1. Three investment alternatives (A, B, and C) are being considered. The discounted present worth (PW) for the alternatives are $35,000, $30,000, and $37,000, respectively. The three alternatives have different rankings in terms of employee morale (EM) and vendor reputation (VR). The following weights have been assigned to the three factors (PW, EM, and VR): 40, 35, and 25. On a scale from 1 to 10, the following ratings have been assigned to the three alternatives for the three factors:
A B C
PW 9.2 8 10
EM 9 10 8.5
VR 9.5 10 9
Using the weighted factor comparison method, which investment alternative would be recommended?
2. In problem 1, what change, if any, would occur in the recommendation if the ratings on:
(d) PW had been 9.5, 8.5, and 10?
(e) EM had been 10, 9.5, and 9?
(f) VR had been 7.5, 10, and 8.5?
3. What do you find to be the greatest weakness in using the weighted factor comparison method?
4. Given the present worth data in problem 1, what weights would you have assigned to the various alternatives for the present worth factor? What logical process did you use to assign the weights?
2. An investment proposal has the following probability distribution of returns:
Year 1 Year 2 Year 3
Return Probability Return Probability Return Probability
6,000 0.2 8,000 0.5 7,000 0.3
8,000 0.4 12,000 0.5 11,000 0.5
9,000 0.4 17,000 0.2
The events of each year are independent of other years. The outlay on the project is fixed at $ 22,000 and the appropriate discount rate figure is 10 per cent.
Find the expected net present value.
3. A project has an initial outlay fixed at 1,500. Return in year 1 could be 1,350 with probability 0.4 or 900 with probability 0.6. If in year 1 the 900 return transpires then in year 2 there can be 1200 (p=0.2) or 1050 (p=0.8). If the 1st year return had been 1350, then in the second year there is a seven-tenths chance of 600 and three-tenths chance of 150. The discount rate is 10 per cent. Find the expected net present value of the project.
Hints: draw a tree to represent the scenarios indicating cash flow and probabilities; the probability for each branch is the product of the probabilities for each year. Calculate p*NPV for each branch and ENPV is the sum of all p*NPV.
4. An oil company can purchase exploration rights in either of two blocks of the North Sea. If it acquires block A there is a 0.4 probability of striking oil, which would give a profit of $14m. If it fails to strike oil, it can relocate the rig within the block and drill once more when there would be an even chance of an oil strike with a net profit of $12m. Failure to strike oil at the second attempt would mean a loss of $5m. Alternatively, having failed to strike oil first time the company could opt to cut its losses and lose $3m. If the company acquires block B there is an even chance of striking oil first time with a profit of $10m. If it has no success, it can pull out (losing $3m) or relocate the rig once with a 0.7 chance of striking oil and an $8m profit or a 0.3 chance of a dry well at the second attempt and an overall $5m loss. Which block should the company acquire?
5. A company introducing a new product can construct a large plant or a standard size plant. If it constructs the large plant and demand for the product is subsequently high, a profit of $10m is made. There is, however, a 0.6 probability of low demand and a loss of $3m.
If the firm chooses the small plant and demand is high (probability 0.4) it will make a profit of $3.5m. If on the other hand, demand was low a profit of $2m would follow.
Which size of plant should be built?
The company is considering whether a consultant should be engaged to carry out a market research so that the level of demand for the product can be determined with certainty (after the market research). As the market research has not been carried out, it is assumed that there is an even chance the market research will indicate a high demand with a probability of 0.5 and a low demand 0.5. The cost of the market research is $1 million dollars. Should the company carry out the market research?
6. A choice is to be made between two alternative courses of action on the basis of utility index. Alternative one has an expected value of 20 with standard deviation 8. Alternative two has expected value 26 with standard deviation 10.
Find out which alternative is selected on the basis of utility index.
7. A plant has been constructed to manufacture a new product. Fixed costs amount to $8000 per week. The unit variable cost of the product is $7 and the selling price is $12. Maximum plant capacity is an output of 3200 units per week. Find:
a. The break-even output level and associated capacity utilisation.
b. Determine the price at which the break-even output does not exceed 75 per cent capacity utilisation.
c. What is the maximum weekly profit?
8. A firm can choose between two types of plant to produce a new product. The product will sell at a price of $25. Plant A has fixed costs per month of $20,000 and a unit variable cost of $15. Plant B has a monthly fixed cost of $15,000 but has a unit variable cost of $17. The maximum capacity of either plant is 3000 units of output per month.
a. Find out which plant has the lower break-even output level.
b. Which has the greater profit potential if full capacity can be used?
c. What is the minimum value of monthly demand for the product that would result in the choice of plant A on profit grounds?