I.

E QUESTIONS & FORMULA

(CHAPTER: COST, BREAK-EVEN ANALYSIS)

Formula

1. Prime Cost/Direct Cost=Direct labour cost +Direct material cost+ Direct expense

(Direct expenses are cost of design, drawing, cost of experimental work done, procuring of
special types of pattern, jigs, moulding etc.)

2. Factory Cost/Work Cost= Prime cost+ Factory expense/ Factory Overhead

(Factory expenses are cost like lubrication oils, grease, coolant, cotton waste, polishing material,
salary of supervisors, inspectors, sweeper, watchman, helper etc.)

3. Manufacturing Cost=Factory cost+ Administrative expenses

(Administrative expense are salary of manager, office superintendents, clerk, typist, welfare
officer, personnel officer, medical officer, canteen employee, security staff etc.)

4. Total cost=Manufacturing cost/Production cost+ Selling expenses+ Distribution

expense+ Administrative Overhead

(Selling expense are salary of agent, sales manager , advertisement cost and publicity, tender
preparation cost etc.)

(Distribution expense are cost of packing, holding , dispatching, salary of package men, store
officer, storekeeper and assistant etc.)

5. Selling Price=Total cost+ Profit or loss

1. A certain product is manufactured in batches of 100. The direct material cost is Rs. 500, direct
labour costs is Rs 750 and factory overhead are 50% of the prime cost. If the selling expenses
are 30% of the factory cost, what would be the selling price of each product so that the profit is
10% of the total cost ?

2. The catalogue price of drilling m/c is Rs. 600 and the discount allowed to distributor is 20 % .
The administrative and selling expense are 50% of the factory cost and the material cost, labour
cost and factory overheads are in the ratio of 1:3:2. If the cost of labour on the manufacture of
the machine is Rs. 1200, determine the profit on each machine.

3. A factory owner employed 100 worker during the month of April 1985. The following are the
details of expenditure :

(a) Cost of material -Rs. 40,000

(b) Rate of wages for each worker = Rs. 2 per hour of normal duty and Rs. 4 per hour of
overtime duty.

(c) Man hours per day of normal duty=8 hours .

(d) Number of holidays per month (without wages) = 5 days

(e) Total overhead expenses = Rs. 10,000. The worker were paid over time for 300 hours.

Determine : 1. Total cost/month

2. Man hour rate on costs.

4. A company manufacture pocket transistors. The details of its expenditure are as follows:

Direct material cost = Rs. 1000

Direct labour cost =200 hour at the rate of Rs. 5 per hour

125 hours at the rate of Rs. 4 per hour

Applied overhead (factory overheads) =10% of prime cost

other overheads=10% of work cost.

Profit=20% of total cost

Number of units manufacturing per month=200

Estimating the selling price unit.

5. A product can be manufactured either by hand or by machine under mass production. In the
first cases. The time consumed per product is 2 hours and the factory overheads are 20% of the
labour costs. In the second case. time consumed to manufacture 100 products in hours but
factory overheads are 120% of the labour cost. If the material cost per product is Rs. 2.50 and the
labour cost is Rs. 2.00 per man hour in each case, determine the ratio of their factory costs.

6. A factory manufactures steel bolts and nuts and makes an estimates as shown below on the
basis of lots of 2000bolts and nuts.

1. Direct Material cost Rs. 750.00

2. Direct Labour cost

(a) Forging shop

Cutting to length Rs. 30.00

Setting up Rs. 120.00

(b) Machine shop

Milling heads Rs. 100

Threading Rs. 75

Drilling Rs. 50

Chambering Rs. 45

3. Direct Expenses

cost of tools Rs. 75

4. on costs

(a) Forging shop 150% of labour cost

(b) Machine shop 100% of labour cost

(c) Office Establishment 20% of factory cost

(d) Packing and transporting Rs. 50

If the selling price of each nut and bolt is Rs. 1.50, determine whether the factory is making a
profit or loss. If so, by what amount per piece?

7. In a factory cost of an article made from solid brass bar 38 mm diameter and 25mm length.
The machining time taken to finish the part is 90 minutes and the labour rate is Rs. 5.00 per hour.
Factory overhead are 40% of direct labour cost. The density of the material is 8.6 gm per cub-
cm and its cost is Rs. 4.5 per netwon.

