1. The gold mine is expected to be exhausted within 20 years. With annual costs of $750,000 and $120/ton, it earns $450/ton and has annual output of 25,000 tons. The property valuation is $53,745,535.
2. The timber land was bought for $8,000,000 and sold for $200,000 after 14 years of $1,400,000 average annual profits. The investment rate is 13.2%.
3. For a company with 4 machines, the total annual straight-line depreciation charge is $49,600 by group depreciation and $47,666.67 by composite depreciation.
Decoding the Tweet _ Practical Criticism in the Age of Hashtag.pptx
Gold Mine Valuation and Depreciation Calculations
1. 1. A gold mine in Mount Province has an annual output of 25,000 tons of ore. It is expected that
the ore body will be exhausted within a period of 20 years. The management cost annually is
P750,000 , and the operating cost of the mine and the smelter plants is P120 per ton. The
processed ore produce an income of P450 per ton. If the annual dividend rate is 12% payable
annually,andthe sinkingfundrate is9% annually,determine the valuation of the propertynow.
GIVEN:
n = 20 r = 12% i = 9%
REQ’D:
P = ?
SOLUTION:
Annual gross income = (25000)(P450) = P11, 250, 000
Annual management and operating costs = P750, 000 + 25000(120) = P3, 750, 000
R = P11, 250, 000 - P3, 750, 000 = P7, 500 000
𝑃 =
𝑅
𝑟 + ( 𝐴 𝐹⁄ ,9%, 𝑛)
=
7500000
0.12 + 0.0195 4648
= P53, 745, 535. 31 ans.
2. Timber land in Palawan was purchased for P8,000,000 and earned an average annual profit of
P1,400,000 for 14 years,at the endof whichtime the landwas sold for P200,000. Assuming that
a sinkingfundearning7%wasestablishedto provide for depletion, determine the investment
rate.
GIVEN:
n = 14 years i = 7% R = P1, 400, 000
REQ’D:
r = ?
SOLUTION:
𝑃 = 8,000,000 − 200,000(1.07 )−14
= P7, 922, 436.55
𝑃 =
𝑅
𝑟 + (𝐴 𝐹, 𝑖%, 𝑛)⁄
𝑟 =
𝑅
𝑃
− (𝐴 𝐹⁄ , 𝑖%, 𝑛)
𝑟 =
1400000
7922436.
−
0.07
(0.0771)14 − 1
= 𝟎. 𝟏𝟑𝟐
r = 13.2%
3. The San FernandoManufacturingCompany owns four different production machine with data
tabulated below :
Machine Number Number Owned First Cost Salvage Value Expected Life
1 8 P40, 000 P12, 000 12
2 6 32, 000 8, 000 10
3 4 18, 000 4, 000 10
4 4 24, 000 6, 000 8
2. One-half of the machines of the kindwillbe replacedafter8yearsand the restwill be sold after
12 years. Compute the total annual straight-line depreciation charges by (a) the group
depreciation method, and (b) the composite depreciation method.
SOLUTION:
a.) Group Depreciation Method
𝐴𝑉𝐸𝑅𝐴𝐺𝐸 𝐷𝐸𝑃𝑅𝐸𝐶𝐼𝐴𝑇𝐼𝑂𝑁 =
12 + 10 + 10 + 8
4
= 𝟏𝟎 𝒚𝒆𝒂𝒓𝒔
𝐴𝑁𝑁𝑈𝐴𝐿 𝐺𝑅𝑂𝑈𝑃 𝐷𝐸𝑃𝑅𝐸𝐶𝐼𝐴𝑇𝐼𝑂𝑁 =
𝑇𝑂𝑇𝐴𝐿 𝐷𝐸𝑃𝑅𝐸𝐶𝐼𝐴𝑇𝐼𝑂𝑁 𝐴𝑀𝑂𝑈𝑁𝑇
𝐴𝑉𝐸𝑅𝐴𝐺𝐸 𝐿𝐼𝐹𝐸
=
8(40000) − 12000) + 6(32000 − 8000) + 4(18000 − 4000) + 4(24000 − 6000)
10
=
496000
10
= 𝐏𝟒𝟗, 𝟔𝟎𝟎 𝒑𝒆𝒓 𝒚𝒆𝒂𝒓
𝐴𝑁𝑁𝑈𝐴𝐿 𝐷𝐸𝑃𝑅𝐸𝐶𝐼𝐴𝑇𝐼𝑂𝑁 𝑀𝐴𝐶𝐻𝐼𝑁𝐸⁄ =
49000
8 + 6 + 4 + 4
= 𝐏𝟐𝟐𝟓𝟒. 𝟓𝟓 𝑴𝑨𝑪𝑯𝑰𝑵𝑬⁄
DEPRECIATION FOREACH YEAR IS SHOWN IN THE TABLE BELOW.
