math help

data provided – setup N
PV

,000,000

$ 1.75

0.01

$ 1.90

0.01

$ 1.90

0.01

7.895 0.01

0.01

$ 2.45

0.01

.465

0.01

10%

2.00

2.50

Price Ratio

Year # of players per thousands retail price per ball Ball sold in millions

$ (5,000,000.00)

0 1999

$ 0.65

$ 1,570,283

$ 0.65

$ 1,570,283

$ 0.65

$ 1,570,283

$ 0.65

$ 1,570,283

$ 0.65

$ 1,570,283

$ 0.65

$ 1,570,283

$ 0.65

$ 1,570,283

$ 0.65

$ 1,570,283

$ 0.65

$ 1,570,283

$ 0.65

$ 1,570,283

$ 0.65

$ 1,570,283

——>

																					New Ball	$	0	5
Wodraw Ball	$ 0. Save Time On Research and Writing Hire a Pro to Write You a 100% Plagiarism-Free Paper. Get My Paper					9
Rate							1		0%
Low fixed Cost						4
High fixed Cost						6
							Year				# of players per thousands			retail price per ball				Ball sold in millions	Balls/Player(000)
19					8	600		$ 1.				7	5.9				3			0.01
1986	635	6.229
1987	655	$ 1.80	6.506
1988	700			$ 1.90	6.820
1989	730	7.161
1990	762		7.895
1991	812	$			2.0
1992	831	$ 2.20	8.224
1993	877		$ 2.45	8.584
1994	931	9.026
1995	967	$ 2.60	9.491
1996	1,020	$		2.5	9.996
1997	1,077		$	2.50						10
1998	1,139														$ 2.50	10.981
Player Growth Rate for 10 yrs
			Price Ratio			% who would buy new ball
		0.5
		1.0		1	1%
		1.5		41%
	76%
	9	5%
		3.0		100%
Net Present Value if selling the ball at												$ 0.65
	$ 3.85
			Incremental Years		Profit
									1999			$ (5,000,000.00)
			1,253				12.079										$ 1,570,283
						2000				1,378			13.287	$ 1,727,311
						2001				1,516			14.616	$ 1,900,042
						2002				1,668			16.077	$ 2,090,047
						2003				1,834			17.685	$ 2,299,051
						2004				2,018			19.454	$ 2,528,956
						2005				2,220			21.399	$ 2,781,852
						2006				2,442			23.539	$ 3,060,037
						2007				2,686			25.893	$ 3,366,041
						2008				2,954			28.482	$ 3,702,645
						2009				3,250			31.330	$ 4,072,910
		NPV	$ 12,273,113
	I have done it for 10 years – you can stretch it further if need be

Mean of initial investment
Assuming ball/player ratio will remain constant in the future
since price ratio is greater than 3 adoption rate will be 100%
10% per year growth in players
Based on int rate of 10%

data provided – setup NPV

Chart for Q7
% who would buy new ball

part a – b

Incremental Years Year # of players per thousands retail price per ball Ball sold in millions Profit PV
0 1999 $ (5,000,000.00) $ (5,000,000.00)

0 1999 1,253 $ 2.50

1 2000 1,378 $ 2.50

2 2001 1,516 $ 2.50

3 2002 1,668 $ 2.50

.04

$ 3,501,632

4 2003 1,834 $ 2.50

.25

$ 3,851,795

5 2004 2,018 $ 2.50

6 2005 2,220 $ 2.50

.25

$ 4,660,672

7 2006 2,442 $ 2.50

.47

$ 5,126,739

8 2007 2,686 $ 2.50

.42

$ 5,639,413

9 2008 2,954 $ 2.50

10 2009 3,250 $ 2.50

.24

$ 6,823,690

NPV ——>

I have done it for 10 years – you can stretch it further if need be

Price Ratio 0.5 1.0 1.5 2.0 2.5 3.0

$ 2.50

% who would buy new ball 0% 11% 41% 76% 95% 100%
Incremental Years Year # of players per thousands

Ball sold in millions Ball sold in millions Ball sold in millions Ball sold in millions Ball sold in millions Ball sold in millions

