Yola
ACCA P4
Advanced Financial Management
Education Class 1
Session 1 & 2
Chapter 2
Patrick Lui
hklui2007@.hk
| |
Chapter 2 Option Pricing Theory in Investment Decisions
|LEARNING OBJECTIVES |
| |
|1. Apply the Black-Scholes Option Pricing model to financial product valuation and to asset valuation. |
|(a) Determine, using published data, the five principal drivers of option value (value of the underlying, exercise price, time to |
|expiry, volatility and the risk free rate). |
|(b) Discuss the underlying assumptions, structure, application and limitations of the Black-Scholes model. |
|2. Evaluate embedded real options within a project, classifying them into one of the real option archetypes. |
|3. Assess, calculate and advise on the value of options to delay, expand, redeploy and withdraw using the Black-Scholes model. |
[pic]
1. Basic Concepts
1.1 Option terminology
1.1.1 Option terminology
|Terminology |Explanation |
|An option |The right but not an obligation, to buy or sell a particular good at an |
| |exercise price, at or before a specified date. |
|Call option |The right but not an obligation to buy a particular good at an exercise price. |
|Put option |The right but not an obligation to sell a particular good at an exercise price.|
|Exercise/strike price |The fixed price at which the good may be bought or sold. |
|American option |An option that can be exercised on any day up until its expiry date. |
|European option |An option that can only be exercised on the last day of the option. |
|Premium |The cost of an option. |
|Trade option |Standardised option contracts sold on a futures exchange (normally American |
| |options). |
|Over the counter (OTC) option |Tailor-made option – usually sold by a bank (normally European options). |
|Long and short position |When an investor buys an option the investor is long, and when the investor |
| |sells an option the investor has a short position. |
1.1.2 Price quotations
It should be noted that, for simplicity, only price is quoted for each option in the national newspapers. In practice, there will always be two prices quoted for each option, i.e. a bid and an offer price. For example, the January option could be quoted as 500/550. This can be interpreted to mean that it would cost an investor 550 to buy those options and the he would receive 500 for selling it.
[pic]
1.2 Profiles of call options at expiration
A. Long call
1.2.1 A call option will be exercised at expiration only if the price of the underlying is higher than the exercise price. Otherwise, the option will not be exercised.
1.2.2 Since the buyer of a call option has paid a premium to buy the option, the profit from the purchase of the call option is the value of the option minus the premium paid.
|Example 1 |
|Suppose that you buy the October call option with an exercise price of 550. The premium is 21 cents. Calculate the potential profit/loss|
|at expiration. |
| |
|Solution: |
| |
|The profit/loss will be calculated for possible values of the underlying at expiration. Here we examine the profit/loss profile for |
|prices ranging from 500 to 600. |
| |
|Value of underlying at expiration |
|Value of underlying – exercise price |
|Value of option |
|Profit/loss |
| |
|500 |
|-50 |
|0 |
|-21 |
| |
|530 |
|-20 |
|0 |
|-21 |
| |
|540 |
|-10 |
|0 |
|-21 |
| |
|550 |
|0 |
|0 |
|-21 |
| |
|560 |
|10 |
|0 |
|-11 |
| |
|570 |
|20 |
|20 |
|-1 |
| |
|600 |
|50 |
|50 |
|29 |
| |
| |
| |
|[pic] |
B. Short call
1.2.3 The seller of a call loses money when the option is exercised and gains the premium if the option is not exercised.
1.2.4 The profit of the short position at expiration = premium received – value of call option
1.2.5 A short call option has a maximum profit, which is the premium, but unlimited losses.
|Example 2 |
|Suppose that you sell the October call option with an exercise price of 550. The premium is 21 cents. Calculate the potential |
|profit/loss at expiration for the writer of the option. |
| |
|Solution: |
| |
|The profit/loss will be calculated for possible values of the underlying at expiration. Here we examine the profit/loss profile for |
|prices ranging from 500 to 600. |
| |
|Column A |
| |
|Value of underlying at expiration |
|Column B |
| |
|Value of underlying – exercise price |
|Column C – |
|Maximum of zero and the difference between the value of the underlying and the exercise price |
|Negative Column C + Profit/loss |
| |
|500 |
|-50 |
|0 |
|21 |
| |
|530 |
|-20 |
|0 |
|21 |
| |
|540 |
|-10 |
|0 |
|21 |
| |
|550 |
|0 |
|0 |
|21 |
| |
|560 |
|10 |
|0 |
|11 |
| |
|570 |
|20 |
|20 |
|-1 |
| |
|600 |
|50 |
|50 |
|-29 |
| |
| |
|[pic] |
1.3 Profiles of put options at expiration
A. Long put
1.3.1 A put will be exercised at expiration only if the underlying asset is lower than the exercise price of the option.
1.3.2 The value of the option when exercised is the difference between the exercise price and the value of the underlying.