YEAR NUMBER IN SERVICE ANNUALDEPRECIATION ACCOMULATED
1 2 3 4 DEPRECIATION
1 – 8 8 6 4 4 P49, 600 P396, 400
9 – 12 4 3 2 2 P24, 000.05 P198, 400.40
P595, 200.05
DEPRECIATION FORYEARS 9 – 12 = P2254.55(4 + 3 + 2 + 2) = P24, 800.05
b.) Composite DepreciationMethod:
The annual depreciationamountsforeachmachine are:
𝐷1 =
8(40000 − 12000)
12
= 𝐏𝟏𝟖, 𝟔𝟔𝟔. 𝟔𝟕 𝒚𝒆𝒂𝒓⁄
𝐷2 =
6(32000 − 8,000)
10
= 𝐏𝟏𝟒, 𝟒𝟎𝟎 𝒚𝒆𝒂𝒓⁄
𝐷3 =
4(18000 − 4000)
10
= 𝐏𝟓, 𝟔𝟎𝟎 𝒚𝒆𝒂𝒓⁄
𝐷4 =
4(24,000 − 6000)
8
= 𝐏𝟗, 𝟎𝟎𝟎 𝐲𝐞𝐚𝐫⁄
Composite Depreciationamounts:
Years 1 – 8:
P18, 600.67 + P14, 400 + P5, 600 + P9, 000 = P47, 666.67
AccumulatedDepreciationafter8years= 8(47, 666.67) = P381, 333.36
Years 9 – 10:
18, 666.67 + P14, 400 + P5, 600 = P38, 666.67
AccumulatedDepreciationafter10years= P381, 333.36 + 2(38, 666.67) = P458, 666.70
3. Years 11 – 12: (Machine 1 only)
AccumulatedDepreciationafter12 years= P450, 666.70 + 2(P18, 666.67) = P496, 000.00
The total accumulateddepreciationbyeithermethodafter12years= P496, 000.00
4. A firm plans to market a new minicomputer that will sell for $10,000. This financing scheme is
being considered by the company: Payments of $872 each year for 20 years would be made by
the purchaser after an initial down payment is made. If their interest is charge is 6%
compounded monthly, what down deposit should the company request?
GIVEN:
Cost = $10, 000
A =$872
n = 20 years
i = 6% compounded monthly
REQ’D:
DOWN DEPOSIT = ?
SOLUTION:
𝐸𝑅 = [1 + (
0.06/12
12
)12 − 1]
𝐶𝑂𝑆𝑇 = 𝐷𝑂𝑊𝑁 𝐷𝐸𝑃𝑂𝑆𝐼𝑇 + 𝐴( 𝑃 𝐴⁄ , 𝑖, 𝑛)
1000 = 𝐷𝑂𝑊𝑁 𝐷𝐸𝑃𝑂𝑆𝐼𝑇 + 872 [
(1 + 0.06167781)20 − 1
0.061617781(1 + 0.06167781)20
]
𝐷𝑂𝑊𝑁 𝐷𝐸𝑃𝑂𝑆𝐼𝑇 = 10000 − 9866.95
𝑫𝑶𝑾𝑵 𝑫𝑬𝑷𝑶𝑺𝑰𝑻 = $𝟏𝟑𝟑.𝟎𝟓
5. A man deposit $2,000 an a savings account when his son was born. The nominal interest rate
was 8% per year, compounded continuously. On the son’s birthday, the accumulated sum is
withdrawn from the account. How much would this accumulated amount be?
GIVEN:
P = $2000
Nominal rate of interest = 8% per year compound continuously
N = 18
REQ’D:
F = ?
