Part A-
1. The following are the cash flows of two projects:
|
Year
|
Project A
|
Project B
|
|
0
|
-$260
|
-$260
|
|
1
|
140
|
160
|
|
2
|
140
|
160
|
|
3
|
140
|
160
|
|
4
|
140
|
|
a. If the opportunity cost of capital is 11%, calculate the NPV for both projects.
b. Which of these projects is worth pursuing?
-Project A
-Project B
-Both
-Neither
2. The following are the cash flows of two projects:
|
Year
|
Project A
|
Project B
|
|
0
|
-$310
|
-$310
|
|
1
|
140
|
210
|
|
2
|
140
|
210
|
|
3
|
140
|
210
|
|
4
|
140
|
|
a. Calculate the NPV for both projects if the discount rate is 10%.
b. Suppose that you can choose only one of these projects. Which would you choose?
-Project B
-Project A
-Neither
3. The following are the cash flows of two projects:
|
Year
|
Project A
|
Project B
|
|
0
|
-$230
|
-$230
|
|
1
|
110
|
130
|
|
2
|
110
|
130
|
|
3
|
110
|
130
|
|
4
|
110
|
|
If the opportunity cost of capital is 11%, what is the profitability index for each project?
Is the project with the highest profitability index also the one with the highest NPV?
-Yes
-No
4. The following are the cash flows of two projects:
|
Year
|
Project A
|
Project B
|
|
0
|
-$310
|
-$310
|
|
1
|
140
|
210
|
|
2
|
140
|
210
|
|
3
|
140
|
210
|
|
4
|
140
|
|
What is the payback period of each project?
5. A project that costs $3,200 to install will provide annual cash flows of $900 for each of the next 6 years.
Calculate the NPV if the discount rate is 12%.
Is this project worth pursuing?
-Yes
-No
How high can the discount rate be before you would reject the project?
6. A new computer system will require an initial outlay of $19,500, but it will increase the firm's cash flows by $3,900 a year for each of the next 6 years.
a. Calculate the NPV and decide if the system is worth installing if the required rate of return is 8%. What if it is 13%?
b. How high can the discount rate be before you would reject the project?
7. Here are the cash flows for a project under consideration:
|
C0
|
C1
|
C2
|
|
-$7,590
|
+$5,520
|
+$19,320
|
a. Calculate the project's net present value for discount rates of 0, 50%, and 100%.
b. What is the IRR of the project?
8. Consider projects A and B with the following cash flows:
|
|
C0
|
C1
|
C2
|
C3
|
|
A
|
-$27
|
+ $16
|
+$ 16
|
+ $16
|
|
B
|
- 52
|
+ 27
|
+ 27
|
+ 27
|
a1. What is the NPV of each project if the discount rate is 10%?
a2. Which project has the higher NPV?
-Project B
-Project A
b1. What is the profitability index of each project?
b2. Which project has the higher profitability index?
-Project A
-Project B
c1. Which project is most attractive to a firm that can raise an unlimited amount of funds to pay for its investment projects?
-Project B
-Project A
c2. Which project is most attractive to a firm that is limited in the funds it can raise?
-Project A
-Project B
-Both
9. Here are the expected cash flows for three projects:
|
|
|
Cash Flows (dollars)
|
|
Project
|
Year:
|
0
|
1
|
2
|
3
|
4
|
|
A
|
|
-6,500
|
+1,375
|
+1,375
|
+3,750
|
0
|
|
B
|
|
-2,500
|
0
|
+2,500
|
+2,750
|
+3,750
|
|
C
|
|
-6,500
|
+1,375
|
+1,375
|
+3,750
|
+5,750
|
a. What is the payback period on each of the projects?
b. If you use a cutoff period of 2 years, which projects would you accept?
Project A
Project B
Project C
Project A and Project B
Project B and Project C
Project A and Project C
Projects A, B, and C
None
c. If you use a cutoff period of 3 years, which projects would you accept?
Project A
Project B
Project C
Project A and Project B
Project B and Project C
Project A and Project C
Projects A, B, and C
None
d1. If the opportunity cost of capital is 12%, calculate the NPV for projects A, B, and C.
d2. Which projects have positive NPVs?
Project A
Project B
Project C
Project A and Project B
Project B and Project C
Project A and Project C
Projects A, B, and C
None
e. "Payback gives too much weight to cash flows that occur after the cutoff date." True or false?
