## Sarah Gets a Diamond Case Solution

**INTRODUCTION:**

The case is regarding the story of people who are going to be married in their coming future. This case is about aguy named “Greg” and a girl named “Sarah”. The Greg is a graduate in engineering from the South Eastern University. After his graduation, he starts working as a structural engineer with a national defense contractor in eastern Virginia where he meets “Sarah”. They quickly become close friends. After sometimes they split due to their different jobs with different locations. Greg wants to propose her and finally they meet again after 3 years at a place named Naples.

**PROBLEM STATEMENT:**

After 3 years of wait, Greg finally gets his chance to meet “Sarah” on his trip to Naples. He wants to propose her and for that reason he decides to buy something valuable like a wedding ring, which will enlighten Sarah. Now the problem is to find that ring, but after a suggestion from his close friend he decides to buy a diamond stone for Sarah so that she can decide her choice. He collects a data of 6000 diamonds plus another 3142 diamonds and wants to analyze from this data, regarding which one is cheap.

**ANALYSIS:**

The analysis is based on a simple comparison between the actual prices of a diamond and the fore casted prices through two regression methods proposed by Greg. There were three methods he proposed to work on. However,the first one named Simple linear method considered to be irrelevant and insensible. In this model the prices of two different diamonds increase such as one is 1 carat diamond and the other one is 2 carat will be same as if the price in creased from 2 carat to 3 carat, then that would not be the actual case. He also assumed in that model that the same color change in 2 carat diamond will have the same amount of increment in the dollar as that in at the case of 3 colors change, which is also not the case.

The diamond has many value drivers that determine its quality, which ultimately reflects its final price. The major value drivers that are the most important ones in determining its value are cut, color, clarity and carat weight.

The cut is typically considered as the most important value driven factor from all of them. It describes the ability of a stone to reflect and refract light.The grading includes poor, fair, good, very good, ideal and signature ideal.

The second color is a kind of filter, which blocks the reflection of light. The more noticeable color is lower in quality. Grading includes completely colorless (D), Colorless (E – F), Nearly Colorless (G-H & I- J) and Noticeable color.

**The third one is clarity, which determines the purification level of diamond.**

The last prime factor is carat weight, which means more weight,the more the value of the diamond. These cond model he proposed was the linear model in which he considered multiple factors like we have discussed above to arrive at the mathematical equation that will be equal to the natural log of the price. The calculation based on this model is given in the Excel spreadsheet.

**SECOND MODEL (LOG-LINEAR)**

The first step before starting off includes the 2^{nd} and final model, which will be discussed below to collect the sample data of 6000 diamonds that is given in the case file along with samples from another 3142 diamonds. The prices for those samples of other 3142 diamonds have been taken from the following website (content. washing tondiamond.com/diamond-price-calculator). After that we have fore casted the value of the diamond from the models proposed by Greg.

In this, we have calculated the forecasted price of diamond through a formula given in the case file. The forecasted price is then matched with the actual price to determine whether it is under priced or overpriced.In order to arrive at the forecasted price, we have first calculated the natural log of the price by using the formula and in the second step; we have forecasted the price by using exponent function applied to natural log values.

For example if we look at the figures calculated in the excel spreadsheet of the diamond having the ID number from 1 to 5, thy were all under priced as the forecasted prices of these diamonds are higher than their current market price, which will be considered as an opportunity for them. There are also other diamonds’prices, which are under priced like ID 5997, 9140 and 9142........................

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