1.3.3 Profit = Value of option at expiration – premium paid
1.3.4 As in the case of the long call option, the buyer of the option has limited losses, that is the premium if the option is not exercise, but unlike the long call which has unlimited upside, the maximum value of the put option is X, which is attained when the price of the underlying is zero.
|Example 3 |
|Suppose that you buy the October put option with an exercise price of 550. The premium is 46 cents. Calculate the potential |
|profit/loss at expiration. |
| |
|Solution: |
| |
|Column A |
|Value of underlying at expiration |
|Column B |
|Exercise price – Value of underlying |
|Column C – |
|Maximum of Column B and zero |
| |
| |
|Column C – premium |
| |
|0 |
|550 |
|550 |
|504 |
| |
|500 |
|50 |
|50 |
|4 |
| |
|530 |
|20 |
|20 |
|-26 |
| |
|540 |
|-10 |
|10 |
|-36 |
| |
|550 |
|0 |
|0 |
|-46 |
| |
|560 |
|-10 |
|0 |
|-46 |
| |
|570 |
|-20 |
|0 |
|-46 |
| |
|600 |
|-50 |
|0 |
|-46 |
| |
| |
|[pic] |
B. Short put
1.3.5 Value of put option at expiration is the maximum of the difference between the exercise price and the value of the underlying at expiration and zero.
1.3.6 Profit = Premium received – value of put option.
1.3.7 The maximum profit for the writer of a put option is the premium received which occurs when the put option is not exercised (that is, when the value at expiration = 0). This happens when the value of the underlying at expiration is greater than the exercise price.
1.3.8 The profit will be zero when the value of the underlying at expiration is equal to the sum of the exercise price and the premium paid.
1.3.9 The highest loss occurs when the value of the underlying = 0. The maximum loss will be equal to the exercise price.
|Example 4 |
|Suppose that you sell the October put option with an exercise price of 550. The premium is 46 cents. Calculate the potential |
|profit/loss at expiration. |
| |
|Solution: |
| |
|Column A |
|Value of underlying at expiration |
|Column B |
|Exercise price – Value of underlying |
|Column C – |
|Maximum of Column B and zero |
| |
| |
|Column C + premium |
| |
|0 |
|550 |
|-550 |
|-504 |
| |
|500 |
|50 |
|-50 |
|-4 |
| |
|530 |
|20 |
|-20 |
|26 |
| |
|540 |
|-10 |
|-10 |
|46 |
| |
|550 |
|0 |
|0 |
|46 |
| |
|560 |
|-10 |
|0 |
|46 |
| |
|570 |
|-20 |
|0 |
|46 |
| |
|600 |
|-50 |
|0 |
|46 |
| |
| |
|[pic] |
2. Determinants of Option Values
2.1 The factors affecting the price of an option
(Jun 14)
2.1.1 Options are financial instruments whose value changes all the time. In this section we shall identify the factors that affect the price of an option prior to expiration.
