FREDERICK OWUSU PREMPEH

EXCEL PROFESSIONAL INSTITUTE 3.3 ADVANCED FINANCIAL MANAGEMENT LECTURES SLIDES FREDERICK OWUSU PREMPEH

EXCEL PROFESSIONAL INSTITUTE Lecture 5 Advanced Investment Appraisal & Application of option pricing theory in investment decisions

The internal rate of return (IRR) of any investment is the discount rate at which the NPV is equal to zero. Alternatively, the IRR can be thought of as the return that is delivered by a project. The IRR is used to calculate the exact discount rate at which NPV is equal to zero. In calculating IRR manually we use the interpolation method as follows. (a) Calculate an NPV using a discount rate that gives a whole number and gives an NPV close to zero. (b) Calculate a second NPV using another discount rate. If the first NPV was positive, use a rate that is higher than the first rate; if it was negative, use a rate that is lower than the first rate. (c) Use the two NPVs to calculate the IRR. The formula to apply is:

Where; a = the lower of the two rates of return used b = the higher of the two rates of return used NPVa = the NPV obtained using rate a NPVb = the NPV obtained using rate b The project should be accepted if the IRR is greater than the cost of capital or target rate of return.

A project being accepted based on IRR may be misleading if the cash flows from the project are not normal. The MIRR is quicker to calculate than the IRR and effectively assumes that the cash flows are reinvested at the Cost of Capital. Where; PVR = the PV of the return phase (the phase of the project with cash inflows) PVI = the PV of the investment phase (the phase of the project with cash outflows) re = the cost of capital

Example: Consider a project requiring an initial investment of $24,500, with cash inflows of $15,000 in years 1 and 2 and cash inflows of $3,000 in years 3 and 4. The cost of capital is 10%. Read on advantages & disadvantages of IRR and MIRR

EXCEL PROFESSIONAL INSTITUTE Application of option pricing theory in investment decisions

An option is a contract that gives the buyer the right, but not an obligation, to buy or sell an underlying asset at a specific price on or before a certain date Exercise price The exercise or strike price is the price at which the future transaction will take place. Premium Premium is the price paid by the option buyer to the seller, or writer, for the right to buy or sell the underlying shares. Call and put options The buyer of a call option acquires the right, but not the obligation, to buy the underlying at a fixed price. The buyer of a put option acquires the right, but not the obligation, to sell the underlying shares at a fixed price.

A European option can only be exercised at expiration, An American option can be exercised any time prior to expiration. A Bermudan option is an option where early exercise is restricted to certain dates during the life of the option. It derives its name from the fact that its exercise characteristics are somewhere between those of the American and the European style of options.

When an investor buys an option the investor is setting up a long position, and when the investor sells an option the investor has a short position..

Long call : A call option that has been purchased (ie a long call) will be exercised at expiration only if the price of the underlying is higher than the exercise price. The value of a call option at expiration is the higher of: The difference between the value of the underlying security at expiration and the exercise price, if the value of the underlying security > exercise price Or: Zero, if value of the underlying security is equal to or less than the exercise price. profit = value of call option premium paid for the purchase of the option

Suppose that you buy the October call option with an exercise price of 550. The premium is 21c. Calculate the potential profit/loss at expiration for value of underlying assets ranging between 500 to 600

Short call : The seller of a call loses money when the option is exercised and gains the premium if the option is not exercised. The value of the call option for a seller is exactly the opposite of the value of the call option for the buyer. The profit of the short position at expiration is: Profit = premium received value of call option A short call option has a maximum profit, which is the premium, but unlimited losses.

Suppose that you sell the October call option with an exercise price of 550. The premium is 21c. Calculate the potential profit/loss at expiration for the writer of the option for value of underlying assets ranging between 500 to 600

Long put : A put that has been purchased (ie a long put) will be exercised at expiration only if the price of the underlying asset is lower than the exercise price of the option. The value of the option when exercised is the difference between the exercise price and the value of the underlying. The profit from a long position is the difference between the value of the option at expiration and the premium paid.

Suppose that you buy the October put option with an exercise price of 550. The premium is 46c. Calculate the potential profit/loss at expiration for value of underlying assets ranging between 500 to 600

The highest loss occurs when the value of the underlying = 0. The maximum loss will be equal to the exercise price. Short put : The seller of a put loses money when the option is exercised and gains the premium if the option is not exercised. The value of the put option for a seller is exactly the opposite of the value of the put option for the buyer. The profit of the short position at expiration is: Profit = premium received value of put option The maximum profit for the writer of a put option is the premium paid 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. 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.

Suppose that you sell the October put option with an exercise price of 550. The premium is 46c. Calculate the potential profit/loss at expiration for value of underlying assets ranging between 500 to 600

Read on determinants of option values

The Black-Scholes model predicts the value of an option for given values of its determinants. The Black-Scholes formula for the value of a European call option is given by:

Since American call options can be valued using the Black-Scholes model, one could in principle use the Black-Scholes model to estimate the value of the real options There are certain differences between the application of the Black-Scholes model to financial options and real options. The main practical problem is the estimation of volatility. Note: Pa is the value of the project or PV of cash flows of project (both inflows & outflows) Pe is the additional investment involved in expansion or Salvage value of abandonment The option to abandon is a put option and its value is given by:

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 PV of expected cash flows is $254 million. While the NPV of $4 million is small, assume that Four Seasons International has the option to abandon this project any time 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 PV 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.

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