Grade I Grade II

Material cost per machine Rs. 1500 Rs. 1250

Labour cost per machine Rs. 900 Rs.750

Office on cost 10% of work cost 10% of work cost

Selling Price Rs. 4000 Rs. 3200

8. Find the factory of an article made from solid brass bar 38mm diameter and 25mm length.
The machining time taken to finish the part is 90 minutes and the labour rate Rs. 5.00 per hour.
Factory overheads are 40 % of direct labour cost. The density of the material is 8.6 gm per cub-
cm and its cost is Rs. 4.5 per newton.

9. An article is being sold in the market for Rs. 300.00. Find the manufacturing cost assuming
25% profit of the selling price and selling expenses to be 40% of production cost. If the cost of
material used for the article is Rs. 75.00 and the overhead of charges are 40% of labour cost find
the time taken for its manufacture if the labour rate is Rs. 800 per hour.

10. The output of an electric bulb factory is 400bulbs per month. Its variable cost is Rs.3 each
and the fixed overheads are Rs. 6.00 per month. The selling price is Rs. 5 per bulb. Work out the
minimum monthly production which may not cause any loss to the owner.

11. From the following data, find (a) material cost (b) Prime cost (c)Direct cost (d)Factory cost

(e) Administrative Overhead (f) Cost of production (g)Selling and distribution overhead (h)
Total cost (i) Selling cost. Assume a net Profit of Rs. 10,000.

Rs

1. Material in April 1, 1975 of 60, 000

2. New material purchased 250,000

3.Direct fees 3500

4. Advertising etc. 12,000

5. Depreciation on sales department car 1200

6. Printing or stationary charges 300

7. Plant depreciation 5000

8. Wages of direct worker 70,000

9. Wages of indirect (factory ) worker 10,000

10. Rent of factory building 5,000

11. Postage, telephone or telegraph 200

12. Water or electricity for factory 1000

13. Office salaries 2000

14. Rent of the office 500

15. Rent of the show room 1500

16. Commission of sales man 2500

17. Sales department car expenses 1500

18. Material in March 31, 1976 50,000

19. Variable direct expenses 750

20. Plant repair and maintenance 3,000

21. Heating , lighting, and water for office use 2,500

22.Cost of distributing goods 2000

12. A factory producing 150 electric bulbs a day, involves direct material cost of Rs.250 , direct
labour cost of Rs. 200 and factory overheads of Rs. 225. Assuming a profit of 10% of the selling
price and selling on cost (overhead) 30% of the factory cost, calculate the selling price of one
electric bulb.

13. A cast iron foundry employs thirty persons, It consumes material worth Rs. 25,000, pays
workers at the rate of Rs.10 per hour and incurs total overhead of Rs. 10,000. In a particular
month (25days) worker had an overtime of 150 hours and were paid at double their normal rate.
Find (i) the total cost (ii) main hour rate of overheads. Assume an eight hour working day.

14. Two molder can cast twenty five gears in a day. Each gear weight 3kg and the gear material
costs Rs. 12.50 per kg. If the overhead expense are 150% of direct labour cost and two molders
are paid Rs.70 per day. calculate the cost of producing one gear.

15. A drill process costs of Rs. 6,000 . A discount of 25% of this price is given to the distributor.
If labour cost, material cost and factory overheads are as 4:1:2 and selling expenses are 25% of
the factory , calculate the profit of the factory for one drill press. Assume a factory overheads of
Rs. 800.

16. A factory is making a pipe of fitting by (a) casting (b) forging . The cost data is as follows

Casting Forging

material cost per piece Rs.2 Rs. 2

Labour rate Rs 0.8 per hour Rs 0.8 per hour

Time require to make one fitting 3hours 48 minutes

Overheads 25% of labour cost 150 % of labour cost

Calculate and compare the total cost of each piping fitting in two cases.

17. A fabrication concern for the year of 1975-1976 had factory overheads of Rs. 4000 and the
direct labour cost of Rs. 12,000. (a) Find the percentage overhead using percentage of direct
labour cost method.

(b) If the production order "z" had a direct labour cost of Rs. 60, find the overhead cost for the
production order.