|Factors |Explanation |
|1. The exercise price |The higher the exercise price, the lower the probability that a call will be exercised. So call |
| |prices will decrease as the exercise price increase. |
| |For the put, the effect runs in the opposite direction. A higher exercise price means that there|
| |is higher probability that the put will be exercised. So the put price increases as the exercise|
| |price increases. |
|2. The price of the underlying |As the current stock price goes up, the higher the probability that the call will be in the |
| |money. As a result, the call price will increase. |
| |As the stock price goes up, there is a lower probability that the put will be in the money. So |
| |the put price will decrease. |
|3. The volatility of the underlying |Both the call and put will increase in price as the underlying asset becomes more volatile. |
| |The buyer of the option receives full benefit of favourable outcomes but avoids the unfavourable|
| |ones (option price value has zero value). |
|4. The time to expiration |Both calls and puts will benefit from increased time to expiration. |
| |The reason is that there is more time for a big move in the stock price. |
| |But there are some effects that work in the opposite direction. |
| |As the time to expiration increase, the PV of the exercise price decreases. This will increase |
| |the value of the call and decrease the value of the put. |
| |Also, as the time to expiration increase, there is a greater amount of time for the stock price |
| |to be reduced by a cash dividend. This reduces the call value but increases the put value. |
|5. The interest rate |The higher the interest rate, the lower the present value of the exercise price. As a result, |
| |the value of the call will increase. |
| |The opposite is true for puts. The decrease in the PV of the exercise price will adversely |
| |affect the price of the put option. |
|6. The intrinsic value |The price of an option has two components – intrinsic value and time value. |
| |Intrinsic value is the value of the option if it was exercised now. |
| |Call options: Intrinsic value = Underlying stock’s current price – call strike price |
| |Put options: Intrinsic value = Put strike price – underlying stock’s current price. |
| |If the intrinsic value is positive the option is in the money. If the intrinsic value is zero, |
| |the option is at the money and if the intrinsic value is negative the option is out of the |
| |money. |
|7. The time value |The difference between the market price of an option and its intrinsic value is the time value |
| |of the option. |
| |Buyers of at the money or out of the money options are simply buying time value, which decreases|
| |as an option approaches expiration. |
| |The more time an option has until expiration, the greater the option’s chance of ending up in |
| |the money and the larger its time value. |
| |On the expiration day the time value of an option is zero and all an option is worth is its |
| |intrinsic value. It is either in the money or it is not. |
3. The Black Scholes Pricing Model
(Dec 07, Dec 09, Jun 11, Jun 12, Dec 13)
3.1 Introduction
3.1.1 The Black Scholes model values European call option before the expiry date and takes account of all five factors that determine the value of an option.
3.2 The Black Scholes Formula
3.2.1 The formula for the value of a European call option is given by:
|Value of a call option = [pic] |
Where: Pa = the current price of the underlying asset
Pe = the exercise price
r = the continuously compounded risk-free rate
t = the time to expiration measured as a fraction of one year, for example t = 0.5 means that the time to expiration is 6 months
e = the base of the natural logarithms (= 2.71828)
|[pic] |
|[pic] |
Where: s = volatility of the share price (as measured by the standard deviation expressed as a decimal)
3.3 Value of European put options
3.3.1 The value of a European put option can be calculated by using the Put Call Parity relationship which is given to you in the exam formulae sheet.
|p = c – Pa + Pe e-n |
Where: p = the value of the put option
c = the value of the call option
3.4 Value of American call options
3.4.1 Although American options can be exercised any time during their lifetime, it is never optimal to exercise an option earlier. The value of an American option will therefore be the same as the value of an equivalent European option and the Black-Scholes model can be used to calculate its price.
3.5 Value of American put options
3.5.1 Unfortunately, no exact analytic formula for the value of an American put option on a non-dividend-paying stock has been produced. Numerical procedures and analytic approximations for calculating American put values are used instead.
|Normal distribution |
|The normal distribution table (provided in the exam) can be used to calculate N(d), the cumulative normal distribution function needed|
|for the Black-Scholes model of option pricing. |
| |
|(a) If d > 0, add 0.5 to the relevant number from normal distribution table. |
|(b) If d < 0, subtract the relevant number from 0.5. |
| |
|For example, if d is 1.05, N(d) = 0.3531 + 0.5 = 0.8531. |
| |
|Note: N(d) is the area under the normal curve up to d in the shaped area of the figure beow. |
| |
|[pic] |
|Example 5 |
|Consider the situation where the stock price 6 months from the expiration of an option is $42, the exercise price of the option is |
|$40, the risk-free interest rate is 10% p.a. and the volatility is 20% p.a. This means Pa = 42, Pe = 40, r = 0.1, s = 0.2, t = 0.5. |
| |
|Solution: |
| |
|[pic] |
|[pic] |
|and |
|[pic] |
|The values of the standard normal cumulative probability distribution can be found from the tables and are |
|N(0.77) = 0.5 + 0.2794 = 0.7794 |
|N(0.63) = 0.5 + 0.2357 = 0.7357 |
| |
|Hence if the option is a European call, its value, is given by: |
|c = (42 × 0.7794) – (38.049 × 0.7357) = 4.76 |
| |
|If the option is a European put, its value is given by: |
|p = 4.76 – 42 + 38.049 = 0.81 |
| |
|The stock price has to rise by $2.76 for the purchaser of the call to break even. Similarly, the stock price has to fall by $2.81 for |
|the purchaser of the put to break even. |
4. Real Options
4.1 Introduction
4.1.1 An option exists when the decision maker has the right, but not the obligation, to take a particular action. They add value as they provide opportunities to take advantage of an uncertain situation as the uncertainty resolves itself over time.
