Blank L., Tarquin A. Engineering Economy (McGraw-Hill Series in Industrial Engineering and Management)
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SECTION 16.6
Depletion Methods
MACRS simplifies depreciation computations, but it removes the flexibility
of
model selection for a business or corporation. In general, an economic com-
parison that includes depreciation may be performed more rapidly and usually
without altering the final decision by applying the classical straight-line model,
in
lieu
of
MACRS,
to
the cash flow estimates.
16.5 DETERMINING THE MACRS RECOVERY PERIOD
The expected useful I ife
of
property
is
estimated in years and used as the n value in
alternative evaluation and in depreciation computations. For book depreciation the
n value should be the expected useful life. However, when the depreciation will be
claimed as tax deductible, the n value should be lower. The advantage
of
a recov-
ery period shorter than the anticipated useful life is leveraged by the accelerated
depreciation models which write off more
of
the basis B in the initial years. There
are tables which assist in determining the life and recovery period for tax purposes.
The
U.S. government requires that all depreciable property be classified into a
property class which identifies its MACRS-allowed recovery period. Table
16-4,
a summary
of
material from IRS Publication 946, gives examples
of
assets and
the MACRS n values. Virtually any property considered in an economic analysis
has a MACRS
n value
of
3,5,7,
10, 15, or 20 years.
Table
16-4
provides two MACRS n values for each property. The first is the
general depreciation system
(GDS) value, which we use in examples and prob-
lems. The depreciation rates
in
Table
16-2
correspond to the n values for the GDS
column and provide the fastest write-off allowed. The rates utilize the DDB method
or the
150% DB method with a switch to SL depreciation. Note that any asset not
in a stated class
is
automatically assigned a 7-year recovery period under GDS.
The far right column
of
Table
16-4
lists the alternative depreciation system
(ADS) recovery period range. This alternative method allows the use
of
SL de-
preciation over a longer recovery period than the GDS. The half-year conven-
tion applies, and any salvage value is neglected, as it
is
in regular MACRS. The
use
of
ADS is generally a choice left to a company, but it
is
required for some
special asset situations. Since it takes longer to depreciate the asset, and since the
SL model
is
required (thus removing the advantage
of
accelerated depreciation),
ADS is usually not considered an option for the economic analysis. This elec-
table SL option
is,
however, sometimes chosen by businesses that are young and
do not need the tax
benefit
of
accelerated depreciation during the first years
of
operation and asset ownership.
If
ADS is selected, tables
of
d,
rates are available.
16.6 DEPLETION METHODS
Up to this point, we have discussed depreciation for assets that can
be
replaced.
Depletion, though similar to depreciation, is applicable only to natural resources.
When the resources are removed, they cannot be replaced or repurchased in the
same manner as can a machine, computer, or structure. Depletion is applicable to
natural deposits removed from mines, wells, quarries, geothermal deposits,
forests, and the like. There are two methods
of
depletion-cost
depletion and
545
546
CHAPTER
16
Depreciation Methods
TABLE
16-4
Example MACRS Recovery Periods for Various Asset
Descriptions
Asset Description (Personal and Real Property)
Special manufacturing and handling
devices, tractors, racehorses
Computers and peripherals, oil and gas drilling
equipment, construction assets, autos, trucks,
buses, cargo containers, some manufacturing
equipment
Office furniture; some manufacturing
equipment; railroad cars, engines, tracks;
agricultural machinery; petroleum and
natural gas equipment;
all property
not in another class
Equipment for water transportation,
petroleum refining, agriculture product
processing, durable-goods manufacturing,
ship building
Land improvements, docks, roads, drainage,
bridges, landscaping, pipelines, nuclear
power production equipment, telephone
distribution
Municipal sewers, farm buildings, telephone
switching buildings, power production
equipment (steam and hydraulic), water
utilities
Residential rental property (house,
mobile home)
Nonresidential real property attached to
the land, but not the land itself
GDS
3
5
7
10
15
20
27
.5
39
MACRS
n Value, Years
ADS Range
3-5
6-9.5
10-15
15-19
20-24
25-50
40
40
percentage depletion. Details for U.S. taxes are provided in IRS Publication 535,
Business Expenses.
Cost depletion,
sometimes referred to as factor depletion, is based on the level
of
activity or usage, not time, as in depreciation.
It
may be applied to most types
of
natural resources.