SOLUTION:
𝐸𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑅𝑎𝑡𝑒 𝑜𝑓 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 = 𝑒0.08 – 1 = 0.0832 8708
𝐹 = 𝑃(1 + 𝑖) 𝑛
𝐹 = $2000(1 + 0.08333)18
F = $8, 441
4. 6. Maintenance costs for a new bridge with an expected 50-year life are estimated to be $1,000
each yearfor the first5 years,followed by a $10,000 expenditure in the 15th
year and a $10,000
expenditure inyear30. If I = 10% per year, what is the equivalent uniform annual cost over the
entire 50-year period?
GIVEN:
i = 10%
n = 50 years
A1 = $ 1,000 maintenance costeachyearfor the first5 years
C1 = 1,000 [
(1+0.10)5−1
0.10
] = $ 6,105.1 moneyworthafter5 years
C2 = $ 10,000 expenditure duringthe 15th
year
C3 = $ 10,000 expenditure duringthe 30th
year
Required:
P = ? & A = ?
SOLUTION:
𝐹 = 6,105.1 (1 + 0.10)45 + 10,000 (1 + 0.10)35 + 10,000 (1 + 0.10)20
𝐹 = $ 793,303.0599
Since,
𝐹 = 𝑃 (1 + 𝑖) 𝑛
𝑃 =
793,303.0599
(1+0.10)50
𝑷 = $ 𝟔, 𝟕𝟓𝟕. 𝟕𝟗
Therefore;
𝐴 =
𝐹𝑖
(1+𝑖) 𝑛−1
=
793,303.0599 (0.10)
(1+0.10)50−1
= $ 𝟔𝟖𝟏. 𝟓𝟗
7. Uncle Wilbur’s trout ranch is now for sale for $40,000. Annual property taxes, maintenance,
supplies, and so on, are estimated to continue to be $3,000 per year. revenues from the ranch
are expectedtobe $10,000 nextyearand then decline by $500 per year thereafter through the
tenthyear.if you boughtthe ranch, youwouldplanto keepitonly5 yearsand at the time sell it
for the value of the land, which is $15,000. If your desired annual rate of return is 12% should
you become a trout rancher?
SOLUTION:
TOTAL EXPENSES = 15, 000+ 40, 000 = $55, 000 for 5 years
An expenses every year = 11, 000
TOTAL REVENGE = 45, 000 + 15, 000 = $60, 000 for 5 years
An expenses every year = 12, 000
FPROFIT EVERY YEAR = 12, 000 – 11, 000 = 1, 000
𝑅𝐴𝑇𝐸 𝑂𝐹 𝑅𝐸𝑇𝑈𝑅𝑁 =
1000
12000
x 100 = 𝟗. 𝟎𝟗% < 12% (𝒅𝒐 𝒏𝒐𝒕 𝒃𝒖𝒚 𝒕𝒉𝒆 𝒓𝒂𝒏𝒄𝒉)
8. The heat lossthroughthe exteriorwallsof acertainpoultryprocessingplantisestimated tocost
the owner $3,00 next year. a salesman from super fier Insulation, Inc. has told you, the plant
engineer,thathe canreduce the heatlossby 80% withthe insallationof $15,000 worth of Super
fiber now. If the cost of heat loss rises by $200 per year (gradient) after next year and the
5. ownderplanstokeepthe presentbuildingfor 10 more years, what would yoy recommended if
the money is 12% per year?
Illustration:
1 2 3 4 5 6 7 8 9 10
WithoutSuperFiberInsulation
1 2 3 4 5 6 7 8 9 10
WithSuperFiberInsulation
SOLUTION:
Wheni = 12%
WithoutSuperFiberInsulation
𝐹 = 3000 [
(1+0.12)10−1
0.12
] +
200
0.12
[
(1+0.12)10−1
0.12
− 10] = $ 𝟔𝟓,𝟐𝟐𝟕. 𝟒𝟑𝟎𝟑𝟑
𝑃 =
65,227.43033
(1 + 0.12)10 = $ 𝟐𝟏, 𝟎𝟎𝟏.𝟒𝟗
WithSuperFiberInsulation
𝐹 = 600[
(1+0.12)10−1
0.12
] +
200
0.12
[
(1+0.12)10−1
0.12
− 10] + 15000(1 + 0.12)10 = $ 𝟔𝟗,𝟔𝟗𝟖. 𝟏𝟖𝟗𝟐𝟗
𝑃 =
69,698.18929
(1+0.12)10
= $ 𝟐𝟐,𝟒𝟒𝟎. 𝟗𝟓
Therefore:
The ownermust not accept the offerofthe Salesman.
