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Investment Opportunities as Real Options

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. Investment Opportunities as Real Options

  2. 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？

  3. 1. 投資時機 – 確定的未來 • 例1：

  4. 1. 投資時機 – 確定的未來 • 例1：

  5. 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%。

  6. 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？

  7. 2. 投資 – 不確定的未來 • 例2：

  8. 2. 投資 – 不確定的未來 • 例2：

  9. 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%)

  10. 2. 投資 – 不確定的未來 • 例2：

  11. NPV concept Cash flow Good news Invest Cash flow Bad news Cash flow Good news Do not invest Bad news Cash flow

  12. Real option concept Cash flow Invest Good news Do not invest Cash flow Cash flow Invest Bad news Do not invest Cash flow

  13. 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

  14. Substitute NPVq for NPV Source: Timothy A. Luehrman (1998)

  15. Source: Timothy A. Luehrman (1998)

  16. 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

  17. Example 1:Capital Investment Decision of Franklin Chemical

  18. 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

  19. Discounted-Cash-Flow Valuation

  20. 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

  21. 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

  22. Recognize the Option and Describe It

  23. 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)

  24. 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

  25. 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

  26. 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

  27. 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

  28. The value of the whole project must be at least $16.3 million Rearrange the DCF Projections

  29. 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

  30. Establish a Benchmark forPhase Ⅱ’s Option Value

  31. Establish a Benchmark forPhase Ⅱ’s Option Value

  32. 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

  33. Attach Values to the Option-pricing Variables

  34. Attach Values to the Option-pricing Variables

  35. 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

  36. Combine the Five Option-pricing Variables into Metrics

  37. 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

  38. Look up Call Value as a % of Asset Value By interpolation≒19

  39. 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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