The
cost depletion factor for year
t,
denoted by PI' is the
ratio
of
the first cost
of
the resource to the estimated number
of
units recoverable.
first cost
p =
[1~1~
I resource capacity
The annual depletion charge is
PI
times the year's usage or volume. The total cost
depletion cannot exceed the first cost
of
the resource.
If
the capacity
of
the property
SECTION 16.6
Depletion Methods
is
reestimated some year in the future, a new cost depletion factor is determined
based upon the undepleted amount and the new capacity estimate.
EXAM
PLE
16.5
,I,
Temple-Inland Corporation has negotiated the rights
to
cut timber on privately held for-
est acreage for
$700,000. An estimated 350 million board feet
of
lumber are har-
vestable.
(a) Determine the depletion amount for the first 2 years if
15
million and 22 million
board feet are removed.
(b) After 2 years the total recoverable board feet was reestimated to be
450
million
from the time the rights were purchased. Compute the new cost depletion factor
for years 3 and later.
Solution
(a) Use Equation [16.15] for
PI
in
dollars per million board feet.
$700,000 .
PI
= 350 = $2000 per mIllion board feet
Multiply
PI
by the annual harvest to obtain depletion
of
$30,000 in year 1 and
$44,000
in
year
2.
Continue using
PI
until a total
of
$700,000 is written off.
(b) After 2 years, a total
of
$74,000 has been depleted. A new
P,
value must be calcu-
lated based on the remaining
$700,000 - 74,000 = $626,000 investment.
Additionally, with the new estimate
of
450 million board feet, a total
of
450 -
15
- 22 = 413 million board feet remain. For years t = 3, 4,
..
. , the cost
depletion factor is
$626,000
PI
= 413 = $1516 per million board feet
Percentage depletion, the second depletion method, is a special consideration
given for natural resources. A constant, stated percentage
of
the resource's gross
income may be depleted each year provided it does not exceed
50%
of
the com-
pany's taxable income. For oil and gas property, the limit is 100%
of
taxable in-
come. The annual depletion amount is calculated as
Percentage depletion amount = percentage
x gross income from property [16.16]
Using percentage depletion, total depletion charges may exceed first cost with no
limitation. The U.
S.
government does not generally allow percentage depletion
to
be applied
to
oil and gas wells (except small independent producers)
or
timber.
The depletion amount each year may be determined using either the cost
method or the percentage method, as allowed by law. Usually, the percentage
depletion amount
is
chosen because
of
the possibility
of
writing off more than the
original cost. However, the law also requires that the cost depletion amount be
547
548
CHAPTER
16
Depreciation Methods
chosen
if
the percentage depletion
is
smaller in any year.
The
guideline is:
Calculate both
amounts-cost
depletion ($Depl)
and
percentage deple-
tion (%
Depl)-and
apply
the
following logic each year.
. { % Depl
if
% Depl
2:
$Depl
Annual depletIOn
= $Depl
if
%Depl < $Depl
[16.17]
The
annual percentage depletion for some common natural deposits
is
listed
below for
U.S. tax law. These percentages may change from time to time.
Deposit
Sulfur, uranium, lead, nickel, zinc,
and some other ores and minerals
Gold, silver, copper, iron ore,
and some oil shale
Oil and natural gas wells (varies)
Coal, lignite, sodium chloride
Gravel, sand, peat, some stones
Most other minerals, metallic ores
Percentage
22%
15
15-22
10
5
14
A gold mine was purchased for $10 million. It has an anticipated gross income
of
$5.0
million per year for years I to 5 and $3.0 million per year after year 5. Assume that de-
pletion charges do not exceed 50%
of
taxable income. Compute annual depletion
amounts for the mine. How long will it take to recover the initial investment at
i = O%?
Solution
A 15% depletion applies
to
gold. Depletion amounts are
Years 1 to
5:
Years thereafter:
0.15(5.0 million) = $750,000
O.
I 5(3.0 million) = $450,000
A total
of
$3.75 million is written off
in
5 years, and the remaining $6.25 million
is
writ-
ten off at
$450,000 per year. The total number
of
years
is
5 + $6.25 million = 5 + 13.9 = 18.9
$450,000
In
19
years, the initial investment could be fully depleted.
CHAPTER SUMMARY
Depreciation may be determined for internal company records (book depreciation)
or for income tax purposes (tax depreciation). In the
U.S., the MACRS method
is
the only one allowed for tax depreciation. In many other countries, straight line
and declining balance methods are applied for both tax and book depreciation.