0 1999 1,253 12.079

1.329

12.079

1 2000 1,378 13.287 – 0 1.462

13.287

2 2001 1,516 14.616 – 0 1.608

14.616

3 2002 1,668 16.077 – 0 1.769

16.077

4 2003 1,834 17.685 – 0 1.945

17.685

5 2004 2,018 19.454 – 0 2.140

19.454

6 2005 2,220 21.399 – 0 2.354

21.399

7 2006 2,442 23.539 – 0 2.589

23.539

8 2007 2,686 25.893 – 0 2.848

25.893

9 2008 2,954 28.482 – 0 3.133

28.482

10 2009 3,250 31.330 – 0 3.446

31.330

Selling Price $ 5.00 $ 2.50 $ 1.67 $ 1.25 $ 1.00 $ 0.83

Year

1999

2000 $ – 0

2001 $ – 0

2002 $ – 0

2003 $ – 0 $ 3.85

2004 $ – 0

2005 $ – 0

$ 6.70

2006 $ – 0

2007 $ – 0

$ 8.11

2008 $ – 0

$ 8.92

2009 $ – 0

A) Base Case
Base Case in this situation would be the worst adoption rate; ie, what would happen if we go ahead and produce the balls and there is minimal adoption
	1.329	$ 2,630,827.98	$ 2,630,828
	1.462	$ 2,893,910.78	$ 2,893,911
	1.608	$ 3,183,301.86	$ 3,183,302
	1.769		$ 3,501,632
	1.945		$ 3,851,795
	2.140	$ 4,236,974.77	$ 4,236,975
	2.354		$ 4,660,672
	2.589		$ 5,126,739
	2.848		$ 5,639,413
	3.133	$ 6,203,354.76	$ 6,203,355
	3.446		$ 6,823,690
$ 43,752,313
B) Sensitivity Analysis
				Selling Price		$ 5.00					$ 1.67			$ 1.25	$ 1.00	$ 0.83
	Potential Balls that can be sold (millions)
							– 0	4.952	9.180	11.475
5.448	10.098	12.623
5.992	11.108	13.885
6.592	12.219	15.273
7.251	13.441	16.801
7.976	14.785	18.481
8.774	16.263	20.329
9.651	17.889	22.362
10.616	19.678	24.598
1	1.678	21.646	27.058
12.845	23.811	29.764
	Contribution Margin Analysis		Contribution Margin (MILLIONS)
							$ – 0	$ 2.63	$ 5.68		$ 6.70	$ 5.51	$ 3.78
$ 2.89	$ 6.25	$ 7.37	$ 6.06	$ 4.16
$ 3.18	$ 6.87		$ 8.11	$ 6.66	$ 4.58
$ 3.50	$ 7.56		$ 8.92	$ 7.33	$ 5.04
$ 8.31	$ 9.81	$ 8.06	$ 5.54
$ 4.24	$ 9.15	$ 10.79	$ 8.87	$ 6.10
$ 4.66	$ 10.06	$ 11.87	$ 9.76
$ 5.13	$ 11.07	$ 13.06	$ 10.73	$ 7.38
$ 5.64	$ 12.17	$ 14.37	$ 11.81
$ 6.20	$ 13.39	$ 15.80	$ 12.99
$ 6.82	$ 14.73	$ 17.38	$ 14.29	$ 9.82

10% per year growth in players
Assuming ball/player ratio will remain constant in the future
Mean of initial investment
Based on int rate of 10%
since price ratio 1, adoption rate will be 11%
since worst adoption is at price ratio of 1, so it means we will also sell same price as competition

part a – b

$5.00
$2.50
$1.67
$1.25
$1.00
$0.83

Goal Seek

Price Ratio 0.5 1.0 1.5 2.0 2.5 3.0
Selling Price $ 5.00 $ 2.50 $ 1.67 $ 1.25 $ 1.00 $ 0.83

% who would buy new ball 1%

Incremental Years Year # of players per thousands Potential Balls that can be sold (millions) Ball sold in millions Ball sold in millions Ball sold in millions Ball sold in millions Ball sold in millions Ball sold in millions

0 1999 1,253 12.079

1 2000 1,378 13.287

2 2001 1,516 14.616

3 2002 1,668 16.077

4 2003 1,834 17.685

5 2004 2,018 19.454

6 2005 2,220 21.399

1.678

7 2006 2,442 23.539

8 2007 2,686 25.893

9 2008 2,954 28.482

10 2009 3,250 31.330

Selling Price $ 5.00 $ 2.50 $ 1.67 $ 1.25 $ 1.00 $ 0.83
Contribution Margin Analysis Year Contribution Margin (MILLIONS)

