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Chapter 10
Cash Flow Estimation and Risk Analysis
Problems
1. Erosion costs. Fat Tire Bicycle Company currently sells 40,000 bicycles per year.
The current bike is a standard balloon-tire bike, selling for $90 with a production and
shipping cost of $35. The company is thinking of introducing an off-road bike with a
projected selling price of $410 and a production and shipping cost of $360. The
projected annual sales are 12,000 off-road bikes. The company will lose sales in fattire bikes of 8,000 units per year if it introduces the new bike, however. What is the
erosion cost from the new bike? Should Fat Tire start producing the off-road bike?
2. Erosion costs. Heavenly Cookie Company has the following annual sales and costs
for its current product line:
Heavenly is thinking of adding Mississippi mud brownies to the product line. The
ultra-rich brownies would sell for $0.99 a piece and cost $0.81 to produce. The
forecasted brownie volume is 250,000 per year. Introduction of brownies, however,
will reduce cookie sales by 250,000 with the following drop in sales per cookie:
130,000 in chocolate chip, 60,000 in snickerdoodle, 40,000 in peanut butter, 10,000
in lemon drop, and 10,000 in cream-filled. What is the erosion cost of introducing the
brownies? What is the net change in annual margin if Mississippi mud brownies are
added to the product line?
3. Opportunity costs. Revolution Records will build a new recording studio on a
vacant lot next to the operations center. The land was purchased five years ago for
$450,000. Today the value of the land has appreciated to $780,000. Revolutionary
Records did not consider the value of the land (it had already spent the money to
acquire the land long before this project was considered). The NPV of the recording
studio was $600,000. Should Revolution Records consider the land as part of the
cash flow of the recording studio? If yes, what value should be used, $450,000 or
$780,000? How will the value affect the project?
4. Opportunity cost. Richards’ Tree Farm, Inc. has branched into gardening over the
years and is now considering adding patio furniture to its product lineup. Currently,
the area where the patio furniture is to be displayed is a vacant slab of concrete
attached to the indoor shop. The company originally paid $8,500 to put in the slab of
concrete three years ago. It would now cost $12,000 to put in the same slab of
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concrete. Should Richards consider the concrete slab when expanding its outdoor
garden shop to include patio furniture? If yes, which value should it use?
5. Working capital cash flow. Cool Water, Inc. sells bottled water. The firm keeps in
inventory plastic bottles at 10% of the monthly projected sales. These plastic bottles
cost $0.005 each. The monthly sales for the coming year are as follows:
Show the anticipated cost of plastic bottles each month for these projected sales, the
beginning inventory volume and ending inventory volume each month, and the
monthly increase or decrease in cash flow for inventory given that an increase is a
use of cash and a decrease is a source of cash.
6. Working capital cash flow. Tires for Less is a franchise of tire stores throughout the
greater Northwest. It has projected the following unit sales per tire and costs of tires
for the coming year:
The company policy is to have the next month’s anticipated sales for each tire type in
the warehouse. Shipments are made to the various stores throughout the Northwest
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from the central warehouse. Show the anticipated cost of tires each month for these
projected sales by tire type, the beginning inventory volume and ending inventory
volume each month for each tire, and the monthly increase or decrease in cash flows
for inventory given that an increase is a use of cash and a decrease is a source of
cash. Find the total cost of goods sold and change in monthly working capital cash
flows for all tires. What do you notice about the working capital change when you
combine all four tires?
7. Depreciation expense. Brock Florist Company buys a new delivery truck for
$29,000. It is classified as a light-duty truck.
a. Calculate the depreciation schedule using a five-year life, straight-line
depreciation, and the half-year convention for the first and last years.
b. Calculate the depreciation schedule using a five year life and MACRS
depreciation.
c. Compare the depreciation schedules from parts (a) and (b) before and after
taxes with a 30% tax rate. What do you notice about the difference between
these two methods?
8. Depreciation expense. Richards’ Tree Farm, Inc. has just purchased a new aerial
tree trimmer for $91,000. Calculate the depreciation schedule using the property
class category of a single-purpose agricultural and horticultural structure (from Table
10.3) for both straight line depreciation and MACRS. Use the half-year convention for
both methods. Compare the depreciation schedules before and after taxes using a
40% tax rate. What do you notice about the difference between these two methods?
9. Cost recovery. Brock Florist Company sold their delivery truck in problem (see
Problem 7) after three years of service. If MACRS was used for the depreciation
schedule, what is the after-tax cash flow from the sale of the truck (continue to use
30% tax rate) if
a. the sales price was $15,000?
b. the sales price was $10,000?
c. the sales price was $5,000?
10. Cost recovery. Jake Richards sold the tree trimmer (see Problem 8) after four years
of service. If MACRS was used for the depreciation schedule, what is the after-tax
cash flow from the sale of the trimmer (continue to use a 40% tax rate) if
a. the sales price was $35,000?
b. the sales price was $28,428.40?
c. the sales price was $21,000?