4.1.2 Real options are actual options – that is, actual choices that a business can make in relation to investment opportunities.
4.1.3 For example, a natural resource company may decide to suspend extraction of copper at its mine if the price of cooper falls below the extraction cost. Conversely, a company with the right to mine in a particular area may decide to begin operations if the price rises above the cost of extraction. Such options can be extremely important when valuing potential investments but are often overlooked by traditional investment appraisal techniques (e.g. NPV). They can significantly increase the value of an investment by eliminating potentially unfavourable outcomes.
4.2 Limitations of the NPV rule
4.2.1 Dealing with uncertainty:
(a) Although the cash flows are discounted at an appropriate cost of capital, NPV does not explicitly deal with uncertainty when valuing the project.
(b) A risk-adjusted discount rate reduces the PV of the cash flows rather than giving the decision maker an indication of the range of cash flows that a project may deliver.
(c) The use of single discount rate means that risk is defined in one measure. This does not allow for the many sources of uncertainty that may surround the project and its cash flows.
4.2.2 Flexibility in responding to uncertainty:
(a) NPV fails to consider the extent of management’s flexibility to respond to uncertainties surrounding the project. Such flexibility can be an extremely valuable part of the project and by failing to account for it, NPV may significantly underestimate the project’s value.
(b) NPV will only provide an accurate estimate of the project’s value if there is not flexibility or no uncertainty, i.e. flexibility will have no value as management knows exactly what is going to happen.
4.3 Option to delay
(Dec 07, Jun 11, Jun 12)
4.3.1 When a firm has exclusive rights to a project or product for a specific period, it can delay taking this project or product until a later date.
4.3.2 A traditional investment analysis just answers the question of whether the project is a ‘good’ one if taken today. Thus, the fact that a project is not selected today either because its NPV is negative, or its IRR is less than its cost of capital, does not mean that the rights to this project are not valuable.
|Example 6 |
|Consider a situation where a company considers paying an amount C to acquire a licence to mine copper. The company needs to invest an |
|extra amount (say, I) in order to start operations. The company has three years over which to develop the mine, otherwise it will lose|
|the licence. Suppose that today copper prices are low and the NPV from developing the mine is negative. The company may decide not to |
|start the operation today, but it has the option to start any time over the next three years provided that the NPV is positive. Thus |
|the company has paid a premium C to acquire an American option on the present value of the cash flows from operation, with an exercise|
|price equal to the additional investment (I). The value of the option to delay is therefore: |
| |
|NPV = PV – I if PV > I |
|NPV = 0 otherwise |
| |
|The payoff of the option to delay is shown below and it is the same as the payoff of a call option, the only difference being that the|
|underlying is the present value (that is in this case S = PV) and the exercise price is the additional investment (X = I). |
| |
|[pic] |
4.4 Option to expand
4.4.1 The option to expand exists when firms invest in projects which allow them to make further investments in the future or to enter new markets. The initial project may be found in terms of its NPV as not worth undertaking.
4.4.2 However, when the option to expand is taken into account, the NPV may become positive and the project worthwhile. The initial investment may be seen as the premium required to acquire the option to expand.
4.4.3 Expansion will normally require an additional investment, call it I. The extra investment will be undertaken only if the present value from the expansion will be higher than the additional investment, i.e. when PV > I . If PV ≤ I , the expansion will not take place. Thus the option to expand is again a call option of the present value of the firm with an exercise equal to the value of the additional investment.
[pic]
4.5 Option to abandon/withdraw
(Dec 13)
4.5.1 Whereas traditional capital budgeting analysis assumes that a project will operate in each year of its lifetime, the firm may have the option to cease a project during its life. This option is known as an abandonment option.
4.5.2 Abandonment options, which are the right to sell the cash flows over the remainder of the project's life for some salvage value, are like American put options.
4.5.3 When the present value of the remaining cash flows (PV) falls below the liquidation value (L), the asset may be sold. Abandonment is effectively the exercising of a put option.
4.5.4 These options are particularly important for large capital intensive projects such as nuclear plants, airlines, and railroads. They are also important for projects involving new products where their acceptance in the market is uncertain and companies would like to switch to more alternative uses.
[pic]
4.6 Option to redeploy/switch
4.6.1 The option to redeploy exists when the company can use its productive assets for activities other than the original one. The switch from one activity to another will happen if the PV of cash flows from the new activity will exceed the costs of switching. The option to abandon is a special case of an option to redeploy.