Depreciation does not result in actual cash flow directly. It is a book method by
CHAPTER SUMMARY
which the capital investment
in
tangible property is recovered. The annual depre-
ciation amount is tax deductible, which can result in actual cash flow changes.
Some
important points about the straight line, declining balance,
and
MACRS
models are presented below.
Common
relations for each method are summarized
in Table
16-5.
Straight
Line (SL)
• It writes
off
capital investment linearly over n years.
• The estimated salvage value is always considered.
• This
is
the classical, non accelerated depreciation model.
Declining Balance (DB)
• The model accelerates depreciation compared to straight line.
• The book value is reduced each year by a fixed percentage.
• The most used rate is twice the
SL
rate, which is called double declining bal-
ance (DDB).
• It has
an
implied salvage that may be lower than the estimated salvage.
•
It
is not
an
approved tax depreciation method in the United States. It is fre-
quently used for book depreciation purposes.
Modified Accelerated Cost Recovery System (MACRS)
• It is the only approved tax depreciation system in the United States.
• It automatically switches from
DDB
or
DB to
SL
depreciation.
• It always depreciates to zero; that is, it assumes S =
o.
• Recovery periods are specified by property classes.
• Depreciation rates are tabulated.
• The actual recovery period
is
1 year longer due to the imposed half-year con-
vention.
• MACRS straight line depreciation is an option, but recovery periods are
longer than for regular
MACRS.
Cost and percentage depletion
method
s recover investment
in
natural re-
sources. The annual cost depletion factor is applied to the amount
of
resource re-
moved. No more than the initial investment can be recovered with cost depletion.
Percentage depletion, which can recover more than the initial investment, re-
duces the investment value by a constant percentage
of
gross income each year.
TABLE
16-5
Summary
of
Common Depreciation Method Relations
Model
MACRS
Sl
DDS
Fixed depreciation rate d
Not defined
1 2
-
n
n
Annual rate
d,
Table
16-2
d
(1
- d)r-1
n
Annual depreciation D,
d,8
8-S
d(
BV
t
_
l
)
n
Book vallle BV,
BV,_,
- D,
B -
tD
t
8CI
-d)'
549
550
CHAPTER
16
Depreciation Methods
PROBLEMS
Fundamentals
of
Depreciation
16.1 Write another term that may be used in
lieu
of
each
of
the following that has the
same interpretation
in
asset deprecia-
tion:
depreciation rate,
fair
market value,
recovery period, and tangible property.
16.2 State the difference between book depre-
ciation and tax depreciation.
16.3 Explain why the recovery period used for
tax depreciation purposes may be differ-
ent from the estimated
n value
111
an
engineering economy study.
16.4 Explain why
in
the United States the ex-
plicit consideration
of
depreciation and
income taxes
in
an
engineering economy
study may make a difference
in
the deci-
sion to accept
or
reject an alternative to
acquire a depreciable asset.
16.5 Visit the
U.S. Internal Revenue Service
website at www.irs.gov, and answer the
following questions about depreciation
and
MACRS
by consulting online the
current version
of
Publication 946,
How
to Depreciate Property.
(a) What
is
the definition
of
deprecia-
tion according to the IRS?
(b) What
is
the description
of
the term
salvage value?
(c)
What are the two depreciation sys-
tems within MACRS, and what are
the major differences between
them?
(d)
What are the properties listed that
cannot be depreciated under
MACRS?
16.6 Visit the Canada Customs and Revenue
Agency website at ccra-adrc.gc.caltax
and answer the following questions about
depreciation in Canada, using the glos-
sary under the
taxes-businesses
section.
(a) What is the definition
of
depre-
ciation?
(b)
What
is capital cost allowance
(CCA) and what is the closest equiv-
alent term
in
the U.S. system
of
depreciation?
(c)
What
is
the complete definition
of
real property?
16.7 Status Corporation purchased for
$350,000 a new numerical controller
during the last month
of
2002. Extra in-
stallation costs were
$40,000. The recov-
ery period was 7 years with an estimated
salvage value
of
10%
of
the original pur-
chase price. Status sold the system at the
end
of
2005 for $45,000.
(a) What are the values needed to de-
velop a depreciation schedule at
purchase time?
(b) State the numerical values for the
following: remaining life at sale
time, market value in
2005, book
value at sale time
if
65%
of
the un-
adjusted basis had been depreciated.