True
False
Part B-
1. Quick Computing currently sells 13 million computer chips each year at a price of $14 per chip. It is about to introduce a new chip, and it forecasts annual sales of 20 million of these improved chips at a price of $18 each. However, demand for the old chip will decrease, and sales of the old chip are expected to fall to 6 million per year. The old chip costs $7 each to manufacture, and the new ones will cost $11 each. What is the proper cash flow to use to evaluate the present value of the introduction of the new chip?
2. Tubby Toys estimates that its new line of rubber ducks will generate sales of $8.00 million, operating costs of $5.00 million, and a depreciation expense of $2.00 million. Assume the tax rate is 40%.
a. Calculate the operating cash flow for the year by using all three methods: (a) adjusted accounting profits; (b) cash inflow/cash outflow analysis; and (c) the depreciation tax shield approach.
b. Are the above answers equal?
Yes
No
3. The owner of a bicycle repair shop forecasts revenues of $212,000 a year. Variable costs will be $63,000, and rental costs for the shop are $43,000 a year. Depreciation on the repair tools will be $23,000. Prepare an income statement for the shop based on these estimates. The tax rate is 40%.
4. Laurel's Lawn Care, Ltd., has a new mower line that can generate revenues of $129,000 per year. Direct production costs are $43,000, and the fixed costs of maintaining the lawn mower factory are $16,500 a year. The factory originally cost $0.86 million and is being depreciated for tax purposes over 20 years using straightline depreciation. Calculate the operating cash flows of the project if the firm's tax bracket is 30%.
5. Gluon Inc. is considering the purchase of a new high pressure glueball. It can purchase the glueball for $90,000 and sell its old lowpressure glueball, which is fully depreciated, for $16,000. The new equipment has a 10year useful life and will save $20,000 a year in expenses. The opportunity cost of capital is 8%, and the firm's tax rate is 40%. What is the equivalent annual savings from the purchase if Gluon uses straightline depreciation? Assume the new machine will have no salvage value.
6. Johnny's Lunches is considering purchasing a new, energyefficient grill. The grill will cost $33,000 and will be depreciated according to the 3year MACRS schedule. It will be sold for scrap metal after 3 years for $8,250. The grill will have no effect on revenues but will save Johnny's $16,500 in energy expenses per year. The tax rate is 30%. Use the MACRS depreciation schedule (https://lectures.mhhe.com/connect/0077640748/MACRS%20depreciation%20schedule.png).
a. What are the operating cash flows in each year?
b. What are the total cash flows in each year?
c. If the discount rate is 10%, should the grill be purchased?
Yes
No
7. Revenues generated by a new fad product are forecast as follows:
|
Year
|
Revenues
|
|
1
|
$40,000
|
|
2
|
30,000
|
|
3
|
10,000
|
|
4
|
5,000
|
|
Thereafter
|
0
|
Expenses are expected to be 40% of revenues, and working capital required in each year is expected to be 20% of revenues in the following year. The product requires an immediate investment of $42,000 in plant and equipment.
a. What is the initial investment in the product? Remember working capital.
b. If the plant and equipment are depreciated over 4 years to a salvage value of zero using straightline depreciation, and the firm's tax rate is 20%, what are the project cash flows in each year? Assume the plant and equipment are worthless at the end of 4 years.
c. If the opportunity cost of capital is 10%, what is the project's NPV?
d. What is project IRR?
8. Kinky Copies may buy a highvolume copier. The machine costs $40,000 and will be depreciated straightline over 5 years to a salvage value of $6,000. Kinky anticipates that the machine actually can be sold in 5 years for $12,000. The machine will save $6,000 a year in labor costs but will require an increase in working capital, mainly paper supplies, of $3,000. The firm's marginal tax rate is 35%, and the discount rate is 14%. (Assume the net working capital will be recovered at the end of Year 5.)
Calculate the NPV.
Should Kinky buy the machine?
Yes
No
9. Quick Computing installed its previous generation of computer chip manufacturing equipment 3 years ago. Some of that older equipment will become unnecessary when the company goes into production of its new product. The obsolete equipment, which originally cost $35 million, has been depreciated straightline over an assumed tax life of 5 years, but it can be sold now for $17 million. The firm's tax rate is 30%. What is the aftertax cash flow from the sale of the equipment?