18. (a) A sugar mill had its overheads Rs. 60,000 while it purchased sugarcane worth of Rs.
240000. Find the percentage overhead using the percentage of direct labour cost method.

(b) If a particular batch had a direct material cost of Rs 30,000, determine it overheads.

19. A fabrication and assembly shop had its total overheads of Rs. 10,000. It used direct material
worth Rs. 10,000 and paid Rs. 15,000 as direct labour charge. Calculate the % overhead.

(b) If one product has its prime cost as Rs. 5,000, determine overheads or on cost related to it

20. A fabrication and assembly shop had its factory overheads of Rs. 120000 and the
production for the period in terms of direct labour was 24,000 hours. Find the rate per direct
labour hour

(b) If a particular job takes 20 labour hours , calculate the overhead applied.

21. A machine shop has 10 lathes, 6 drill pressed and 2 milling machines. Calculate the
machine hour rate for lathes if the factory expenses for a particular period and other data are as
follows.

1. Area occupied by lathes 10m2.

2. Area occupied by drill press 3m2

3. Area occupied by milling machine 2m2

4. cost of indirect materials and labour Rs. 120,000

5. Rent for building Rs. 36,000

6. Insurance Rs. 15,000

7. Depreciation for lathes is Rs. 20,000

Depreciation for drillings is Rs. 15,000

Depreciation for millings is Rs. 20,000

8. Power consumed for lathes Rs 18,000

Power consumed for drillings Rs. 6000

Power consumed for millings Rs. 900

9. Repair maintenance for lathes Rs. 10,000

Repair maintenance for drillings Rs. 4000

Repair maintenance for millings Rs. 4000

10. Machine hours for lathes 10,000

Machine hours for drillings 6000

Machine hours for millings 2000

22. Using the data given in the above example, calculate rate per machine hour for

(a) drill press

(b) Milling machines

23. If the estimated overhead costs of factory making two band transistor ratio is Rs. 8000 in a
particular period and if the number of transistor ratio produced during that period is 400

(a) calculate the overhead rate per transistor ratio.

(b) If the production order "Z" schedule making 100 such radios, determine the factory
overhead to be applied to the production order " Z".

24. A certain product is to be manufacture in batch es of 100 . The direct material cost if found
to be Rs. 320, direct labour cost Rs. 560, overheads chargeable to Rs. 420. If the selling cost is
50% of the factory cost, What will be the selling price of each product to realize a profit of 15%
of the selling price?

Break-Even Analysis/Break Even Point

Formula

Sales−SalesatBEP Χ 100
Margin of safety in %= Sales

Pr ofit Χ Sales
Sales−Variable cos t

=Profit/P/V ratio

Profit Volume ratio (P/V ratio)

P/V ratio =

P/V ratio = Contribution ×100 = Increase in profit×100

Sales Increase in sales

= Total sale-total varible costs

Total sales

= S-V×100

or Fixed costs+Profit×100

Sales

=Prices per unit-cost per unit

Price per unit

B.E.P= F

SP-VC

=FC/C

where SP= Sales per unit

C==Contribution per unit (SP-VC)

ii) BEP= FC×SP

SP-VC

iii) BEP= Fixed cost-Depreciation+ Annual installment of term loan

Sales price per unit -Variable cost per unit

Safety Margin= Sales-Sales at BEP

Sales

iv) Target Sales volume= Fixed cost+ Target profit

Contribution margin per unit

v) BEP= FC

P/V ratio

vi) Profit=Sales-total cost

• TR = P × N = F + ( V × N )

Where P= price per unit N = number of units sold F = fixed costs

V= variable costs per unit , TR = total revenue or sales = P × N

• N = F/P-V i.e. Break-even point in units (B.E.P.) (shown in figure 4.1)

And B.E.P. in money value (TR)=F/1-V/P

Figure 4.2 Make-or-buy decision

Uses of Break-Even Point:

• The break-even point in the analysis can be used to determine the followings

1. Safety margin in percentage with proposed volume=

• Sales volume – sales at B.E.P. × 100%

Sales volume

2.Quantity needed to get the desired profit.

• Desired quantity =Fixed cost + desired profit

Contribution/unit

• 3.Effect of change in price

• N =F + Profit

• P–V

• N1=F + Profit

• P1 – V where N1= new break-even point P1 = new selling price.

