와 동일

실물옵션가치 결정

)(809.6

3445.8)5346.0(3445.283445.83445.28

억원

)(305.6)1%,8,/(809.6 억원FP

5346.0

7361.123445.83445.28

)(853.3

305.6)5346.0(19

305.619

억원

f

f

f

Page 39: Free Powerpoint Templates Page 1 Free Powerpoint Templates Kim, Gyutai Department of Industrial Engineering Chosun University The Optimal Allocation of

Free Powerpoint TemplatesPage 39

실물옵션가치 결정

만원억억원만원억

530,84

1530,83

ROP

ROP

ROPNPVSNPV