4.6.2 These options are particularly important in agricultural settings. For example, a beef producer will value the option to switch between various feed sources, preferring to use the cheapest acceptable alternative.
4.6.3 These options are also valuable in the utility industry. An electric utility, for example, may have the option to switch between various fuel sources to produce electricity. In particular, consider an electric utility that has the choice of building a coal-fired plant or a plant that burns either coal or gas.
5. Valuation of Real Options
5.1 Black-Scholes option analysis
5.1.1 The Black-Scholes equation is well suited for simple real options, those with a single source of uncertainty and a single decision date. To use the model we need to identify the five key input variables as follows:
|Original variables |Project variables |
|Exercise price (Pe) |For most real options (e.g. option to expand, option to delay), the capital |
| |investment required can be substituted for the exercise price. These options |
| |are examples of call options. |
| |For an option to abandon, use the salvage value on abandonment. This is an |
| |example of a put option. |
|Value of the underlying asset (e.g. share |It is usually taken to be the PV of the future cash flows from the project |
|price) (Pa) |(i.e. excluding any initial investment). |
| |This could be the value of the project being undertaken for a call option (e.g.|
| |option to expand, option to delay), or the value of the cash flows being |
| |foregone for a put option (e.g. option to abandon). |
|Time to expiry (t) |E.g. Project life |
|Volatility (s) |The volatility of the underlying asset (here the future operating cash flows) |
| |can be measured using industry sector risk. |
|Risk-free rate (r) |Many writers continue to use the risk-free rate for real options. |
| |However, some argue that a higher rate should be used to reflect the extra |
| |risks when replacing the share price with the PV of future cash flows. |
|Example 7 |
|Assume that Four Seasons International is considering taking a 20-year project which requires an initial investment of $ 250 million |
|in a real estate partnership to develop time share properties with a Spanish real estate developer, and where the present value of |
|expected cash flows is $254 million. While the net present value of $ 4 million is small, assume that Four Seasons International has |
|the option to abandon this project anytime by selling its share back to the developer in the next 5 years for $ 150 million. A |
|simulation of the cash flows on this time share investment yields a variance in the present value of the cash flows from being in the |
|partnership of 0.09. The 5 year risk-free rate is 7%. |
| |
|Calculate the total NPV of the project, including the option to abandon. |
| |
|Solution: |
| |
|The value of the abandonment option can be estimated by determining the value of the put option using the Black-Scholes formula. |
| |
|Call option = [pic] |
|Put option = c – Pa + Pe e-n |
| |
|Where: |
|Pa (Value of underlying asset) = PV of cash flows from project = $254m |
|Pe (Strike price) = Salvage value from abandonment = $150m |
|Variance in underlying asset’s value = 0.09 (standard deviation (s) = 0.3) |
|Time to expiration = life of the project = 5 years |
|Risk-free rate (r) = 7% |
| |
|Value of call option |
|[pic] |
|[pic] |
| |
|[pic] |
|[pic] |
| |
|Using normal distribution tables: |
|N(d1) = 0.5 + 0.4495 = 0.9495 |
|N(d2) = 0.5 + 0.3340 = 0.8340 |
| |
|Value of call option = 254 × 0.9495 – 150 × 0.8340 e-0.07×5 = 214.17 – 88.16 = 153.01 |
| |
|The value of put option can be calculated as follows: |
|Put option = 153.01 – 254 + (150 × e-0.07×5) = $4.71m |
| |
|The value of this abandonment option is added to the project's NPV of $4m, which gives a total NPV with abandonment option of $8.71m. |
|Example 8 |
|A UK retailer is considering opening a new store in Germany with the following details: |
| |
|Estimated cost |
|€12m |
| |
|PV of net receipts |
|€10m |
| |
|NPV |
|–€2m |
| |
| |
|These figures would suggest that the investment should be rejected. However, if the first store is opened then the firm would gain the|
|option to open a second store (an option to expand). |
| |
| |
|Suppose this would have the following details: |
| |
|Timing (t) |
|5 years’ time |
| |
|Estimated cost (Pe) |
|€20m |
| |
|PV of net receipts (Pa) |
|€15m |
| |
|Volatility of cash flows (s) |
|28.3% |
| |
|Risk-free rate (r) |
|6% |
| |
| |
|By Black-Scholes formula: |
| |
|[pic] |
|[pic] |
| |
|[pic] |
|[pic] |
| |
|Using normal distribution tables: |
|N(d1) = 0.5 + 0.1293 = 0.6293 |
|N(d2) = 0.5 – 0.1179 = 0.3821 |
| |
|Call option = [pic] |
|Value of call option = 15 × 0.6293 – 20 × 0.3821 e-0.06×5 = €3.8m |
| |
|Summary: |
| |
|€m |
| |
|Conventional NPV of first store |
|(2) |
| |
|Value of call option on second store |
|3.8 |
| |
|Strategic NPV |
|1.8 |
| |
| |
|The project should thus be accepted. |
6. Assumptions of the Black-Scholes Model
(Dec 07, Jun 14)
6.1 Assumptions:
(a) Lognormality. The model assumes that the return on the underlying asset follows a normal distribution which means the return itself follows a lognormal distribution.