• 4.Effect of change in costs.

• There being two costs—variable and fixed, change takes place in both variable and fixed
costs

• N= F + Profit

• P-V

• N1= F + Profit

• P1 – V1

• where V1 = new variable cost and P1 = new price

• If sales volume is same, N = N1

• then P1 – V1 = P–V

• or P1= (P – V) + V1 = P + (V1 – V)

• Similarly P1=P + F1 – F

• N

• where F1 =new fixed cost

• Contribution ratio = [(P–V)/P]×100%

• The different methods of calculation (allocation ) of overhead costs are:

• 1. % on Prime cost

• % Overhead Cost= Total Overhead ×100

Prime cost
 2. % on direct labour cost

• %Overhead Cost= Total Overhead ×100

Direct labour cost

3. % on direct material cost

• %Overhead Cost= Total Overhead ×100

Direct Material cost

4. Man hour rate

Man hour rate(Overhead cost/man hr.) = Total Overhead Cost

Total man hour spent

Questions of Break -Even-Analysis

1. Following details are available

Sales Profit

Rs. Rs.

Period I 2,00000 20,000

Period II 3,00000 40,000

Find out the Break even sales; and P/V ratio

2. The following figures related to a small manufacturing company :

Sales (Rs) 60000

Variable cost (Rs) 450000

Fixed cost (Rs.) 45,000

Calculate (i) BEP (ii) P/V ratio

3. A factory producing only one item, which itself for Rs. 12.50 per unit has a fixed cost
equal to Rs. 60,000 and variable cost Rs. 7.50 per unit

Find out (i) The number of units to be produced to break even.

(ii) No. of units to be produced to earn a profit of Rs. 12,000

(iii) The profit, if 25,000 units are produced and solid.

4. Following details are available

Actual sales =Rs. 30,000

Break even sales= Rs. 15,000

Fixed cost= 6000

Find out the profit at actual sales

5. The following figures relate to a small manufacturing concern :

Sales= Rs. 50,00000

P/V ratio = 50%

Margin of safety= 40%

Find out the BEP and profit

6. The fixed costs for the year 1984-85 are Rs. 1,00000. The estimated sales are Rs.
3,00,000. The variable cost per unit for the single product made is Rs. 5.00. If each unit
sells at Rs. 30 and the number of units involved coincided with the expected volume of
output, construct the break even chart.

7. The fixed costs for the years 1987-90 are Rs. 8,00000, variable cost per unit is Rs. 30.
The estimated sales for the period are valued at Rs. 24,00,000. Each unit sells at Rs.
180.

Determine

(I) B.E.P

(II) Rs. 18,00,000 will be the likely sales turn over for the next budget period. calculate
the estimated contribution and profit.

(III) If a profit target of Rs. 950000 has been budget. compute the turn over required

8. The fixed costs for the years 1975-76 are Rs. 80,000. The estimated sales for the period
are valued at Rs. 20000. The variable cost per unit for the single product made is Rs. 4.
If each unit sells at Rs. 20, and number of units involved coincides with the expected
volume of output, construct the Break even chart

(i) Determine the break- even point

(ii) Above how many units, the company should produce in order to seek profit
(iii) Determine the profit earned at a turnover of Rs. 160,000.

(iv) Find margin of safety

(v) Measure the angle of incident

8. A drill press costs Rs. 60,000. A discount of 25% of this price is given to the
distributor. If the labour cost, material cost and factory overheads are 4:1:2; and selling
expenses are 25% of the factory cost, calculate the profit of the factory for one drill
press. Assume factory overheads of Rs. 8000.

9. A factory is making a pipe filling by

(a) Casting (b) Forging

The data is as follows

Casting Forging

Material cost per piece Rs. 20 Rs. 20

Labour rate Rs. 8 per hour Rs. 8 per hour

Time required to make one fitting 25% of labour 125% of labour

Calculate and compare the total cost of each pipe fitting in two cases.

10. Find the factory cost of a component made from solid steel bar 5cm along and 2cm
diameter. The machining operation requires 1.5 hours. Assume the following date:

(a) Density of mild steel 8gm/cc

(b) Cost of mild steel Rs. 2 per kg

(c) Labour charge Rs. 1 per hour

(d) Overhead charges 50% of direct labour cost

11. A factory is producing 6000 components per month. The fixed overheads for the
month are Rs. 9000 and the variable cost of each components is Rs. 10. If the selling
price of each components Rs. 12 , estimate the minimum montly production that may not
cause any loss to the factory owner.

