The company should decide whether to go ahead with the Citic Tower II project or not. The following alternatives can be used to address the problem: NPV: Net present value (NPV) is defined as the total present value (PV) of a time series of cash flows. It is a standard method for using the time value of money to appraise long-term projects. The method is used for capital budgeting, and widely throughout economics, it measures the excess or shortfall of cash flows, in present value terms, once financing charges are met.

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OPTION PRICING: The buyer of a call option gets the right to buy the underlying the underlying asset at affixed price, where as the buyer of a put option obtains the right to sell the underlying asset at a fixed price. Alternatives to the binomial model In the binomial option pricing model, the underlying asset and risk free lending or borrowing are combined to create a portfolio that had the same cash flows as the option being valued; we called this portfolio the replicating portfolio.

Although the binomial model provides the intuitive feel for the determinants of the option value, it requires a large number of inputs in terms of expected future prices at each node. As we can make time periods shorter in the binomial model, we can make assumptions about asset prices. We can assume that price changes becomes smaller as time periods approaches zero leading to continuous price process.

## The Black – Scholes Model

When the price process is continuous, that is price changes become smaller as time period gets shorter, the binomial model for pricing options converges on the Black – Scholes model. The model allows us to estimate the value of any option using a small number of inputs, and it has shown to be remarkably robust in valuing many listed options. The Black-Scholes model is used to calculate a theoretical call price (ignoring dividends paid during the life of the option) using the five key determinants of an option’s price: stock price, strike price, volatility, time to expiration, and short-term (risk free) interest rate. The original formula for calculating the theoretical option price (OP) is as follows: Where: The variables are: S=stock price X=strike price = time remaining until expiration, expressed as a percent of a year r = current continuously compounded risk-free interest rate v = annual volatility of stock price (the standard deviation of the short-term returns over one year). See below for how to estimate volatility. ln = natural logarithm N(x) = standard normal cumulative distribution function e = the exponential function

## Volatility

Volatility refers to the amount of uncertainty or risk about the size of changes in a security’s value. A higher volatility means that a security’s value can potentially be spread out over a larger range of values. This means that the price of the security can change dramatically over a short time period in either direction. A lower volatility means that a security’s value does not fluctuate dramatically, but changes in value at a steady pace over a period of time. CASE BACKGROUND Citic Pacific Limited was a real estate company incorporated in Hong Kong. The CPL’s activities include civil facilities such as complex bridge, road and tunnel facilities to power generation, environmental projects, aviation and telecommunications.

The development of Citic tower represented an impressive achievement in development management. In 1999, despite the property market being affected by the post-Asian financial crisis, weak demand and falling prices, Citic tower still maintained a relatively high occupancy rate. Given the cyclical nature of the market, CPL’s property revenues were significantly less predictable than the revenues from the company’s infrastructure assets. Property investment projects were generally based on 12 percent required return on investment based on CLP’s weighted average cost of capital.

The present issue that Larry Yung, Chairman of Citic Pacific Limited is facing is regarding the impressive Victoria harbour and an undeveloped prime waterfront site, which he planned to call as Citic Tower II. Larry thought CPL could acquire the site and develop it into another grade A office building in central. The asking price of the land was HK $1 Billion, and the estimated scale of the building and development costs were comparable to those of Citic tower. On going through the feasibility report, Larry found to his disappointment that investing in Citic tower II did not seem to bring about clear positive returns.

Under the rigid assumptions set by property development team and the Net Present Value, the present reflected a present value of around HK $1. 54 billion and a cost of around HK $1. 6 Billion. Larry intuitively felt that the decision was too deterministic, as it did not allow for any flexibility, managerial discretion or strategic actions. The option to purchase the land would allow CPL to defer the decision to develop for one year. It also involves some risks. If the project was truly a winner, waiting would mean a loss or deferral of its early cash flows.

However, since the project did not appear to be clearly attractive at this point, waiting could prevent a big mistake. CPL was hoping that the seller would grant CPL an option to defer purchase on the land, exercisable at the end of one year, thereby allowing CPL to defer the whole project for one year. With the talks, the seller had shown an interest in granting an exclusive option for 12 months. However, as the price of the option, it had requested an equity stake of 5% in the completed project.

