investment opportunities as real options
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Investment Opportunities as Real Options. 1. 投資時機 – 確定的未來. 例 1 : 有一片森林,如果今年砍伐,可以賺取 50 ,如果一年後砍伐,可賺 64.4 ;兩年後賺 77.5 ;三年後賺 89.4 ;四年後賺 100 ;五年後賺 109.4 。如果資金成本是 10% ,請問應在何時砍伐?. 1. 投資時機 – 確定的未來. 例 1 :. 1. 投資時機 – 確定的未來. 例 1 :. 2. 投資 – 不確定的未來. 例 2 : - PowerPoint PPT PresentationTRANSCRIPT
Investment Opportunities as Real Options
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1. 投資時機 – 確定的未來▪例 1:
•有一片森林,如果今年砍伐,可以賺取 50,如果一年後砍伐,可賺 64.4;兩年後賺 77.5;三年後賺 89.4;四年後賺 100;五年後賺 109.4。如果資金成本是 10%,請問應在何時砍伐?
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1. 投資時機 – 確定的未來▪例 1:
0 1 2 3 4 5
現金流量
50.0 64.4 77.5 89.4 100.0
109.4
PV(10%)
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1. 投資時機 – 確定的未來▪例 1:
0 1 2 3 4 5
現金流量
50.0 64.4 77.5 89.4 100.0
109.4
PV(10%)
50.0 58.5 64.0 67.2 68.3 67.9
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2. 投資 – 不確定的未來▪例 2:
•考慮是否購買油井開採權。油井總價值為產量五百萬桶,取得開採權後必須立刻開採,開採費用 104百萬。一年後才可賣油,油價每桶目前 20元,一年後有 1/2的機會漲為 36元,另 1/2的機會跌至 12元。 risk-free rate 8%。
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2. 投資 – 不確定的未來▪例 2:
– 油井預期未來現金流量是多少?
– 折現率該用多少?
– 是否應該購買開採權?
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2. 投資 – 不確定的未來▪例 2:
36
20
12
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2. 投資 – 不確定的未來▪例 2:
180
X
60
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3. 延後投資▪例 3 :
•延續例 2。如果油井可以一年後開採,開採後可以立即賣油。是否購買油井開採權?(開採費用每年成長 8%)
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2. 投資 – 不確定的未來▪例 2:
X
開採
不開採
180-104*1.08=67.68
0
60-104*1.08=-52.32
0
不開採
開採
67.68
0
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NPV concept
Invest
Do not invest
Good news
Good news
Bad news
Bad news
Cash flow
Cash flow
Cash flow
Cash flow
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Real option concept
Good news
Bad news
Invest
Invest
Do not invest
Do not invest
Cash flow
Cash flow
Cash flow
Cash flow
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2. 投資 – 不確定的未來▪房地產開發▪開採天然資源▪有限公司股權▪策略性投資
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Substitute NPVq for NPV
Source: Timothy A. Luehrman (1998)
Source: Timothy A. Luehrman (1998)
) (
PriceExercisePV
ValueAssetUnderlyingNPVq
I. Exercise Now
II. Maybe now
NPV>0 and NPVq>1 Wait if possible
Otherwise, exercise early
VI. Exercise Never
V. Probably NeverNPV<0, NPVq<1, and cumulative variance is low. Doubtful prospects
IV. Maybe later
NPV<0 and NPVq<1. Less promising, but high cumulative variance. These projects require active development
III. Probably laterNPV<0, but very promising because NPVq>1 and cumulative variance is high
Low
Cumulative Variance
High
Out of the money 1.0 In the money
t2
Example 1:Capital Investment
Decision of Franklin Chemical
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Capital Investment Decision:
Franklin Chemical▪ Phase expansion project
– Build a new commercial-scale plant immediately to exploit innovations in process technology
– The construction will be finished within 1 year
– Expand the plant’s capacity and enter into two new markets after 3 years
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Discounted-Cash-Flow Valuation
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Option Pricing on the Project
1. Recognize the option and describe it1. Recognize the option and describe it
2. Map the project’s characteristics onto call option variables2. Map the project’s characteristics onto call option variables
3. Rearrange the DCF projections3. Rearrange the DCF projections
4. Establish a benchmark for phase ’s option valueⅡ4. Establish a benchmark for phase ’s option valueⅡ
5. Attach values to the option-pricing variables5. Attach values to the option-pricing variables
6. Combine the five option-pricing variables into metrics6. Combine the five option-pricing variables into metrics
7. Look up call value as a percentage of asset value7. Look up call value as a percentage of asset value
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Option Pricing - Step 1
1. Recognize the option and describe it1. Recognize the option and describe it
2. Map the project’s characteristics onto call option variables2. Map the project’s characteristics onto call option variables
3. Rearrange the DCF projections3. Rearrange the DCF projections
4. Establish a benchmark for phase ’s option valueⅡ4. Establish a benchmark for phase ’s option valueⅡ
5. Attach values to the option-pricing variables5. Attach values to the option-pricing variables
6. Combine the five option-pricing variables into metrics6. Combine the five option-pricing variables into metrics
7. Look up call value as a percentage of asset value7. Look up call value as a percentage of asset value
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Recognize the Option and Describe It
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Recognize the Option and Describe It
▪ The option here is a call option▪ The value of the project
NPV (entire proposal) = NPV (phase I assets) +call value (phase Ⅱ assets)
t=0
t=1
t=2
t=3
t=4
t=5
t=6
Phase I Phase Ⅱ
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Option Pricing - Step 2
1. Recognize the option and describe it1. Recognize the option and describe it
2. Map the project’s characteristics onto call option variables2. Map the project’s characteristics onto call option variables
3. Rearrange the DCF projections3. Rearrange the DCF projections
4. Establish a benchmark for phase ’s option valueⅡ4. Establish a benchmark for phase ’s option valueⅡ
5. Attach values to the option-pricing variables5. Attach values to the option-pricing variables
6. Combine the five option-pricing variables into metrics6. Combine the five option-pricing variables into metrics
7. Look up call value as a percentage of asset value7. Look up call value as a percentage of asset value
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Map the Project’s Characteristics
onto Call Option VariablesPresent value of the assets acquired when and if the company exercises the option
Present value of the assets acquired when and if the company exercises the option
The expenditures required to acquire the phase Ⅱ assets
