Question

SPD Tax Service is a regional tax preparation firm that competes with such national chains as H&R Block. The company is considering expanding and needs a financial model to analyze the decision to open a new store. Key factors affecting this decision include the demographics of the proposed location, price points that can be achieved in the target market, and the availability of funds for marketing and advertising. Capital expenditures will be ignored because unused equipment from other locations can often be shifted to a new store for the first year until they can be replaced periodically through the fixed cost budget. SPD’s target markets being considered are communities with populations between 30,000 and 50,000, assumed to be uniformly distributed. Market demand for tax preparation service is directly related to the number of households in the territory; approximately 15% of households are anticipated to use a tax preparation service. Assuming an average of 2.5 people per household, this can be expressed as 0.15*population/2.5. SPD estimates that its first year demand will have a mean of 5% of the total market demand, and for every dollar of advertising, the mean increases by 2%. The first year demand is assumed to be normal with a standard deviation of 20% of the mean demand. An advertising budget of $5,000 has been approved but is limited to 10% of annual revenues. Demand grows fairly aggressively in the second and third year and is assumed to have a triangular distribution with a minimum value of 20%, most likely value of 35%, and maximum value of 40%. After year 3, demand growth is between 5% and 15%, with a most likely value of 7%. The average charge for each tax return is $175, and increases at a rate that is normally distributed with a mean of 4% with a standard deviation of 1.0% each year. Variable costs average $15 per customer, and increase annually at a rate that is normally distributed with a mean of 3% with a standard deviation of 1.5%. Fixed costs are estimated to be approximately $35,000 for the first year, and grow annually at a rate between 1.5% and 3%. Develop a Monte Carlo simulation model to find the distribution of the net present value of the profitability of a new store over a 5-year period using a discount rate of 5%.

Answer 1

Monte Carlo Simulation is a mathematical or statistical technique of forecasting risk or uncertainty which is based on the probabilistic pattern of random variable.The method is modelled based on various probability distributions of random variable such as normal, log normal, triangular, geometric and so forth.It provides a probabilistic estimation or risk or future uncertainty which is based on stochastic measurement. Therefore, basically Monte Carlo simulates the prediction about future on the basis of previous or past events or certain probablistic pattern that these events will follow.

In this case,we can arrive at the results of Monte Carlo Simulation looking at certain information or data given such as data about yearly demand, some cost estimations and their impact on the demand etc. First, based on the probability distribution of demand for 3 years we can find a stochastic pattern where it changes from normal distribution in the first year to triangular distribution in the 2nd and 3rd year. The demand is likely to grow steadily from 1st to 2nd and 3rd year indicating that more percentage of people from the households will use the tax service or many households will start using it. Alternatively or simultaneously, SPD might increase their advertisement spending which would generate higher mean demand for the future.

Concerning at the charge for tax return, the average is given as $175 and increases annually with normal distribution hinting with increasing demand during the 2nd and 3rd year SPD can get wide range of customers and thus charge them different service charge. According to the law of large numbers, increae in the revenue or the service charge for tax return can obtain a normal distribution if the firm can get more and more customers in the future which is consistent with the hypothesis of increased demand during the 2nd and 3rd year. Thus, it would help us to get an estimation about future revenue of the copmany which is likely to show a rising pattern.

Aside from revenue, another important component to consider while estimating the profitability would be the cost. The variable is likely to increase following a normal distribution and averages at $15 per customer implying that if SPD is able to capitalize on future demand hike, it's variable cost will increase but only by a mean of 3% which is not by much. The assumption is again based on law of large numbers which also applies in the case of Fixed cost which is likely to increase but only by 1.5% to 3%.

Therefore, based on all the information and distribution of the random variables mentioned, it can be estimated that the profitability is more likley to follow a normal distribution if SPD is able to take advantage of the increasing yearly demand that has been predicted. However, more accurate prediction under Monte Carlo Simulation would more exact estimation of difference between revenue and cost growth rates which might lead towards any non-normal distribution. But the key is defenitely law of large numbers and higher sample size meaning increase in the number of customers in the future which collectively hint towards normal distribution regardless of the difference between the growth rates of revenue and cost.