# Data Gathering Essay

## Data Sources

It is important to collect data as accurate as possible if the objective is to produce an accurate result. For the purpose of research, I have collected data regarding the cost, maintenance and operation of all types of home appliances from one of the biggest private residential camps in the world (it currently is the largest private residential camp in the Eastern Province of the Kingdom of Saudi Arabia).

Data for the following appliances was available for a period of four years (2002 to 2005 inclusive):

- Dish Washer – 199 data points
- Ovens – 199 data points
- Clothes Dryers – 200 data points
- Washing Machines – 196 data points
- Refrigerators – 198 data points

There were some missing values in the dataset which were automatically adjusted to equal $50. This is an assumption in the light of the general identification of $50 as maintenance cost in most appliances so that it has been assumed for each of the appliances.

## Data Description

The total number of machines of each type that has been used in the experiment are as follows:

- Dish Washer – 4,278 items
- Ovens – 5,815 items
- Clothes Dryers – 1,962 items
- Washing Machines – 2,015 items
- Refrigerators – 6,064 items

The above information can be displayed in the following graph:

As is visible from the graph, the quantity of clothes dryers and washing machines used was approximately the same at the 2000 level signifying that a smaller population (of data) was available for research for these appliances. Ovens and refrigerators’ data, on the other hand, was derived form a far greater number of appliances making the results more accurate and closer to the actual values. The dishwashers used were also considerably higher than the clothes dryers but less than the number of ovens. Thus, accuracy wise, refrigerators were the leaders and clothes dryers were the trailers.

The appliances used were not all of the same age. Instead of ensuring an equal distribution of the appliances, the numbers of appliances of different ages are as follows:

• Dish Washers

o More than 5 years: 0

o 5-10 years: 4,184

o 10-15 years: 94

o More than 15 years: 0

• Ovens

o More than 5 years: 0

o 5-10 years: 419

o 10-15 years: 252

o More than 15 years: 5,393

• Clothes Dryers

o More than 5 years: 1,465

o 5-10 years: 316

o 10-15 years: 177

o More than 15 years: 4

• Washing Machines

o More than 5 years: 0

o 5-10 years: 0

o 10-15 years: 0

o 15-20 years: 2,015

o More than 20 years: 0

• Refrigerators – 6,064 items

o More than 5 years: 0

o 5-10 years: 132

o 10-15 years: 231

o 15-20 years: 3,252

o More than 20 years: 2,449

### Measuring Investment

One of the most daunting tasks in a thesis is to be able to use a suitable measurement technique to draw conclusions upon. There are several models available based on different assumptions and approaches. Major techniques include Present Value, Future Value, Average Value and so on and so forth. Valuation techniques depend on the situation, the scope and the nature of the data available. Thus choosing the most appropriate valuation technique is very important to make sound evaluations.

For this purpose, I have decided to use the Present Worth technique in order to make assumptions and draw inferences during the course of this thesis. The Present Worth or Present Value (as is mostly referred to as in the corporate world) is an evaluation of the net worth of the asset (or the investment) in terms of today. The Present Worth method adjusts each cash transfer (whether its positive or negative) to a value that would be the same as enacting the transaction today at this very time (Ross, 2004). This means that each and every inflow or outflow (revenue or cost incurred) on an asset or investment should be converted to its equivalent value “today” by dividing by the relevant interest rate factor.

The interest rate factor is often referred to as the discount rate and is in effect the adjusting factor by which the cash inflow and outflows are adjusted. Since countries generally experience inflation, the value of a future inflow or outflow will have reduced effects in today’s terms. This means that a future payment is worth less today and a future cost would cost less today – it has both sides to the coin.

The following formulae can be used for the calculations of the Present Worth of any cash flow (inflow or outflow). A positive means an inflow while a negative means an outflow.

*Legend:*

PV=Present Value of the cash flow

FV=Future Value of the cash flow

r=Discount Rate

t=Time period assuming today=0 [i.e. 1 year after now t=1 on a yearly scale and so on]

If there are a series of equal payments, then they can be grouped using the annuity formula:

*Legend:*

PV=Present Value of the cash flow

R=Payment per period

r=Discount Rate

t=Time period assuming today=0 [i.e. 1 year after now t=1 on a yearly scale and so on]

It is not necessary that the time period be measured in years. However, correlation between the units of the different quantities is a must. If the cash flow is given in monthly terms, then the annual interest rate should be converted to a monthly interest rate.

On the other hand, if the interest rate is given monthly, the cash flow will NOT be converted to a monthly rate. Instead the discount rate will be compounded into a yearly discount rate. 6 The technique of Present Worth is best explained using an example:

Let us say that we want to pay $10 to a certain person after four years. That $10 is not equivalent to $10 spent today, it is much lesser due to the fact that those dollars spent after four years have a much lesser value in terms of today’s currency. This means that those dollars are less valuable today due to the Time Value of Money (La Grega, Buckingham & Evan, 1994). Exactly how much less they are in today’s terms is something which needs to be calculated using existing formulae on Present Value and Future Value. Assuming the discount rate to be 10%, we can calculate is as follows:

Thus, it follows form the above calculations that a $10 payment after four years is equivalent to $6.83 paid today. The longer the time distance from the current period, the lesser is the value of the payment/inflow in today’s terms.

