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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 ：

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## 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？**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： • 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%。**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？**2. 投資 – 不確定的未來**• 例2：**2. 投資 – 不確定的未來**• 例2：**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%)**2. 投資 – 不確定的未來**• 例2：**NPV concept**Cash flow Good news Invest Cash flow Bad news Cash flow Good news Do not invest Bad news Cash flow**Real option concept**Cash flow Invest Good news Do not invest Cash flow Cash flow Invest Bad news Do not invest Cash flow**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**Substitute NPVq for NPV**Source: Timothy A. Luehrman (1998)**VI. Exercise Never**I. Exercise Now V. Probably Never NPV<0, NPVq<1, and cumulative variance is low. Doubtful prospects II. Maybe now NPV>0 and NPVq>1 Wait if possibleOtherwise, exercise early 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 Out of the money 1.0 In the money Low Cumulative Variance High**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**Option Pricing on the Project**1. Recognize the option and describe it 2. Map the project’s characteristics onto call option variables 3. Rearrange the DCF projections 4. Establish a benchmark for phase Ⅱ’s option value 5. Attach values to the option-pricing variables 6. Combine the five option-pricing variables into metrics 7. Look up call value as a percentage of asset value**Option Pricing －Step 1**1. Recognize the option and describe it 2. Map the project’s characteristics onto call option variables 3. Rearrange the DCF projections 4. Establish a benchmark for phase Ⅱ’s option value 5. Attach values to the option-pricing variables 6. Combine the five option-pricing variables into metrics 7. Look up call value as a percentage of asset value**t=0**t=1 t=2 t=3 t=4 t=5 t=6 Recognize the Option and Describe It Phase I Phase Ⅱ • The option here is a call option • The value of the project NPV (entire proposal) ＝NPV (phase I assets) ＋call value (phase Ⅱ assets)**Option Pricing －Step 2**1. Recognize the option and describe it 2. Map the project’s characteristics onto call option variables 3. Rearrange the DCF projections 4. Establish a benchmark for phase Ⅱ’s option value 5. Attach values to the option-pricing variables 6. Combine the five option-pricing variables into metrics 7. Look up call value as a percentage of asset value**Map the Project’s Characteristicsonto Call Option**Variables Variables Values Methods The value of the underlying assets S Present value of the assets acquired when and if the company exercises the option Calculate through step 3 and step 4 The exercise price X The expenditures required to acquire the phase Ⅱ assets Calculate through step 3 and step 4 Time to expiration t 3 years According to the projections given in the DCF analysis Risk-free rate rf 5.5% The market rate of interest on a three-year U.S. govern-ment bond The standard deviation of returns on these operating assets σ 40% • Take an educated guess • Gather some data • Simulate σ**Option Pricing －Step 3**1. Recognize the option and describe it 2. Map the project’s characteristics onto call option variables 3. Rearrange the DCF projections 4. Establish a benchmark for phase Ⅱ’s option value 5. Attach values to the option-pricing variables 6. Combine the five option-pricing variables into metrics 7. Look up call value as a percentage of asset value**Separate the cash flow of phase I from phase Ⅱ**Step 3 Calculate the net present value for phase I Isolate and obtain S and X for phase Ⅱ Step 4 Calculate NPVq Step 5 and 6 Rearrange the DCF Projections • Reasons for rearranging the DCF projections**The value of the whole project must be at least $16.3**million Rearrange the DCF Projections**Option Pricing －Step 4**1. Recognize the option and describe it 2. Map the project’s characteristics onto call option variables 3. Rearrange the DCF projections 4. Establish a benchmark for phase Ⅱ’s option value 5. Attach values to the option-pricing variables 6. Combine the five option-pricing variables into metrics 7. Look up call value as a percentage of asset value**Option Pricing －Step 5**1. Recognize the option and describe it 2. Map the project’s characteristics onto call option variables 3. Rearrange the DCF projections 4. Establish a benchmark for phase Ⅱ’s option value 5. Attach values to the option-pricing variables 6. Combine the five option-pricing variables into metrics 7. Look up call value as a percentage of asset value**Option Pricing －Step 6**1. Recognize the option and describe it 2. Map the project’s characteristics onto call option variables 3. Rearrange the DCF projections 4. Establish a benchmark for phase Ⅱ’s option value 5. Attach values to the option-pricing variables 6. Combine the five option-pricing variables into metrics 7. Look up call value as a percentage of asset value**Option Pricing －Step 7**1. Recognize the option and describe it 2. Map the project’s characteristics onto call option variables 3. Rearrange the DCF projections 4. Establish a benchmark for phase Ⅱ’s option value 5. Attach values to the option-pricing variables 6. Combine the five option-pricing variables into metrics 7. Look up call value as a percentage of asset value**Look up Call Value as a % of Asset Value**By interpolation≒19**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

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