10. Bottoms Up Diaper Service is considering the purchase of a new industrial washer. It can purchase the washer for $6,900 and sell its old washer for $2,100. The new washer will last for 6 years and save $1,900 a year in expenses. The opportunity cost of capital is 18%, and the firm's tax rate is 40%.
a. If the firm uses straightline depreciation to an assumed salvage value of zero over a 6year life, what is the annual operating cash flow of the project in years 1 to 6? The new washer will in fact have zero salvage value after 6 years, and the old washer is fully depreciated.
b. What is project NPV?
c. What is NPV if the firm uses MACRS depreciation with a 5year tax life? Use the MACRS depreciation schedule. (https://lectures.mhhe.com/connect/0077640748/MACRS%20depreciation%20schedule.png)
11. Canyon Tours showed the following components of working capital last year:
|
|
Beginning
|
End of Year
|
|
Accounts receivable
|
$27,800
|
$24,900
|
|
Inventory
|
13,900
|
16,300
|
|
Accounts payable
|
16,400
|
20,300
|
a. What was the change in net working capital during the year?
b. If sales were $37,900 and costs were $25,900, what was cash flow for the year? Ignore taxes.
12. A house painting business had revenues of $16,100 and expenses of $9,100 last summer. There were no depreciation expenses. However, the business reported the following changes in working capital:
|
|
Beginning
|
End
|
|
Accounts receivable
|
$1,300
|
$4,600
|
|
Accounts payable
|
720
|
310
|
Calculate net cash flow for the business for this period.
13. Better Mousetraps has developed a new trap. It can go into production for an initial investment in equipment of $5.7 million. The equipment will be depreciated straight line over 6 years to a value of zero, but in fact it can be sold after 6 years for $518,000. The firm believes that working capital at each date must be maintained at a level of 10% of next year's forecast sales. The firm estimates production costs equal to $1.50 per trap and believes that the traps can be sold for $6 each. Sales forecasts are given in the following table. The project will come to an end in 6 years, when the trap becomes technologically obsolete. The firm's tax bracket is 35%, and the required rate of return on the project is 9%. Use the MACRS depreciation schedule. (https://lectures.mhhe.com/connect/0077640748/MACRS%20depreciation%20schedule.png)
|
Year
|
0
|
1
|
2
|
3
|
4
|
5
|
6
|
Thereafter
|
|
Sales (millions of traps)
|
0
|
.4
|
.5
|
.6
|
.6
|
.4
|
.2
|
0
|
a. What is project NPV?
b. By how much would NPV increase if the firm depreciated its investment using the 5year MACRS schedule?
14. The efficiency gains resulting from a justintime inventory management system will allow a firm to reduce its level of inventories permanently by $444,000. What is the most the firm should be willing to pay for installing the system?
15. Better Mousetraps has developed a new trap. It can go into production for an initial investment in equipment of $5.4 million. The equipment will be depreciated straight line over 6 years to a value of zero, but in fact it can be sold after 6 years for $668,000. The firm believes that working capital at each date must be maintained at a level of 15% of next year's forecast sales. The firm estimates production costs equal to $1.60 per trap and believes that the traps can be sold for $6 each. Sales forecasts are given in the following table. The project will come to an end in 6 years., when the trap becomes technologically obsolete. The firm's tax bracket is 35%, and the required rate of return on the project is 9%. Use the MACRS depreciation schedule.
|
Year
|
0
|
1
|
2
|
3
|
4
|
5
|
6
|
Thereafter
|
|
Sales (millions of traps)
|
0
|
.6
|
.8
|
1.0
|
1.0
|
.9
|
.6
|
0
|
Suppose the firm can cut its requirements for working capital in half by using better inventory control systems. By how much will this increase project NPV?
Part C-
1. In a slow year, Deutsche Burgers will produce 2.4 million hamburgers at a total cost of $3.9 million. In a good year, it can produce 4.2 million hamburgers at a total cost of $4.8 million.
a. What are the fixed costs of hamburger production?
b. What is the variable cost per hamburger?
c. What is the average cost per burger when the firm produces 1 million hamburgers?
d. What is the average cost per burger when the firm produces 2 million hamburgers?
e. Why is the average cost lower when more burgers are produced?
The fixed costs are spread across more burgers.
Fixed costs are constant per burger.
Variable costs are lower per burger.