12. AC. foundry employes 25 persons. It consumes material worth Rs. 35000 pays
worker at the rate of Rs. 5 per hour and incurr total overheads of Rs. 20,000. In a
particular month (25 days) , workers had an overtime of 150 hours and were paid double
than the normal rate find (i) the total cost and (ii) the man hour rate of overheads
Assume an 8 hours working days.

Q.13. A small firm at Allahabad is producing 1000 pens per days. The cost of direct
material is Rs. 1600 and that of direct labour is Rs. 2000,factory overheads chargeable to
it are Rs. 2500. If the selling on cost is 40% of the factory cost. what must be the selling
price of each pen to realise a profit of 20% of the selling price?

Q.14. A manufacturer sells the product at Rs. 6 each and variable cost per unit is Rs.
50. The estimated sales revenues are Rs. 25,00,000.Each units sells at Rs. 225 each:

(a) Find B.E.P

(b) What would be the break even point if the firm spends Rs. 4000 on R& D.

(c) If a profit target of Rs. 800000 has been budgeted , compute the turn over required.

Q.15. Following information is given to you about a company for two periods

Period Sales (Rs.) Profit (Rs.)

I 120,000 9,000

II 140,000 13,000

Calculate

(a) P/V ratio

(b) BEP

(c) Profit when sales are Rs. 100,000

(d)Sales required to earn profit of Rs. 20,000

(e) Margin of safety for period II.

Q.16. The fixed costs for the year 1990-91 are Rs. 80,000, the estimated sales for the
period are valued at Rs. 2,00,000. The variable cost per unit is Rs. 4. If each unit sells at
Rs. 20 and the number of units involved coincides with the expected volume of output,
construct the break even chart and determine:

(i) B.E.P

(ii) Profit earned at turn over of Rs. 160,000.

(iii) Margin of safety

(iv) Measure the angle of Incidence

Q.17. The fixed cost for the financial year 1985-86 are Rs. 40,000. The sales for this
period are Rs. 100,000. The variable cost per unit is Rs. 2. Selling price of each product
is Rs. 10 and the number of units involved coincides with the expected volume of output.
Construct the Break -Even Chart and determine.:

(a) BEP

(b) Minimum production to earn profit

(c) Margin of safety

(d) Profit earned at turn over of Rs. 80,000

(e) Angle of incidence

Q.18. A company is planning to launch a new product. For any volume of production
below 400 units the fixed cost is Rs. 6,000 and the variable cost is Rs. 20 per unit. If the
volume is to be more than 400, large equipment will be needed and the fixed cost will
be Rs. 10,000. . However , the variable cost will reduce to Rs. 10 per unit. At any
volume the selling price is Rs. 30 per unit.

(a) What is BEP

(b) What is the profit or loss if the volume is fixed at 500 units/

(c) What are the assumptions made in your analysis.

Q.19. The following data refer to a manufacturing unit

Fixed cost= Rs. 100,000

Variable cost= Rs. 100 per unit

Selling price= Rs. 200 per unit

(i) Calculate the BEP

(ii) If the fixed cost increases to Rs. 125,000 and variable cost reduces to Rs. 90 per unit.
obtain the new BEP

(iii) For (i) calculated the number of components needed to be produced to get a profit of
Rs. 20,000.

Q. The initial cost for machine A is Rs. 12,000 and the unit production cost of the
machine is Rs. 6 each. For the other machine B, the initial cost is Rs. 48,000 and the unit
production cost is Rs. 1.20 each. Do the break even point analysis.
 Depreciation (Formulas & Questions)
Method of calculation Depreciation

1. Straight line method

2. Diminishing balance method

3. Sink fund method

4. The sum of the year method/Fixed Installment method

5. The insurance policy

6. Machine hour basis method

7. Production unit method

8. Annuity Method

9. Revaluation Method

10. The retirement method

1. Straight line method/ Fixed Installment method

Annul Depreciation Charges (ADC)= C-S in rupee

Where C=Initial cost of the machine in rupee

S=Scrap value (salvage value) in rupee

N=Estimated life of the machine in year.

