Question

You are considering two investment projects each having the same cost. Each project is facing the following events, probabilities and net profits:

ALTERNATIVES:   

a1: Newspaper a2: Pamphlet

EVENTS: e1 e2 e3 e1 e2 e3

NET PROFITS: 4000 6000 9000 3000 7000 8000

PROBABILITIE: .25 .50 .25 .30 .50 .20

1. Construct a decision tree and show which project you would chose by using the expected value method ()?

2. Calculate the coefficient of variation of each project, and determine which one should you chose accordingly?

3. Use the Z-table, and show the likelihood that Project and Project 2 will yield a net profit between $7000 and $9000.

4. Assume that the first investment project will cost you $2000 less than the second one. Support how that would change your decision, if at all.

DMUR: Results

Xbar

Sigma

CoV

Normal Dist. %

Answer 1

Newspaper		Pamphlet
X	P(=X=x)	X*P(X)		Y	P(Y=y)	Y*P(Y)
4000	0.25	1000		3000	0.3	900
6000	0.5	3000		7000	0.5	3500
9000	0.25	2250		8000	0.2	1600
Total	1	6250		Total	1	6000

1. Construct a decision tree and show which project you would chose by using the expected value method ()?

The expected value =

Here

Expected profit with newspaper = 6250

Expected profit with pamphlet = 6000

There we should invest in newspaper since it is expected to generate higher profit at same cost.

2. Calculate the coefficient of variation of each project, and determine which one should you chose accordingly?

coefficient of variation = SD(x) / E(x) *100%

SD(x) =

Newspaper
X	P(=X=x)	X*P(X)	x^2*P(X)
4000	0.25	1000	4000000
6000	0.5	3000	18000000
9000	0.25	2250	20250000
Total	1	6250	42250000

SD(X) = 1785.357

Pamphlet
Y	P(Y=y)	Y*P(Y)	y^2*P(Y)
3000	0.3	900	2700000
7000	0.5	3500	24500000
8000	0.2	1600	12800000
Total	1	6000	40000000

SD(Y) = 2000

Coefficient of variance for news paper = 1785.357 / 6250 * 100

Cov (X) = 28.57%

Coefficient of variance for pamphlet= 2000 / 6000 * 100

Cov (Y) = 33.33%

Coeff of variance gives the dispersion of values around the mean. The greater the cov the greater is dispersion meaning less accuracy and vice versa.

So we see that cov (X) < Cov (y), newspaper would be less risky so we would choose newspaper.

3. Use the Z-table, and show the likelihood that Project and Project 2 will yield a net profit between $7000 and $9000.

z-score = (x- )/

Therefore for news paper = (x - 6250) / 1785.357

P(7000 < X < 9000) = P(X < 9000) - P(Z < 7000)

= P(Z < 1.54) - P( Z < 0.42)

= 0.93826 - 0.66279

P(X) = 0.2755

For pamphlet  = (x - 6000) / 2000

P(7000 < X < 9000) = P(X < 9000) - P(Z < 7000)

= P(Z < 1.5)) - P( Z < 0.5)

= 0.93319 - 0.69146

P(X) = 0.24173

4. Assume that the first investment project will cost you $2000 less than the second one. Support how that would change your decision, if at all.

First investment is costing less than pamphlet by 2000. So the netprofits of pamphlets will reduce to 4000 due to increase in cost by 2000. This still favors newspaper investment. So we will still be investing in newspaper.