16.8 A
$100,000 piece
of
testing equipment
was installed and depreciated for 5 years.
Each year the end-of-year book value
decreased at a rate
of
10%
of
the book
value at the beginning
of
the year.
The
system was sold for $24,000 at the end
of
5 years.
(a) Compute the amount
of
the annual
depreciation.
(b) What is the actual depreciation rate
for each year?
(c) At the time
of
sale, what
is
the dif-
ference between the book value and
the market value?
(d)
Plot the book value for each
of
the
5 years.
/
16
.9 An asset with an unadjusted basis
of
$50,000 was depreciated over n
tax
=
10
years for tax depreciation purposes and
over n
book
= 5 years for book depreciation
purposes. The annual depreciation was
lin
using the relevant life value. Use
Excel to plot on one graph the annual book
value for both methods
of
depreciation.
Straight Line Depreciation
16.10 Home Health Care, Inc. (HHCI) pur-
chased a new sonargram imaging unit for
$300,000 and had it mounted on a truck
body for an additional
$100,000, includ-
ing the truck chassis. The unit-truck sys-
tem will be depreciated as one asset. The
functional life is 8 years, and salvage is
estimated at
10%
of
the purchase price
of
the imaging unit. (a) Use classical
straight line depreciation and hand calcu-
lations to determine the salvage value,
annual depreciation, and book value after
4 years.
(b)
Develop the cell reference
worksheet
in
Excel to obtain the answers
in
part (a) for the original data. (c) Use
your Excel worksheet to determine the
answers, if the sonargram unit cost goes
up to
$350,000 and the expected life is
decreased to 5 years.
16.
I I Air handling equipment that costs
$12,000 has a life
of
8 years with a $2000
salvage value. (a) Calculate the straight
line depreciation amount for each year.
(b) Determine the book value after 3 years.
(c) What
is
the rate
of
depreciation?
16.12 As asset has an unadjusted basis
of
$200,000, a salvage value
of
$10,000,
and a recovery period
of
7 years. Write a
single-cell Excel function to display the
book value after 5 years
of
straight line
depreciation.
16.
13
Simpson and Jones Pharmaceuticals pur-
chased a prescription drug tablet-forming
machine
in
2004 for $750,000. They had
PROBLEMS 5
51
planned to use the machine for
10
years,
but due to rapid obsolescence it should
be retired after 4 years. Develop the
spreadsheet for depreciation and book
value amounts necessary to answer the
following.
(a) What is the amount
of
capital in-
vestment remaining when the asset
is retired due to obsolescence?
(b)
If
the asset is sold at the end
of
4 years for $75,000, what
is
the
amount
of
capital investment lost
based on straight line depreciation?
(c)
If
the new technology machine has
an estimated cost
of
$300,000, how
many more years should the com-
pany retain and depreciate the cur-
rently owned machine to make its
book value and the first cost
of
the
new machine equal?
16.14 A special-purpose computer workstation
has
B = $50,000 with a 4-year recovery
period. Tabulate and plot the values for
SL
depreciation, accumulated deprecia-
tion, and book value for each year if
(a) there is no salvage value and
(b)
S =
$16,000. (c) Use a spreadsheet to solve
this problem.
16.
15
A company owns the same asset in a U.S.
plant and in a EU plant. It has B =
$2,000,000 with a salvage value
of
20%
of
B.
For tax depreciation purposes, the
United States allows a straight line write-
off over 5 years, while the
EU
allows
write-off over 8 years. The general man-
agers
of
the two plants want to know the
difference
in
(a) the depreciation amount
for year 5 and
(b) the book value after
5 years.
Use Excel and write cell equations
in only two cells to answer these questions.
Declining Balance Depreciation
16.16 For the declining balance method
of
depre-
ciation, explain the differences between
552
CHAPTER
16
Depreciation Methods
the three rates: fixed percentage rate d,
d
m
ax
, and the annual recovery rate
dr.
16.
17
New equipment to read 96-bit product
codes that are replacing old bar codes
is
to be purchased by General Food Stores.
As a trial,
1000
of
the items will be ini-
tially purchased.
The
DDB IlJethod will
be used to depreciate the total amount
of
$50,000
over
a 3-year recovery period.
Calculate and plot the accumulated de-
preciation and book value curves
(a) by
hand and
(b)
by
computer.