9. Solve forthe value of F below so that the left-hand cash flow diagram is equivalent to the one
on the right. Let I = 8% per year.
P = ?
3000
F = ?
3200
3600
3400
3800
4000
4200
4400
4600
P = ?
F = ?
600
800
1200
1000
1400
1600
1800
2000
2200
2400
15000
4800
6. 10. A corporations floats P200,000 worth of ten-year callable bonds is P1,000 denominations. The
bond rate is 7% compounded annually. Prepare an amortization.
GIVEN:
F = P200, 000 n = 10 i = 7%
SOLUTION:
𝑛𝑜. 𝑜𝑓 𝑏𝑜𝑛𝑑𝑠 =
200000
1000
= 𝐏𝟐𝟎𝟎 𝐛𝐨𝐧𝐝𝐬
A = [
𝑖 ( 1+𝑖 ) 𝑛
( 1+𝑖 ) 𝑛− 1
] 𝐹 = [
0.07( 1+ 0.07 )10
( 1+0.07 )10− 1
]200000 = 𝐏𝟐𝟖, 𝟒𝟕𝟓. 𝟓𝟎
28475.50 – 14000 = P14, 475.50
𝑛𝑜. 𝑜𝑓 𝑏𝑜𝑛𝑑𝑠 =
14475.50
1000
= 𝟏𝟓 𝒃𝒐𝒏𝒅𝒔
YEAR PRINCIPAL
INTEREST AT
7%
NO. OF BONDS
RETIRED
AMOUNT OF
PRINCIPAL
REPAID
YEAR END
PAYMENT
1 P200, 000 P14, 000 14 P14, 000 P28, 000
2 186, 000 13, 020 15 15, 000 28, 020
3 171, 000 11, 970 17 17, 000 28, 970
4 154, 000 10, 780 18 18, 000 28, 780
5 136, 000 9, 520 19 19, 000 28, 520
6 117, 000 8, 190 20 20, 000 28, 190
7 97, 000 6, 790 22 22, 000 28, 790
8 75, 000 5, 250 23 23, 000 28, 250
9 52, 000 3, 640 25 25, 000 28, 640
10 27, 000 1, 890 27 27, 000 28, 890
TOTALS P1, 215, 000 P85, 120 200 P200, 000 P285, 120
11. A man borrowed P150, 000 from a bank for home improvement, to be repaid by month-end
payment for 60 months. The current rate of the interest charge by banks is 19% compounded
monthly. Based on this rate, prepare an amortization schedule.
GIVEN:
P = 150, 000.00
n = 60 months (period)
I = 19% compounded monthly =
19%
12
= 1.5833 3333%
SOLUTON:
A = [
𝑖
1− 𝑖)−𝑛] = 150000[
0.015833333
1 ∓(0.01583333 )−60] = P3891.08
PERIOD
PRINCIPAL AT
THE BEGINNING
OF EACH 6
M0NTHS
INTEREST AT 4%
PER PERIOD
PAYMENT AT
END OF EACH
PERIOD
PERIODIC
PAYMENT TO
PRINCIPAL
1 150000 2374.999995 3891.08 1516.080005
9. On January 2, 1981 extraordinary repairs (almost equivalent to a rebuilding of the
machinery) were performedatacost of P30,400. Because of the thoroughgoingnature of these
repairs,the normal life of machinerywasextendedmaterially;the revisedestimate of useful life
was 4 years in 1981.
Determine the annual provision for depreciation for the years 1978 to 1980 and the
adjustedprovisionforthe depreciationof December 31, 1981. Assume payment in cash for the
machine and the repairs.
13. (ECE Board, August 1975) A broadcasting corporation purchased equipment worth P53,000 and
paidP1, 500 forfreightanddeliviery charges to the site. The equipment has a normal life of 10
yearswitha trade-invalue of P5,000 agianst the purchase of new equipment at the end of life.
(a) Determine the annual depreciation cost by the straight-line method.
(b) Determine the annual depreciation cost by the sinking fund method. Assume
interest is 6% compounded annually.