2. A project currently generates sales of $11 million, variable costs equal 50% of sales, and fixed costs are $2.2 million. The firm's tax rate is 30%. Assume all sales and expenses are cash items.
a. What are the effects on cash flow, if sales increase from $11 million to $12.1 million?
b. What are the effects on cash flow, if variable costs increase to 55% of sales?
3. Finefodder's analysts have come up with the following revised estimates for the Gravenstein store:
|
|
Range
|
|
|
Pessimistic
|
Expected
|
Optimistic
|
|
Investment
|
$4,920,000
|
$4,800,000
|
$4,000,000
|
|
Sales
|
13,000,000
|
19,000,000
|
27,000,000
|
|
Variable costs as % of sales
|
74
|
72
|
71
|
|
Fixed cost
|
$3,100,000
|
$2,900,000
|
$2,700,000
|
Assume the project life is 12 years, the tax rate is 40%, the discount rate is 8%, and the depreciation method is straightline over the project's life. Conduct a sensitivity analysis for each variable and range and compute the NPV for each.
4. The following estimates have been prepared for a project:
Fixed costs: $10,800
Depreciation: $7,200
Sales price per unit: $2
Accounting breakeven: 60,000 units
What must be the variable cost per unit?
5. Dime a Dozen Diamonds makes synthetic diamonds by treating carbon. Each diamond can be sold for $140. The materials cost for a standard diamond is $40. The fixed costs incurred each year for factory upkeep and administrative expenses are $216,000. The machinery costs $2.5 million and is depreciated straightline over 10 years to a salvage value of zero.
a. What is the accounting breakeven level of sales in terms of number of diamonds sold?
b. What is the NPV breakeven level of diamonds sold per year assuming a tax rate of 35%, a 10year project life, and a discount rate of 12%?
6. You are evaluating a project that will require an investment of $18 million that will be depreciated over a period of 15 years. You are concerned that the corporate tax rate will increase during the life of the project.
a. Would this increase the accounting breakeven point?
Yes
No
b. Would it increase the NPV breakeven point?
Yes
No
7. Modern Artifacts can produce keepsakes that will be sold for $60 each. Nondepreciation fixed costs are $1,400 per year, and variable costs are $30 per unit. The initial investment of $5,000 will be depreciated straightline over its useful life of 5 years to a final value of zero, and the discount rate is 12%.
a. What is the accounting breakeven level of sales if the firm pays no taxes?
b. What is the NPV breakeven level of sales if the firm pays no taxes?
c. What is the accounting breakeven level of sales if the firm's tax rate is 20%?
d. What is the NPV breakeven level of sales if the firm's tax rate is 20%?
8. You estimate that your cattle farm will generate $.40 million of profits on sales of $8 million under normal economic conditions and that the degree of operating leverage is 2.
a. What will profits be if sales turn out to be $3.3 million?
b. What if they are $12.0 million?
9. Modern Artifacts can produce keepsakes that will be sold for $120 each. Nondepreciation fixed costs are $1,600 per year, and variable costs are $100 per unit. The initial investment of $4,800 will be depreciated straightline over its useful life of 6 years to a final value of zero, and the discount rate is 20%.
a. What is the degree of operating leverage of Modern Artifacts when sales are $15,000?
b. What is the degree of operating leverage when sales are $28,080?
c. Why is operating leverage different at these two levels of sales?
10. A silver mine can yield 11,000 ounces of silver at a variable cost of $32 per ounce. The fixed costs of operating the mine are $44,000 per year. In half the years, silver can be sold for $48 per ounce; in the other years, silver can be sold for only $24 per ounce. Ignore taxes.
a. What is the average cash flow you will receive from the mine if it is always kept in operation and the silver always is sold in the year it is mined?
b. Now suppose you can shut down the mine in years of low silver prices. Calculate the average cash flow from the mine. Assume fixed costs are incurred only if the mine is operating.
11. An auto plant that costs $110 million to build can produce a line of flexfuel cars that will produce cash flows with a present value of $150 million if the line is successful but only $60 million if it is unsuccessful. You believe that the probability of success is only about 40%. You will learn whether the line is successful immediately after building the plant.
a1. Calculate the expected NPV
a2. Would you build the plant?
Yes
No
Suppose that the plant can be sold for $105 million to another automaker if the auto line is not successful.
b1. Calculate the expected NPV.
b2. Would you build the plant?
Yes
No