(b) Perfect markets. This suggests that the direction of the market cannot be consistently predicted and thus the returns on the underlying asset can go up or down at any given moment in time.
(c) Constant interest rates. The risk-free rate is used in the Black-Scholes model and this rate is assumed to be constant and known.
(d) Constant volatility. The model assumes that the volatility of the project is known and remains constant throughout its life.
(e) Tradability of asset. The model assumes that there is a market for the underlying asset and it can therefore be traded. However, real options and their underlying assets are not traded, therefore it is very difficult to establish the volatility of the value.
(f) Style of option. The Black-Scholes model assumes that the option is a European style option – that is, it can only be exercised at the maturity date. Where the option can be exercised at any point up to the maturity date (that is, an American style option), the results of the Black-Scholes model are invalid.
Examination Style Questions
Question 1 – Option to delay
Digunder, a property development company, has gained planning permission for the development of a housing complex at Newtown which will be developed over a three year period. The resulting property sales less building costs have an expected net present value of $4 million at a cost of capital of 10% per annum. Digunder has an option to acquire the land in Newtown, at an agreed price of $24 million, which must be exercised within the next two years. Immediate building of the housing complex would be risky as the project has a volatility attaching to its net present value of 25%.
One source of risk is the potential for development of Newtown as a regional commercial centre for the large number of professional firms leaving the capital, Bigcity, because of high rents and local business taxes. Within the next two years, an announcement by the government will be made about the development of transport links into Newtown from outlying districts including the area where Digunder hold the land option concerned. The risk free rate of interest is 5% per annum.
Required:
(a) Estimate the value of the option to delay the start of the project for two years using the Black and Scholes option pricing model and comment upon your findings. Assume that the government will make its announcement about the potential transport link at the end of the two-year period. (12 marks)
(b) On the basis of your valuation of the option to delay, estimate the overall value of the project, giving a concise rationale for the valuation method you have used.
(4 marks)
(c) Describe the limitations of the valuation method you used in (a) above and describe how you would value the option if the government were to make the announcement at ANY time over the next two years. (4 marks)
(20 marks)
(ACCA P4 Advanced Financial Management December 2007)
Question 2 – Option to delay
MesmerMagic Co (MMC) is considering whether to undertake the development of a new computer game based on an adventure film due to be released in 22 months. It is expected that the game will be available to buy two months after the film’s release, by which time it will be possible to judge the popularity of the film with a high degree of certainty. However, at present, there is considerable uncertainty about whether the film, and therefore the game, is likely to be successful. Although MMC would pay for the exclusive rights to develop and sell the game now, the directors are of the opinion that they should delay the decision to produce and market the game until the film has been released and the game is available for sale.
MMC has forecast the following end of year cash flows for the four-year sales period of the game.
|Year |1 |2 |3 |4 |
|Cash flows ($ million) |25 |18 |10 |5 |
MMC will spend $7 million at the start of each of the next two years to develop the game, the gaming platform, and to pay for the exclusive rights to develop and sell the game. Following this, the company will require $35 million for production, distribution and marketing costs at the start of the four-year sales period of the game.
It can be assumed that all the costs and revenues include inflation. The relevant cost of capital for this project is 11% and the risk free rate is 3.5%. MMC has estimated the likely volatility of the cash flows at a standard deviation of 30%.
Required:
(a) Estimate the financial impact of the directors’ decision to delay the production and marketing of the game. The Black-Scholes Option Pricing model may be used, where appropriate. All relevant calculations should be shown. (12 marks)
(b) Briefly discuss the implications of the answer obtained in part (a) above.
(7 marks)
(c) Discuss how a decrease in the value of each of the determinants of the option price in the Black-Scholes option-pricing model for European options is likely to change the price of a call option. (6 marks)
(Total = 25 marks)
(Amended ACCA P4 Advanced Financial Management June 2011 Q4)
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ACCA June 2016 Dec 2014
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