1) When a pair of dice is tossed, the results may be any whole number from 2 to 12. In the game of craps one can win by tossing either a 7 or an 11 on the first roll. What is the probability of doing so?

2) Kenan wants to decide whether to invest $1,000 in Kel's speculative venture. He will do so if he thinks he can get his money back in 1 year. He believes that the probabilities of the various outcomes are the following:

RESULTS: PROBABILITY:

$2000 .3

$1500 .1

$1000 .2

$500 .3

0 .1

What is the expected value of this venture?

3) A yearly savings due to an energy efficiency project have a most likely value of $30,000. The high estimate of $40,000 has a probability of 0.25 and the low estimate of $20,000 has a probability of 0.35. What is the expected value for the annual savings?

4) A project has a life of 10 years and no salvage value. The firm uses an interest rate of 12% to evaluate engineering projects. The project has an uncertain first cost and annual net revenue.

First Cost Prob.

$300,000 0.2

$400,000 0.5

$600,000 0.3

Net Revenue Prob.

$70,000 0.3

$90,000 0.5

$100,000 0.2

What is the joint probability for the first cost and net revenue? Define the following scenarios: optimistic, most likely and pessimistic. To do so use both given estimates. What is the NPV for each scenario?

5) Dunder Mifflin Paper Company is examining the purchase of a machine that will cost $50,000. The machine is expected to last 10 years and will have no salvage value. D. Schrute, Assistant to the Regional Manager, mentioned that the firm's interest rate is 15%. Determine the expected return and the risk (St. Dev.) associated with the purchase.

Probability 0.3 0.4 0.3

Annual Benefits $9,000 $10,500 $12,000

6) Krispy K. is considering the purchase of a new equipment. From the estimated NPV and probabilities of the four possible outcomes given, calculate the expected annual worth (EUAW) of the equipment if the life of the equipment is 6 years and interest rate is 8%.

Outcome NPV Probability

1 $34,560 0.15

2 $38,760 0.25

3 $42,790 0.40

4 $52,330 0.20

7) A firm is examining the possible purchase of new machine to produce basketballs at a faster pace and at a lower cost. The industrial engineer in charge must determine if the machine should be purchased. However, the engineer is having trouble because he doesn't know how to evaluate the equipment in terms of annual savings and a possible salvage value. The equipment's initial cost if $500,000 and is expected to last for 8 years. Determine the NPV (NPW) if MARR is 6%. The engineer has the following information concerning savings and salvage value estimates and projected probabilities:

Prob. = 0.20 Prob. = 0.50 Prob. = 0.25 Prob. = 0.05 Savings per Year $65,000 $82,000 $90,000 $105,000

Salvage Value $40,000 $55,000 $65,000 $75,000