Question

Traditional Forecasting application (Due:09/1818) The XYZ company introduced the new technology (currently advertized as U- VERSE) in mid 2010. At the time, the company estimated that their new technology will have a long-term market share of 70% (ie, M-70%) According to the company's records, by January Ist, 201, its market share had reached 5% of its peak, and it reached to 45% of its peak by April first 2013 The company's long-term technology plan calls for starting R&D activities for new technology 2 years before the current technology reaches its peak (or within 1% of its peak). PART I: Determine 1)- The calendar year (call this X) the company's market share will reach its expected peak, and the year R&D activities for the next technology should start 2)- Use a time unit of1 quarter (0.25 year), calculate the market share for each period, from 2013 to year X+2, and graph the corresponding S-Curve. PART I When the technology was introduced, using historical data for similar products, it was determined that A)-Demand for the product in year T will increase for some time in the future and could be estimated using the following equation D(t) = 1.1(1.2010)" +0.5 Yearly demand in million units, B)-The company will realize a long-term average revenue of S150 per unit. C)-Total Cost of R&D activities, promoting the technology introduction and other expenses, will be decided from the following equation Total costs in million-dollar, TC = 260+50*(T-2010.5 +0.8 Using the info 1)- How long will it take the company to recover its investment and rov nine start generating profit. (This is called Break-Even -Point) 2)- Suppose at the end of year 2018, the company sales the technology for S400 Mil to a competitor, Generate profit or loss for the company from the financial outcome of the technol year 213 to the end of 2018. What was the net ogy

Answer 1

Part I

1. The new technology was launched in mid 2010. Let us suppose that it was launched on July 1, 2010. Uptill Jan 1, 2011 there were two quarters. In 2 quarters the market share reached 5% of its peak. By April 1, 2013, it had reached 45% of its peak. From July 1, 2010 to April 1, 2013 there are 11 quarters.

In 11 quarters it reached 45% of its peak. To reach 100% of its peak it would need quarters from June, 2010. This corresponds to July 1, 2016. So it will reach its expected peak in 2016. So the year R&D activities for the next technology should start is 2014.

100 11 × 24.42 45

Part II

1. Suppose it breaks even 'T' years from 2010. Then the demand for the product will increase according to the equation   

D(t) = 1.1(T-2010)2 0.5

So in T years from 2010 its total demand would be

     (the additional 0.5 at the end is to consider demand in year 2010)

1.1(12) 0.51.1(22)0.5+.1(T0.50.5

The sum to T terms of this series is    (Since sum to n terms of the squares of first n natural numbers is [n(n+1)(2n+1)/6])

TT+127++0.5(T+1) 1.1 6

Now multiply this sum by the long term average revenue of 150. This will give the total revenue after T years.

Total revenue after T years is $150*[1.1[\frac{T(T+1)(2T+1)}{6}]+0.5(T+1)]$

Total cost after T years after 2010 is given by 180+50*(T-0.5)+0.8.

At the break even point total revenue must equal total cost. So equate total revenue with total cost and solve for T.

150 1.1 lrT(T+1)( 2T +1) ] + 0.5(T + 1)] = 180 + 50 6

Solving this T=0.63551.

So it will take 0.6 years for the company to break even.