1999

$ 0.45 $ 0.45

2000

$ 0.50 $ 0.50

2001

$ 0.55 $ 0.55

2002

$ 0.61

$ 0.61 $ 0.60

2003

$ 0.67 $ 0.67 $ 0.65 $ 0.67 $ 0.67

2004

$ 0.73 $ 0.73

2005

$ 0.81 $ 0.81

2006

$ 0.89 $ 0.89

2007

$ 0.97 $ 0.97

2008

$ 1.07 $ 1.07

2009

$ 1.18 $ 1.18

Selling Price $ 5.00 $ 2.50 $ 1.67 $ 1.25 $ 1.00 $ 0.83

Year

0 1999

$ (5) $ (5) $ (5) $ (5) $ (5)

0 1999 $ 0.45 $ 0.45 $ 0.45 $ 0.44 $ 0.45 $ 0.45
1 2000 $ 0.45 $ 0.45 $ 0.45 $ 0.44 $ 0.45 $ 0.45
2 2001 $ 0.45 $ 0.45 $ 0.45 $ 0.44 $ 0.45 $ 0.45
3 2002 $ 0.45 $ 0.45 $ 0.45 $ 0.44 $ 0.45 $ 0.45
4 2003 $ 0.45 $ 0.45 $ 0.45 $ 0.44 $ 0.45 $ 0.45
5 2004 $ 0.45 $ 0.45 $ 0.45 $ 0.44 $ 0.45 $ 0.45
6 2005 $ 0.45 $ 0.45 $ 0.45 $ 0.44 $ 0.45 $ 0.45
7 2006 $ 0.45 $ 0.45 $ 0.45 $ 0.44 $ 0.45 $ 0.45
8 2007 $ 0.45 $ 0.45 $ 0.45 $ 0.44 $ 0.45 $ 0.45
9 2008 $ 0.45 $ 0.45 $ 0.45 $ 0.44 $ 0.45 $ 0.45
10 2009 $ 0.45 $ 0.45 $ 0.45 $ 0.44 $ 0.45 $ 0.45
NPV

$ (0) $ (0) $ (0) $ (0) $ (0)

B)Goal Seek
2%	3%	8%	12%	<-- these are calculated using goal seek
0.101	0.230	0.396	0.604	0.947	1.451
0.112	0.253	0.436	0.664	1.042	1.596
0.123	0.278	0.480	0.731	1.146	1.755
0.135	0.306	0.528	0.804	1.260	1.931
0.149	0.336	0.580	0.884	1.386	2.124
0.163	0.370	0.638	0.973	1.525	2.336
0.180	0.407	0.702	1.070	2.570
0.198	0.447	0.772	1.177	1.845	2.827
0.217	0.492	0.850	1.295	2.030	3.110
0.239	0.541	0.935	1.424	2.233	3.421
0.263	0.595	1.028	1.567	2.456	3.763
						$ 0.45	$ 0.44
				$ 0.50	$ 0.48
				$ 0.55	$ 0.53
		$ 0.61		$ 0.60	$ 0.59
				$ 0.67
				$ 0.73	$ 0.71
				$ 0.81	$ 0.78
				$ 0.89	$ 0.86
				$ 0.97	$ 0.95
				$ 1.07	$ 1.04
				$ 1.18	$ 1.14
Financial Analysis
(All Values in Millions)	PV Analysis
					$ (5)
					$ (0)

Chart below shows Contribution Margin (in millions) for different pricing strategis across the years – it can be seen that based on price sensitivity of adoption of the balls, it is most desirables to price it at $1.67 a ball
Note – Fixed initial investment is not considered in the pricing analysis as it will be a mute point and change among different pricing options
Contribution Margin in this case is total revenue less total variable cost; it doesnt include fixed cost
Using Goal seek, we are trying to determine what the minimum response rate should be for each of the pricing strategies to break even for the next 10 years
it shows that we will definitely break even
Potential application of optimization in this case would be determine what is the best price to sell the balls at given that adoption rate is dependent on the pricing strategy; higher the price lower the adoption rate
Objective – Max Profit
Constraints – price ratio can range from 0.5 to 3, price cannot be -ve, adoption cannot be -ve, adoption can range from 0% to 100% which will be a function of price
Note – the sensitivity analysis on ‘solutions tab’ is an optimization through simulation of this case where we determine that best pricing is at $1.67 per ball
—————————————————————————————————————————————————————————————————————————————————————
Potential application of simulation in this case would be determine what the total profit would be for all the different pricing strategies given that adoption rate is dependent on the pricing strategy; higher the price lower the adoption rate
Another situation where simulation can be used is to determine break even points (ie, what should be the adoption rate for each pricing be so that we can break even – like we did using goal seek above)