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11. Operating cash flow. Grady Precision Measurement Tools has forecasted the
following sales and costs for a new GPS system: annual sales of 48,000 units at $18
a unit, production costs at 37% of sales price, annual fixed costs for production at
$180,000, and depreciation expense (straight-line) of $240,000 per year. The
company tax rate is 35%. What is the annual operating cash flow of the new GPS
system?
12. Operating cash flow. Huffman Systems has forecasted the following sales for home
alarm systems to be 63,000 units per year at $38.50 per unit. The cost to produce
each unit is expected to be about 42% of the sales price. The new product will have
an additional $494,000 fixed costs each year, and the manufacturing equipment will
have an initial cost of $2,400,000 and will be depreciated over eight years (straightline). The company tax rate is 40%. What is the annual operating cash flow for the
alarm systems if the projected sales and price per unit are constant over the next
eight years?
13. NPV. Using the operating cash flow information in Problem 11, determine whether
Grady Precision Measurement Tools should add the GPS system to its set of
products. The initial investment is $1,440,000 for manufacturing equipment, which
will be depreciated over six years (using straight-line depreciation) and will be sold at
the end of five years for $380,000. The cost of capital is 10%, and the tax rate is still
35%.
14. NPV. Using the operating cash flow information in Problem 12, determine whether
Huffman Systems should add the home alarm system to their set of products. The
manufacturing equipment will be sold off at the end of eight years for $210,000, and
the cost of capital for this project is 14%.
15. Operating cash flow (growing each year; MACRS). Mathews Mining Company is
looking at a project that has the following forecasted sales: first-year sales are 6,800
units and will grow at 15% over the next four years (a five-year project). The price of
the product will start at $124 per unit and increase each year at 5%. The production
costs are expected to be 62% of the current year’s sales price. The manufacturing
equipment to aid this project will have a total cost (including installation) of
$1,400,000. It will be depreciated using MACRS and has a seven-year MACRS life
classification. Fixed costs will be $50,000 per year. Mathews Mining has a tax rate of
30%.What is the operating cash flow for this project over these five years? Hint: Use
a spreadsheet.
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16. Operating cash flow (growing each year; MACRS). Miglietti Restaurants is looking
at a project with the following forecasted sales: first-year sales quantity of 31,000
with an annual growth rate of 3.5% over the next ten years. The sales price per unit
is $42.00 and will grow at 2.25% per year. The production costs are expected to be
55% of the current year’s sales price. The manufacturing equipment to aid this
project will have a total cost (including installation) of $2,400,000. It will be
depreciated using MACRS and has a seven-year MACRS life classification. Fixed
costs will be $335,000 per year. Miglietti Restaurants has a tax rate of 30%.What is
the operating cash flow for this project over these ten years? Hint: Use a
spreadsheet.
17. NPV. Using the operating cash flow information from Problem 15, find the NPV of the
project for Mathews Mining if the manufacturing equipment can be sold for $80,000
at the end of the five-year project and the cost of capital for this project is 12%. Hint:
Use a spreadsheet.
18. NPV. Using the operating cash flow information from Problem 16, find the NPV of the
project for Miglietti Restaurants if the manufacturing equipment can be sold for
$140,000 at the end of the ten-year project and the cost of capital for this project is
8%. Hint: Use a spreadsheet.
19. Project cash flows and NPV. The managers of Classic Autos Incorporated plan to
manufacture classic Thunderbirds (1957 replicas). The necessary foundry equipment
will cost a total of $4,000,000 and will be depreciated using a five-year MACRS life.
Projected sales in annual units for the next five years are 300 per year. If sales price
is $27,000 per car, variable costs are $18,000 per car, and fixed costs are
$1,200,000 annually, what is the annual operating cash flow if the tax rate is 30%?
The equipment is sold for salvage for $500,000 at the end of year five. What is the
after-tax cash flow of the salvage? Net working capital increases by $600,000 at the
beginning of the project (year 0) and is reduced back to its original level in the final
year. What is the incremental cash flow of the project? Using a discount rate of 12%
for the project, determine whether the project be accepted or rejected with the NPV
decision model.
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20. Project cash flows and NPV. The sales manager has a new estimate for the sale of
the classic Thunderbirds in Problem 19. The annual sales volume will be as follows:
Year one: 240
Year two: 280
Year three: 340
Year four: 360
Year five: 280.
Rework the cash flows for operating cash flows with these new sales estimates and find
the internal rate of return for the project using the incremental cash flows.
Challenge question. A spreadsheet is recommended for this question.
a. Recompute your answers to Questions 4 through 7 assuming sales grow at
12% per year.
b. Recompute your answers to Questions 4 through 7 assuming sales grow at
0% per year.
c. Comment on the sensitivity of the NPV to the rate of growth in sales.
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