2. Diminishing balance method

yearly depreciation factor X= 1-(S/C)1/N

Where X= Fixed percentage for calculating yearly depreciation

C=Initial cost

S=Scrap/Salvage value

N=Estimated life
3. Sink fund method

Rate of depreciation per year D= R(C-S)

(1+R)N-1

Where R is interest rate (in fraction number)

N=Number of year of the life of the asset.

4. The sum of the year method/Fixed Installment method

=Digit associated with the asset's age× (C – S )

Sum of the digits for the asset's estimated life

5. The insurance policy

This method covers the risk if the machine become unserviceable before its estimated
life.

6. Machine hour basis method

Rate of depreciation= Value of asset

Number of production hours

= C-S

Total machine hours over useful life of machines

7. Production unit method

Depreciation cost per unit= C-S

Number of units it is expected to produce

8. Annuity Method

Rate of depreciation= D= [C(1+R)N-S][1-(1+R)]

[1-(1+R)N]

Where N=useful life of machine in year

9. Revaluation Method

Depreciation for this period=Value of the asset at beginning- value of the asset at the end
of the year.
QUESTIONS

Q. 1. A machine costing Rs. 24,000 was purchased on 1st Dec. 1985. The installation
and erection charges were Rs. 1,000 and its useful life is expected to be 10 years. The
scrap value of the machine at the end of the useful life is Rs. 5,000. Calculate the yearly
depreciation by straight line method.

Q.2. An engine lathe was purchased for Rs. 20,000. Its useful life was estimated as ten
years and the salvage value as Rs 5,000. Using the diminishing balance method, calculate
the depreciation ratio (%). Also estimate the depreciation fund at the end of two year.

Q.3. Estimate the rate of depreciation from the following data, using the sinking fund
method:

Cost of machine Rs. 10,000

Scrap value Rs. 4,000

Interest at the rate of 8% compound

Useful life of the machine 5 years

Q.4. If the original cost is Rs. 20,000. Scrap value is Rs. 5,000 and N=5 years. find out
the depreciation using sum of the year method/Fixed Installment method.

Q. 5. A machine costing Rs. 450,000 has a scrap value of Rs. 50,000 after 10 years of
service. The estimated rate of production is 12 units per hour. Using the productive unit
method calculate the rate of depreciation and also depreciation per year. Assume 50
week per and 48 working hours per week.

Q.6. In a shop, if the machine cost is Rs. 11,000.

Scrap value=Rs. 1,000

Life of machine N=10 years

Calculate depreciation charges per hours.

Q.7. Find out the depreciation annuity by the annuity charging method after 3 years
when the cost of the machine is Rs. 8,000 and the scrap value is Rs. 4,000 only. Rate of
interest is 5 percentage. Also calculate the value of the machine after 2 years.

Q.8. A melting unit for a steel foundry was purchased for Rs. 30,000. Rs 5,000 more
were spent on its erection and commissioning. The estimated residual value after 10 years
was Rs. 7000. Calculate (i) annual rate of depreciation .
(ii) Determine the depreciation fund collected at the end of seven years after the purchase
of the melting unit.

Q. 9. An old car was purchased for Rs. 32,000. Its life was estimated as ten years and the
scrap value as Rs.18,000.Using the reducing balance method, calculate

(a) the depreciation rate (%)

(b) Estimate the depreciation fund at the end of two years.

Q.10. Two machines are purchased , each for Rs. 12,000. The estimated useful life of the
machine is 5 years. The estimated scrap value is Rs. 2,000. For a machine A, the straight
line method and for B, the reducing balance method with p=30% is used to calculate the
depreciation every year. Compare the depreciation charge in each case.

Q.11. A machine costing Rs. 2,00,000 has a residual value of Rs. 100000 after 10 years
of service. The estimated rate of production 8 units per hour. Using the production unit
method calculate the rate of depreciation. Assume a 50 week year and 46 hours week.

Q.12. A machine costing Rs.15,000 has scrap value of Rs. 5,000.at he end of 10 years of
its service life. If the machine runs for 2100 hours per years. Calculate the depreciation
rate per hour of the machine and the total annual depreciation.