16.18 An asset has a first cost
of
$12,000, a
recovery period
of
8 years, and an esti-
mated salvage value
of
$2000. (a) Use a
spreadsheet to develop the depreciation
schedule for both the
SL
and DDB meth-
ods.
Plot the book value for SL and DDB
depreciation on a single
xy
scatter chart.
(b) Calculate the DDB annual deprecia-
tion rate for each
of
the years 1 through
8.
16
.19 A warehouse costs $800,000 to construct
for Ace Hardware.
It
has a IS-year life
with an estimated resale value
of
80%
of
the construction cost. However, the build-
ing will be depreciated to zero over a re-
covery period
of
30 years. Calculate the
annual depreciation charge for years 5,
10, and 25, using (a) straight line depreci-
ation and
(b)
DDB depreciation. (c) What
is
the implied salvage value for
DDB?
16.20 Allison and Carl are civil engineers who
own a soil and water analysis business
for which they have purchased computer
equipment for
$25,000. They do not ex-
pect the computers
to
have a positive
salvage or trade-in value after the antici-
pated 5-year life. For book depreciation
purposes, they want book value sched-
ules for the following methods: SL, DB,
and DDB. They want to use a fixed
depreciation rate
of
25% annually for the
DB model. Use a spreadsheet or hand
computation to develop the schedule
s.
16.21 Equipment for immersion cooling
of
electronic components has
an
installed
value
of
$182,000 with an estimated
trade-in value
of
$50,000 after
18
years.
(a) For years 2 and 18, determine the an-
nual depreciation charge using DDB de-
preciation and DB depreciation by hand.
(b)
Use a spreadsheet to answer the ques-
tions above and to determine the year
in
which the estimated salvage value
of
$50,000
is
reached for DDB depreciation.
16.22
Use the estimates B = $182,000, S =
$50,000, and n = 18 years (from Prob-
lem 16.21) to write the Excel DDB func-
tion to determine the depreciation
in
year 18, using the implied depreciation
rate.
16.23 For book depreciation purposes, declin-
ing balance depreciation at a rate
of
1.5
times the straight line rate
is
used for au-
tomated process control equipment with
B = $175,000, n = 12, and S = $32,000.
(a) Compute the depreciation and book
value for years 1 and 12.
(b) Compare the
estimated salvage value and the book
value after 12 years.
(c) Write the
DDB
function for Excel to calculate the depre-
ciation each year.
MA
CRS Depreciation
16.24 (a) Develop a spreadsheet template to
calculate the
MACRS
depreciation
for any value
of
B and all allowed
recovery periods.
(b)
Test your template
by
determining
the depreciation schedule for
B =
$10,000 for n = 3 and n = to years.
16.25 Give at least two specific examples each
of
personal property and real property
that must be depreciated by the MACRS
method.
16.26 Zahra
is
a civil engineer working for
Halcrow Engineering Consultants in the
Middle East where the straight line
method and (in some countries) the de-
clining balance method
of
depreciation
are utilized.
She is about to conduct an
after-tax analysis that involves a
$500,000, lO-year-life piece
of
equip-
ment where accelerated write-off
of
the
capital investment
is
very important.
The
estimated salvage value
is
$100,000. To
show her the effect
of
different methods,
calculate the first-year depreciation for
the following methods: classical
SL,
DDB, 150% DB, and MACRS.
16.27 Claude
is
an engineering economist with
Reynolds. A new
$30,000 personal prop-
erty asset
is
to be depreciated using
MACRS over 7 years.
The
salvage value
is
expected to be $2000.
(a)
Compare the
book values for
MACRS depreciation
and classical
SL
depreciation over
7 years.
(b)
Plot the book values, using a
spreadsheet.
16
.28 An asset for a U.S.-based commercial
farm corporation was purchased for
$50,000 and has a 7-year useful life and
an expected resale value
of
20%
of
the
first cost. An abbreviated recovery pe-
riod
of
5 years is allowed by
MACRS.
(a) Prepare the MACRS annual deprecia-
tion schedule and book values.
(b) Com-
pare these results with
DDB
depreciation
and book value over n
= 7 years that may
be determined
in
another country. (c) De-
velop two Excel
xy
scatter charts for the
comparisons above.
16.29 An automated assembly robot that cost
$450,000 installed has a depreciable life
of
5 years and no salvage value. An ana-
lyst
in
the financial management depart-
ment used classical
SL
depreciation to
determine end-of-year book values for
PROBLEMS 553
the robot when the original economic
evaluation was performed.
