MANAGEMENT ACCOUNTING
CONCEPTS AND TECHNIQUES
By Dennis Caplan, University
at Albany (State University of New York)
CHAPTER 19: Capital Budgeting
19-1:
A) A project requires an initial cash outlay of $800, and
returns $1,000 at the end of year 3 (nothing at the end of years 1 or 2). What
is the approximately Net Present Value of this project, using a cost of capital
of 10%?
B) A project requires an initial cash outlay of $5,000,
and returns $1,000 at the end of each year from Year 1 through Year 10. What is
the project’s approximate Internal Rate of Return.
C)
Refer to the project in part (B). What is the Payback Period of the
Project? Also, what is the Accounting Rate of Return on the average net investment,
assuming that the $5,000 purchase price is for a machine that is depreciated
using straight-line depreciation over 10 years, with zero salvage value?
19-2: A machine costs $4,000 (paid out at the beginning of year 1), and generates year-end net cash inflows of $2,000 per year for five years (this is the useful life of the machine). The machine has zero salvage value. The company uses straight-line depreciation and a 10% cost of capital.
Required:
A) What is the payback period for this project?
B) What is the net present value of this project?
C) What is the accounting rate of return for this project?
19-3: A company purchases an asset for $40,000. The asset has a useful life of seven years. The salvage value is expected to be $10,000. For purposes of computing the accounting rate of return (i.e., the book rate of return), what is the average net investment in the asset, if the salvage value is used to reduce the depreciable basis of the asset?
19-4: What is the net present value of a project that
requires an initial cash outlay of $1,000, and returns $7,000 at the end of
seven years, using a discount rate of 12%?
19-5: An investment of $400 will yield a single, lump-sum
payoff of $1,000 after 10 years. At a discount rate of 7%, what is the Net
Present Value of this project?
19-6: A machine that costs $1,000 will save $200 in
operating costs every year for the next seven years. What is the approximate
Internal Rate of Return of this capital project?
19-7: A project requires an initial investment of $500, and
will return $100 per year for 11 years. Using a discount rate of 9%, what is
this project’s Net Present Value?
19-8: A machine costs $50,000 (paid out at the beginning of year 1), and generates year-end net cash inflows of $8,834 per year for 12 years (this is the useful life of the machine). The machine has zero salvage value. The company uses straight-line depreciation.
Required:
A) What is the internal rate of return?
B) What is the net present value, using a discount rate of 10%?
C) What is the accounting rate of return?
19-9: Using an 11% discount rate, what is the net present
value of a project that requires cash outlays of $10,000 at the beginning of
years one, three and five, and provides cash inflows of $20,000 at the end of
years one, three and five? You may assume that the present value of a cashflow at the end of year X is equivalent to the cashflow of an equivalent amount at the beginning of year X
+ 1 (e.g., December 31, 2005 is the same as January 1, 2006).
19-10: The Seven Flags over the
Required: Calculate the net present value of the new roller coaster, as of January 1, 2007.
19-11: Consider a capital project with a one-year life. The cash outlay for the equipment occurs at the beginning of year one, and a single cash in-flow occurs at the end of year one. The equipment has zero salvage value. Straight-line depreciation is used. Indicate which of the following statements are true.
Required:
A) If the
payback period is less than one, the net present value will be greater than
zero.
B) The
internal rate of return is half of the accounting (book) rate of return.
C) The
inverse of the payback period equals the internal rate of return plus one.
D) The
payback period is the inverse of the internal rate of return.
E) If the
internal rate of return is greater than the discount rate, the net present
value will be greater than zero.
19-12: Consider the following two possible capital projects:
Project |
Initial Cost (incurred at
beginning of year 1) |
Project Life |
Salvage Value |
Positive annual cash flow
(received at the end of each year) |
A |
$200,000 |
16 years |
$0 |
$28,000 |
B |
$56,000 |
14 years |
$0 |
$9,783 |
Using the above information, it can be shown that the
Internal Rate of Return of Project B is higher than the Internal Rate of Return
of project A.
Required:
A)
Is the NPV for Project A higher than, equal to, or lower than, the NPV
for Project B, assuming a 10% discount rate?
B)
Is the Payback Period for Project A better than, equal to, or worse
than, the Payback Period for Project B?
C)
Is the Accounting Rate of Return for Project A higher than, equal to,
or lower than, the Accounting Rate of Return for Project B, assuming
straight-line depreciation?
D) If
the discount rate is 11% instead of 10%, which project has the higher NPV?
E) If the discount
rate is 10%, and both projects have a salvage value of $66,000 (i.e., the
equipment for Project B actually appreciates),
which project would have the higher NPV?
19-13: A machine with a useful life of five years and a
salvage value of $4,000 is purchased for $20,000. The benefit of the machine is
that it reduces normal cash operating expenses by $5,000 per year during the
first two years of the machine’s life, and by $4,000 for each of the following
three years.
Required:
A) Calculate the accounting rate of return for the
project, assuming that the full $20,000 purchase price is depreciated using the
straight-line method, so that at the end of year five, the machine has a book
value of zero, and the salvage value is treated as income in year five.
B) Calculate the accounting rate of return for the project, assuming that the net cost of the machine (purchase price less salvage value) is depreciated using the straight-line method.
19-14: Plain Vanilla Industries purchases a machine for
$120,000. The machine has a six year life and a salvage value of zero. The
company depreciates the machine using the sum-of-the-years-digits method, which
results in depreciation expense in each year as follows:
Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 |
$34,286 28,571 22,857 17,143 11,429 5,714 $120,000 |
The machine increases cash inflows to the firm by
$30,000 in year one, $35,000 in year two, $40,000 in year three, $35,000 in
year four, and $25,000 in year five.
Required: Calculate the accounting rate of return from the
investment in the machine.
19-15: A machine can be purchased for $120,000 that increases
cash flows by $20,000 each year for the next six years. In addition, the
machine has a salvage value of $20,000, which is used to reduce the depreciable
basis of the asset. Assume the purchase price is paid at the beginning of the
first year, and that all cash inflows are received at the end of each year. The
company uses sum-of-the-years-digits depreciation, which results in the
following depreciation schedule:
Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 |
$28,571 23,810 19,048 14,286 9,524 4,761 |
Required: Compute the Accounting Rate of Return.
19-16: A company is considering purchasing a machine that will
reduce its operating costs. The purchase requires a down payment of $5,000, and
three equal annual payments of $3,000, due at the beginning of the second,
third and fourth years of the life of the machine. The machine will reduce
operating expenses in an amount equivalent to $2,000 received at the end of
each year for eight years. The machine has a useful life of eight years, at the
end of which it has a salvage value of $1,500. The company records the purchase
of the machine at $14,000 (i.e., interest expense is not imputed), and treats
the salvage value as a reduction in the depreciable basis of the asset. The
asset is depreciated using straight-line depreciation. The discount rate is 8%.
Required: Calculate the payback period, the net present value, and the average accounting rate of return.
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Management
Accounting Concepts and Techniques; copyright 2006; most recent update:
November 2010
For a printer-friendly version, contact Dennis Caplan at dcaplan@uamail.albany.edu