GIVEN:
𝐶 𝑂 = 53000 + 1500 = P54,500
Delivery Change = P1, 800
N = 10 years
𝐶 𝑛 = P5,000
SOLUTION:
a.) Straight – line Formula
𝑑 =
𝐶 𝑜 − 𝐶 𝑛
𝑛
=
54500 − 5000
10
= 𝑷𝟒, 𝟗𝟖𝟎
b.) Sinking Fund Formula
𝑑 = ( 𝐶 𝑜 − 𝐶 𝑛)(𝐴 𝐹, 𝑖%, 𝑛)⁄
𝑑 = (54500 − 5000) [
0.06
(1.06)10 − 1
]
𝒅 = 𝐏𝟑, 𝟕𝟓𝟓. 𝟒𝟔
14. (M.E. Board, June 1990) A machinery supplier is offering a certain machine on a 10% down
payment and the balance payable in equal year-end payments without interest for 2 years.
Under this arrangement the price is pegged at {150,000. However, for cash purchase the
machine would only cost P195, 000. What is the equivalent interest rate that is charged on the
two-year payment plan of interest is compounded quarterly?
GIVEN:
C1 = P 250,000 Price of the machine for2-yearpayment
C0 = P 195,000 Original costof machine whenprice purchased
n = 2 years
d = downpayment= .10(250,000) = 25,000
C1-new = 250,000 – 25,000 = 225,000 Remainingbalance
CA = 225,000/2 = 112,500 Cash to be paideveryyear-end
C0 = 195,000 – 25,000 = 170,000 Remainingamounttobe paidandto be compounded
Therefore:
𝐹 = 112,500 [
(1+𝑖)2−1
𝑖
] Expectedtotal compoundedamountof moneyafter2years
𝐹 = 170,000 (1 + 𝑖)2 Total compoundedmoneyafter2years
10. SOLUTION:
170,000 (1 + 𝑖)2 = 112,500 [
(1+𝑖)2−1
𝑖
]
170,000
112,500
(1 + 𝑖)2 𝑖 = (1 + 𝑖)2 − 1
68
45
(1 + 𝑖)2 𝑖 = (1 + 𝑖)2 − 1
68(1 + 𝑖)2 𝑖 = 45(1 + 𝑖)2 − 45
68(1 + 𝑖)2 𝑖− 45(1 + 𝑖)2 = −45
(1 + 𝑖)2(68𝑖 − 45) + 45 = 0
By trial and error:
𝒊 = 𝟎. 𝟐𝟎𝟗𝟏effectiverate compoundedannually
(1 + .2091)2(68(.2091) − 45) + 45 = 0.0002616 ≅ 0
To get forthe equivalenteffectiverate compoundedquarterly:
0.2091 = (1 +
𝑖
4
)
4
− 1
1.2091 = (1 +
𝑖
4
)
4
√1.20914
= ∜(1 +
𝑖
4
)
4
1.08614 = 1 +
𝑖
4
𝑖 = 0.194456 ≅ 0.1945
THEREFORE:
15. A debtof P10, 000 withinterestatthe rate law of 8% payable semi-annually is to be amortized
by equal paymentsatthe end of each 6 months for 4 years. Find the semi-annual payment and
contract and amortization schedule.
GIVEN:
P = 10, 000 n = 4(2) = 8 quarters 𝑖 =
8%
2
= 4%
SOLUTION:
A = P (𝐴 𝑃⁄ , 𝑖, 𝑛) = 10000 [
0.04
1−(1.04)−8
] = P1,487.28
PERIOD
PRINCIPALATTHE
BEGINNING OF
EACH 6 M0NTHS
INTEREST AT 4%
PER PERIOD
PAYMENT AT END
OF EACH PERIOD
PERIODIC
PAYMENT TO
PRINCIPAL
1 P10, 000.00 P400.00 P1,485.28 P1, 085.28
2 8, 917.72 356.59 P1,485.28 1,228.69
3 8, 786.03 311.44 P1,485.28 1, 173.84
4 6, 612.19 264.49 P1,485.28 1, 220.79
5 5, 391.70 451.66 P1,485.28 1, 269.62
6 4, 121.78 164.87 P1,485.28 1, 320.41
𝒊 = 𝟏𝟗. 𝟒𝟓 % 𝒄𝒐𝒎𝒑𝒐𝒖𝒏𝒅𝒆𝒅 𝒒𝒖𝒂𝒓𝒕𝒆𝒓𝒍𝒚