The expenditures required to acquire the phase Ⅱ assets
The value of the underlying assets S
The value of the underlying assets S
The exercise price XThe exercise price X
Time to expiration tTime to expiration t
Risk-free rate rfRisk-free rate rf
The standard deviation of returns on these
operating assets σ
The standard deviation of returns on these
operating assets σ
3 years3 years
5.5%5.5%
40%40%
Calculate through step 3 and step 4
Calculate through step 3 and step 4
Calculate through step 3 and step 4
Calculate through step 3 and step 4
According to the projections given in the DCF analysis
According to the projections given in the DCF analysis
The market rate of interest on a three-year U.S. govern-ment bond
The market rate of interest on a three-year U.S. govern-ment bond
1. Take an educated guess
2. Gather some data3. Simulate σ
1. Take an educated guess
2. Gather some data3. Simulate σ
Variables
Values
Methods
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Option Pricing - Step 3
1. Recognize the option and describe it1. Recognize the option and describe it
2. Map the project’s characteristics onto call option variables2. Map the project’s characteristics onto call option variables
3. Rearrange the DCF projections3. Rearrange the DCF projections
4. Establish a benchmark for phase ’s option valueⅡ4. Establish a benchmark for phase ’s option valueⅡ
5. Attach values to the option-pricing variables5. Attach values to the option-pricing variables
6. Combine the five option-pricing variables into metrics6. Combine the five option-pricing variables into metrics
7. Look up call value as a percentage of asset value7. Look up call value as a percentage of asset value
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Rearrange the DCF Projections
▪ Reasons for rearranging the DCF projections
Separate the cash flow of phase I from phase ⅡSeparate the cash flow of phase I from phase Ⅱ
Calculate the net present value for phase ICalculate the net present value for phase I
Isolate and obtain S and X for phase ⅡIsolate and obtain S and X for phase Ⅱ
Calculate NPVqCalculate NPVq
Step 3Step 3
Step 4Step 4
Step 5 and 6Step 5 and 6
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Rearrange the DCF Projections
The value of the whole project
must be at least $16.3
million
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Option Pricing - Step 4
1. Recognize the option and describe it1. Recognize the option and describe it
2. Map the project’s characteristics onto call option variables2. Map the project’s characteristics onto call option variables
3. Rearrange the DCF projections3. Rearrange the DCF projections
4. Establish a benchmark for phase Ⅱ’s option value4. Establish a benchmark for phase Ⅱ’s option value
5. Attach values to the option-pricing variables5. Attach values to the option-pricing variables
6. Combine the five option-pricing variables into metrics6. Combine the five option-pricing variables into metrics
7. Look up call value as a percentage of asset value7. Look up call value as a percentage of asset value
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Establish a Benchmark forPhase Ⅱ’s Option Value
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Establish a Benchmark forPhase Ⅱ’s Option Value
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Option Pricing - Step 5
1. Recognize the option and describe it1. Recognize the option and describe it
2. Map the project’s characteristics onto call option variables2. Map the project’s characteristics onto call option variables
3. Rearrange the DCF projections3. Rearrange the DCF projections
4. Establish a benchmark for phase ’s option valueⅡ4. Establish a benchmark for phase ’s option valueⅡ
5. Attach values to the option-pricing variables5. Attach values to the option-pricing variables
6. Combine the five option-pricing variables into metrics6. Combine the five option-pricing variables into metrics
7. Look up call value as a percentage of asset value7. Look up call value as a percentage of asset value
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Attach Values to the Option-pricing Variables
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Attach Values to the Option-pricing Variables
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Option Pricing - Step 6
1. Recognize the option and describe it1. Recognize the option and describe it
2. Map the project’s characteristics onto call option variables2. Map the project’s characteristics onto call option variables
3. Rearrange the DCF projections3. Rearrange the DCF projections
4. Establish a benchmark for phase ’s option valueⅡ4. Establish a benchmark for phase ’s option valueⅡ
5. Attach values to the option-pricing variables5. Attach values to the option-pricing variables
6. Combine the five option-pricing variables into metrics6. Combine the five option-pricing variables into metrics
7. Look up call value as a percentage of asset value7. Look up call value as a percentage of asset value
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Combine the Five Option-pricing Variables into
Metrics
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Option Pricing - Step 7
1. Recognize the option and describe it1. Recognize the option and describe it
2. Map the project’s characteristics onto call option variables2. Map the project’s characteristics onto call option variables
3. Rearrange the DCF projections3. Rearrange the DCF projections
4. Establish a benchmark for phase ’s option valueⅡ4. Establish a benchmark for phase ’s option valueⅡ
5. Attach values to the option-pricing variables5. Attach values to the option-pricing variables
6. Combine the five option-pricing variables into metrics6. Combine the five option-pricing variables into metrics
7. Look up call value as a percentage of asset value7. Look up call value as a percentage of asset value
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Look up Call Value as a % of Asset Value
By interpolation≒19
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Value of the Project
▪ Call Value (phase Ⅱ assets)=19% $255.7M=$48.6M
▪ NPV (entire proposal) =NPV (phase I assets) Call Value =$16.3M $48.6M=$64.9M VS Original $0.1M