You
are now
performing a replacement analysis after
3 years
of
service and realize that the
robot should have been depreciated using
MACRS with n = 5 years. What
is
the
amount
of
the difference
in
the book
value caused by the classical
SL
method
after the 3 years?
16.30 Develop the
MACRS
depreciation
schedule for a commercial building
purchased by Alpha Enterprises for
$1,800,000.
16.31 Bowlers.com has installed $100,000 worth
of
depreciable software and equipment
that represents the latest in Internet team-
ing and bowling, intended to allow the
bowler to enjoy the sport on the Web
or
at
the alley. No salvage value
is
estimated.
The
company can depreciate using
MACRS for a 5-year recovery period
or
opt for the ADS alternative system over
10 years using the straight line model.
The
SL rates require the half-year con-
vention; that is, only
50
%
of
the regular
annual rate applies for years
I and I
I.
(a) Construct the book value curves for
both models on
one
graph. Answer by
hand
or
by computer.
(b)
After 3 years
of
use, what is the percentage
of
the
$100,000 basis removed for each model?
16.32 A company has purchased special-
purpose equipment for the manufacture
of
rubber products (asset class 30.11
in
IRS Publication 946) and expects to use it
predominately outside the United States.
In this case, the
ADS alternative to
MACRS is required for tax depreciation
purposes.
The
manager wants to under-
stand the difference in the yearly recovery
rates for classical
SL,
MACRS,
and the
ADS alternative to
MACRS
. Using a re-
covery period
of
3 years, except for the
554
CHAPTER 16 Depreciation Methods
ADS alternative which requires a 4-year
SL recovery with the half-year conven-
tion included, prepare a single graph
showing the annual recovery rates (in
percent) for the three methods.
16.33 Explain why shortened recovery periods
coupled with higher depreciation rates in
the initial years
of
an asset's life may be
financially advantageous to a corporation.
Depletion
16
.34 When WTA Corporation purchased rights
to
extract silver from a mine for a total
price
of
$1.1 million 3 years ago, an esti-
mated
350,000 ounces
of
silver was
to
be
removed over the next
10
years. A total
of
175,000 ounces has been removed
and sold thus
far.
(a) What
is
the total
cost depletion allowed over the 3 years?
(b) New exploratory tests indicate that
only
an
estimated 100,000 ounces remain
in the veins
of
the mine. What is the cost
depletion factor applicable for the next
year?
(c)
If
an
additional 35,000 ounces
is
extracted this year and sold at
an
average
of $5.50 per ounce, determine
if
the cost
depletion amount or percentage depletion
amount is allowed for
U.S. income tax
purposes. Assume that
50%
of
the com-
pany's taxable income is not exceeded.
16.35 A company owns copper mining opera-
tions in several states.
One mine has
the taxable income and sales results
FE
REVIEW PROBLEMS
16.37 A machine with a 5-year life has a first
cost
of
$20,000 and a $2000 salvage
value. Its annual operating cost is
$8000 per year. According to the classi-
cal straight line method, the depreciation
Year
2
3
following. Determine the annual percent-
age depletion for the mine.
Use 2000
pounds per ton.
Taxable Sales, Sales Price,
Income, $ Tons
$/Pound
1,500,000
2000 0.80
2,000,000 4500
0.78
1,000,000 2300
0.65
16.36 A highway construction company has
operated a quarry for the past 5 years.
During this time the following tonnage
has been extracted each year:
60,000;
50,000; 58,000; 60,000;
and 65,000 tons.
The mine is estimated
to
contain a total
of
2.5 million tons
of
usable stones and
gravel. The quarry land had an initial cost
of
$3.2 million. The company had a per-
ton gross income
of
$30 for the first year,
$25 for the second year, $35 for the next
2 years, and
$40 for the last year.
(a) Compute the depletion charges each
year, using the larger
of
the values
for the two depletion methods.
(b) Compute the percent
of
the initial
cost that has been written off
in
these 5 years, using the depletion
charges in part
(a).
(c) Use a spreadsheet
to
answer parts
(a) and (b).
(d)
If
the quarry operation
is
reevalu-
ated after the first 3 years
of
opera-
tion and estimated
to
contain
an
-
other 1.5 million tons, rework parts
(a) and (b).
charge in year 2 is nearest to
(a) $3600
(b) $4000
(c) $11,600
(d)
$12,000