The Time Value of Money is a money discounting concept according to which the value of money decreases with time due to the lost interest for it. Thus, the Present Value technique aims to convert each expense and revenue on an investment or asset to a uniform scale – the present value i.e. the value of those inflows or outflows in terms of today. This eradicates the misunderstanding of lost interest and is very useful in comparative analysis on investments and assets (Ross, 2004).

## ASSUMPTIONS

Major Assumptions

It is important to make a few assumptions before we can move ahead with the thesis. The life expectancies and other variables pertaining to energy usage and salvage values should be estimated, in the light of relevant literature, to a certain value. This will enable a comparative analysis framework.

Life Expectancy

It is a matter of general observation and reliance on the manufacturers claim that one can assume the life expectancy of any electrical appliance with theoretical accuracy. The following are the life expectancies of the various electrical appliances:

- Dish Washer – 6 years
- Ovens – 10 years
- Clothes Dryers – 10 years
- Washing Machines – 7 years
- Refrigerators – 12 years (Household Appliances in the US Volume 1, 2009)

Initial Investment Cost

Though the initial investment cost is highly dependent on the models being purchased, there exists a certain average price for each of the appliances. The following is a general estimate based on the average prices:

- Dish Washer – $307
- Ovens – $571
- Clothes Dryers – $440
- Washing Machines – $468
- Refrigerators – $580 (EGEE Final Project Management homepage, 2009)

Energy Cost

Based on the assumption that a household consumes $1,000 of energy per year in the usage of these appliances cumulatively, the following are the energy costs for each of the appliances:

Dish Washer – $110 (normally 11% of total consumption) or 7900 KWh

Ovens – $430 (normally 43% of total consumption) or 32,000 KWh

Clothes Dryers – $60 (normally 6% of total consumption) or 4,320 KWh

Washing Machines – $80 (normally 8% of total consumption) or 5,760 KWh

Refrigerators – $320 (normally 32% of total consumption) or 23,020 KWh (Energy Costs of Electrical Appliances, 2009) Maintenance & Repair Average Cost

Dish Washer

o 2002: $65.38

o 2003: $56.43

o 2004: $111.79

o 2005: $76.95

o Grand Average: $77.64

Ovens

o 2002: $71.31

o 2003: $80.96

o 2004: $67.38

o 2005: $164.83

o Grand Average: $96.12

Clothes Dryers

o 2002: $101.69

o 2003: $83.18

o 2004: $179.79

o 2005: $68.19

o Grand Average: $108.21

Washing Machines

o 2002: $134.32 9

o 2003: $137.69

o 2004: $233.41

o 2005: $82.03

o Grand Average: $146.86

Refrigerators

o 2002: $71.66

o 2003: $78.66

o 2004: $132.97

o 2005: $74.30

o Grand Average: $89.40

Monthly Rent

An assumption here is made: the monthly rent arising from the appliance will be equal to a 4% of the initial cost of the appliance. This is true for all the appliances throughout their entire expected life. After the expected life, the rent will continue to be earned since the equipment is usable. Thus the rent will form the positive cash flow for each of the appliances during their lifetime as well as extend to one more lifetime than the normal expected time.

Salvage Value

Generally speaking, the salvage value of electrical appliances is not very high due to the lower initial investment involved as compared to higher value assets. It may then be estimated that the salvage value becomes zero after the life expectancy of the equipment (just as in any other depreciation of any other asset). However, when the appliance is mid-way between its life expectancy, the salvage value is assu

## MATHEMATICAL ANALYSIS

Alternatives

In order to compute the different costs incurred for the usage of the appliances, I would like to perform three evaluations: there are three alternatives using which the average cost of using the appliance can be found during the course of its usage. Depending upon the situation in which a consumer may be, the alternatives are as follows:

Alternative 1: Using the equipment for the whole life expectancy with replacement in the middle.

Alternative 2: Using the equipment for the whole life expectancy without replacement.

Alternative 3: Using the equipment for the twice its whole life expectancy without replacement. Judging the fact that there are different conditions applied in each of the alternatives, it would be useful if a general equation can be formed for each of the alternatives.

### The Importance of Present Value Method

It is necessary to justify the use of the present Value Method at this stage in formulating the equations for the alternatives. As has been described in the previous section, the Present Value Method converts all cash inflows and outflows to a common base – today – it helps in erasing comparison issues. The life expectancy of two appliances may be different – cash inflows and outflows in different years cannot be compared unless they are brought to a common platform/level. This level can either be the end-point: the future value or the starting point: the present value (Ross, 2004).

Thus the Present Value Method is an important one in order to compare and draw conclusions form the results of the analysis on the data. Had there been no Present Value Method, comparison would have had been entirely impossible and would have had led to a loss of decision making power based on the raw data.