## Problems Identified

- The Larry should decide between whether to allow the board to reject or go ahead with the project based on the analysis that was given. Under the rigid assumptions set by the property development team and the net present Value Rule, the project reflected a present value of around HK $1. 54 billion and a cost of around HK$1. 6 billion. Due to the extremely rigid assumptions the decision was too deterministic, as it did not allow for any flexibility, managerial discretions or strategic actions. So there is a need to go for more exhaustive analysis taking all the factors into consideration and taking into account different types of analysis like discounted flow analysis.
- The decision to delay the development of Citic Tower II will be better than the analysis suggested. When the market is very volatile, the mark of a successful project was when the developer knew when to pull in the reins and when to let them out. With taking this into consideration it is quite possible that the outlook for the project could change if it could be deferred or otherwise rescaled.

With a negative cash value, launching the project at that point of time was unambiguously sub-optimal. However there is a possibility that things could change over time. The property market could be on the upturn again. But while implementing this strategy, some additional costs have to taken care of. In this case the seller did show an interest in granting an exclusive option for 12 months. However, as the price option, it had requested an equity stake of 5 % in the completed project. ANALYSIS: The analysis is done with the help of Black-Scholes model which is generally used for calculating the value of options.

The various inputs required for the model are the value of the underlying asset, the variance in that value, the time to expiration on the option, the strike price, the riskless rate, and the equivalent of the dividend yield. Let us first determine each input required for applying the Black-Scholes model for the current model. S. No 1 Input Value of the current asset Description It is determined by the management team that the project reflected a present value of HK $1. 54 billion. Hence we can take this as the current estimated value of the project.

Also, it is given that the seller requested 5% equity stake in the completed project. Hence 5% of the $1. 54 billion has to be deduced from the value to get the actual value of the project. Value value of the project = 95% of HK $1. 54 billion = HK $1. 463 billion 3 Time to expiration of the option Strike price is the total investment that is required to be made in the project. The investments that are to be made in the different years, in case we have made a decision to invest in the project are given in exhibit 1.

The investment spans across a period of three years. Hence, when determining the strike price of the project, the appropriate value can be obtained by calculating the present value of all the investments to be made for the project. t = 1 year 4 Strike price Strike price is the total investment that is required to be made in the project. The investments that are to be made in the different years, in case we have made a decision to invest in the project are given in exhibit 1. The investment spans across a period of three years.

Hence, when determining the strike price of the project, the appropriate value can be obtained by calculating the present value of all the investments to be made for the project. X = Present value of $1. 79 billion = $1. 6 billion 5 Riskless rate Generally the risk free rate to be considered should correspond to the riskless rate which has a period corresponding to the duration of the option itself, which is one year. Hence, we have to take the riskless rate corresponding to the month of July 2000 and for the 12 month bills = 6. 27% Calculating d1: The value of d1 can be calculated using the formula specified in the beginning in the background knowledge required. This requires inputs which we have already calculated. Hence, calculating d1, we get d1 = 0. 10295 Calculating d2: d2 = -0. 24967 N(d2 ) = 0. 401 N(d1 ) = 0. 541 Calculating the net present value of the project: After calculating all the required values, we just need to substitute all values in the Black-Scholes model to get the final value of the project.

Substituting the values, we get Value of the project using Black Scholes model = HK $188 million Hence, considering the volatilities in the values of the industry, the net value from the project is coming to be positive and significant. This value means that the management has taken a good decision by taking the option of considering the investments in the project.

## Most Probable Solution

The Citic pacific Limited (CPL) deals with the real estate market which is highly volatile. Discounting Cash Flow method (DCF) which is the most common method used in evaluating the projects fails when there is uncertainty(volatility) involved in the future cash flows or if there is huge fluctuation in the discount rates used. Hence Black-Scholes model is can be used to evaluate the investment decisions when volatility is involved. The current investment decision to invest in the Citic Tower II project is evaluated using the BlackScholes model and we got a positive value of HK $188 million. The recommendation for the Citic Pacific Limited would be to go ahead with the project.