Q.13. Cost of air conditioning unit is Rs. 100,000. During an estimated life of 10 year,
two major overhauls were carried out. Each involving Rs. 20,000.If the scrap value of
the plant is Rs. 15,000. Calculate the depreciation rate on the basis of repair provision
method.

Q.14. The cost of the machine is Rs. 6,000. and its scrap value after 4 years is Rs. 3,000.
Assuming the rate of interest is 4% per year. Find the depreciation rate per year.

Q.15. Calculate the annual rate of depreciation from the following data, using the sinking
fund method.

Cost of asset Rs. 6,000 , Scrap value Rs. 3,000, Interest rate 4% (compound), Useful life
period 3 years.

Q. 16. The cost of a vehicle is Rs. 190,000. The residual (scrap) value after a period of 5
year is estimated as Rs. 40,000.Using the sum of the digit method, calculate the
depreciation rate every years.

Q. 17. The cost of a machine is Rs. 75,000 and its scrap value is Rs. 15,000. Estimated
life of the machine is 5 years. Determine the depreciations charges every year by :

(a) Straight line Method

 (b) Sum of the Years Digit Method

Q.18. A car was purchased for Rs. 30,000. Its life was estimated as 10 years and the
scrap value of Rs. 7500 using the Reducing Balance Method. Calculate:

(a) Depreciation percentages

(b) Depreciation fund at the end of two years.

Q. 19. The cost of machine is Rs. 6000 and its scrap value after 4 years is Rs. 3000.
Assuming an interest rate of 6 percent in a year. Find the depreciation rate per year.

Q. 20. An industrial plant with initial value of Rs. 2,20,000 and the scrap value of Rs.
40,000 at the end of 20 years is sold for Rs. 195,000 at the end of 1 year. What is the
profit or loss if sinking fund depreciation method at 8% compounded annually was
adopted?

Q.21. An industrial plant with initial value of Rs. 200000 and the salvage value of Rs.
20,000 at the end of year 20 years but sold for Rs. 145,000 at the end of 10 years. What
is the profit or loss if sinking fund method is adopted and interest charged at 9% is
compounded annually?

Q.22. The original asset of company are Rs. 580,000. The life of the plant is 9 years. If
the scrap value is Rs. 80,000.Calculate the depreciation at the end of each year by Sum
of the year digit method.

• CASH FLOW AND EFFECT OF TIME:

• When customers buy products and pay their bills, a company has a gross cash income.

• The gross cash flow not only pays all of a company's day-to-day expenses, but also
includes money that recovers the decline in the value of machines and buildings because
of their wearing out.

• A company's net cash flow, then is equal to retained profits after taxes and dividends,
plus depreciation on machines, equipment, and buildings, plus any income from the sale
of fixed assets.

• A good bit of this net cash is spent for new machines or other new capital investment
projects as the year goes along.

• The rest of this cash, free of immediate commitment to current bills, comes in company's
credit and the management is to decide how to use the money.

• The cash money received a year from now is valued at less than that received today since
it can be invested and earn interest during the year.
• It can be understood that Rs. 1.10 one year from now is equivalent to Rs. 1.00 received
to-day when the annual interest rate is 10 percent.

• The concept of equivalence allows one to compare alternatives realistically with different
time periods of receipts and disbursements.

• Cash Flow Diagram :-As Engineering Economy deals with sums of money at different
times in future. Cash flow measures the flow of fund s into or out of an enterprise . It is a
series of actual or estimated payment (or cost) and receipts (or income) of an enterprise
over a period of time. The procedure of this graphical called "Cash flow diagram" Refer
figure 5.5

• Beginning of -period payment with uniform series:- In this uniform annual series above ,
the amount "A" occurs at the end of each period. However , if a beginning of period
payment "Ab" is required , it can be done as

• F=A, P= Ab , n=1

• A= Ab (1+i)

• Deffered Annuity:- If the first cash flow does not take place at he end of first period
but after some time periods, the annuity is called as "Deffered Annuity" Refer figure 5.6

• Net worth present (NPW) = Present worth of income- Present worth of costs

• NPV/NPW of an investment =P.V of cash flows in the investment generates -cost of

investment.
∞
TC /Year
∑ (1+I )n
−IΧ Investment
• NPV= n=1

TC /Year
• NPV= I

• Discount Cash flow (DCF):- It is the rate of return for which NPW is zero.

