Pointless Luxuries Ltd (PLL) produces unusual gifts targeted at wealthy consumers. The company is analysing the possibility of introducing one of two new devices designed to attach to the collar of pets, Sonic Dog and Sonic Cat. These devices emit sonic waves that neutralise airplane engine noise, so that pets travelling with their owners can enjoy more peaceful ride. Due to different frequencies and technologies used, the two devices require different initial investment. Sonic Dog requires an immediate investment of 2.5m and Sonic Cat requires 2m. Both products will have a life of three years. If there was no inflation (i.e. todays values), then the demand in units, price per unit sold, and the relevant production costs per unit sold for the three- year life of each of the devices would be:

Item	Sonic Dog	Sonic Cat
Demand	100,000 units	100,000 units
Price	21/unit	19/unit
Materials	8/unit	2/unit
Labour	3/unit	7/unit
Overheads	1/unit	0.5/unit

The cash flows for each product are estimated as revenues minus costs. These cash flows can be assumed to arise at the year-ends of each of the three years. Specific annual inflation rates have been estimated for each of the cash flow elements:

Price	5%
Materials	4%
Labour	10%
Overheads	7%

Furthermore, the price, materials, labour, and overheads for each product were estimated using various pieces of information. The price for each product, for example, may not be precisely as estimated above because of various uncertainties. For this reason, they decided to use probability distributions to allow for a range of possible values for the above variables. The associated distribution for each variable and the parameters for each probability distribution are given in the following tables:

	Triangular Distribution					Pert Distribution
Price (/unit)	Min	Most likely	Max		Materials (/unit)	Min	Most likely	Max
Sonic Dog	19	21	23		Sonic Dog	6	8	10
Sonic Cat	15	19	23		Sonic Cat	1	2	3

	Discrete Probability Distribution
Labour (/unit)	Sonic Dog				Sonic Cat
x-values	2	3	4	5	5	7	8	9
p-values	0.3	0.5	0.1	0.1	0.3	0.5	0.1	0.1

	Normal Distribution
Overheads (/unit)	Mean	Standard Deviation
Sonic Dog	1	0.05
Sonic Cat	0.5	0.01

Finally, the cost of capital is 17 per cent per annum. However, there is a 20% probability that the company will take a loan to finance the development of the products. If that happens the cost of capital will drop to 16 per cent per annum.

1. For the situation described above, develop first a deterministic model for the Net Present Value (NPV) of each product. Use then the information provided for the uncertain variables to run a Monte Carlo simulation and present the results in relevant diagrams (you should at least have two graphs, each showing the simulated distribution of the NPV for each product).

2. Discuss the recommendations you would make to the management of Pointless Luxuries on the basis of these diagrams.

3. Discuss the advantages of using Monte Carlo simulation instead of a deterministic analysis.