investment opportunities as real options

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