• i.e PW of income =PW of costs

• Discount means the time value of money is consider.

• Account Profit (AP):-AP= Revenues- Expenses

• Economic Profit:- It is the profit earned by investing resources in a particular activity.

• Basic Methods of economy studies (Selection method) :- The following are the
• 1. Payback Period method

• 2. Present worth Method

• 3. Annual worth /Annual cost Method

• 4. Internal rate of return

• 5. Explicit Method

• 6. Break even Method

• 1. Payback Period Method

Initialcapitalinvestment
Payback Period method= Annualreturn exp ected

Required Investment
= Annual receipt-annual disbursement

• 2. Present worth

Net P.W= PW of cash inflows (Receipts) -PW of cash out flows (payments)

• 3. Annual worth /Annual cost Method

the annuity equivalent to the capital recovery cost of the initial investment minus the
discounted salvage value (if any), and added to it other annual costs.

4. Internal rate of return /Rate of return (R.O.I)

Netprofit /Cashincome
R.O.I= Su min vested

Cash Flow (Formula )

1 To find the future value (F) given (1+ i )n (F/P, i,

the present worth of a single n)
amount (P)

2 To find the present value (P) given 1/(1+ i )n (P/F, i, n)

the future worth of a single amount
(F)
 3 To find the value of annuity 1/(1+ i )n-1 (A/F, i, n)
payments (A) given the future
worth of the annuity (F)

4 To find the value of annuity i(1+ i )n/(1+ i )n-1 (A/P, i, n)

payments (A) given the present
worth of the annuity (P)

5 To find the future value (F ) given (1+ i )n-1/i (F/A, i, n)

the amount of annuity payments (A
)

6 To find the present value (P) given (1+ i )n-1/i(1+ i )n (P/A, i, n)

the amount of annuity payment (A)

Question (Cash Flow )

Q. 1. A Rs. 2000,000 machine is to be replaced in 20 year . Find the annual

investment that must be made at 10% to provide the sum to replace the
machine, using (a) Sinking fund method (b) Capital recovery factor

[I
n ]
Ans.:- (a)Hint : A=F ( I + I ) −1 where A is Uniform annual amount & F is
total sum available, I =interest, n = time period or Given= F=A(F/A,I%, n)

[ I(1+I )
n
(b) P=F ( I + I ) −1
] or Given A=P (A/P, I%, n)

Q.2. An entrepreneur can make an investment of Rs. 40,000 in a project.

The uniform annual revenue of the project will be Rs. 21,240 for 5 year.
After that, its salvage value will be Rs. 8000.Annual payment per year for
operation and maintenance will be Rs. 12000. Will the project be
economical by using P.W. method if the company is prepared to accept the
project that will earn 10% or more before taxes.
 [
(1+I )n −1
Ans. Hint:-(i) Revenue/Payment= P=A I (1+ I )
n ]
F
n
(ii) Salvage value P= (1+I ) Total cash flow= add both

(b) Investment (given)

[
(1+I )n −1
Payment= P=A I (1+I )
n ] Given P=A(P/A, I%, n)

Total cash flow= Investment +Payment

Q. 3. Machine A operate manually costs Rs. 20000 has a life f 2 years.

Machine B is automatic and costs Rs. 50,000 and has a life of 4 year.
Operating costs of machine A are Rs. 40000 annually while that of machine
B are 30,000. Which machine should be selected . Take I=10%

Ans. Hint:- NPW of A machine for 2 year

PW of expenses for A= Manually cost + Oprt cost. (P/A, I%, n)

Similarly PW of expenses for B for 4 year.

Q.4. Select the economical machine out of A and B for which the data is
given below:

Data A B
First cost. Rs. 46,000 60,000
Salvage value Rs 8000 10,000
Operating charges. Rs. 10,000 9200
Economic Life, years 10 15
Interest rate 8 8

Ans.:- Hint. Annual cost of machine A = (P-S).CRF+ Salvage (I%)+ O

Annual cost of machine B=(P-S).CRF+ Salvage (I%)+ O

Where P=Present estimated value, S=Estimated salvage

 I ( I +I )n
n
CRF=Critical Recovery Factor= (1+I ) −1