Learn Through Technology : Management Accounting Math

Problem 1-Nov'10,11: The Paduka Shoe Company sells five different styles of ladies chappals with identical costs and selling prices. The Company is trying to find out the profitability of opening another store, which will have the following expenses and revenues:

~ Per pair	Taka
Selling price	30.00
Variable cost	19.50
Salesman's Commission	1.50
Total Variable cost	21.00

Annual fixed expenses are:

Rent	60,000
Salaries	2,00,000
Advertising	80,000
Other fixed expenses	20,000
Total	3,60,000

Required:

(i) Calculate the annual Break even point in units and in value. Also determine the profit or loss if 35,000 pairs of chappals are sold;

(ii) The sales commission are proposed to be discontinued, but instead a fixed amount of "Ck. 90,000 is to be incurred in fixed salaries. A reduction in selling price of 5% is also proposed. What will be the Break even point in units?

(iv) It is proposed to pay thr store manager 50 paisa (Tk. 0.50) per pair as further commission. The selling price is also proposed to be increased by 5%. What would be the Break even point in units?

(iv) Refer to original data, if the store manager were to be paid 30 paisa (Tk. 0.30) commission on each pair of chappal sold in excess of Break even point. What ~Nould be the store's net profit, if 50,000 pairs were sold?

[Note: Consider each part of the question separately.]

Solution:

Given information:

Total variable cost = 21.00 Total Fixed cost =3, 60,000

Selling price = 30.00

Required i:

BEP in units = Fixed Cost/Contribution margin per Unit

=Fixed Cost/(Selling price per Unit - Variable cost per unit)

= 3,60,000/(30 - 2 1)

= 40,000 units

The required BEP in units 40,000

Contribution margin = (Contribution margin/sales) X 100

= (30 - 21)/30 X 100

= 30%

So, Break Even Value = Fixed cost/CM ratio

= 3,60,000/0.3

= 12,00,000 Tk.

The Break Even Value is Tk. 12,00,000.

Now, We know,

Sales= Fixed cost+variable cost + Profit or (loss)

Profit or (loss) = Sales - (Fixed cost+variable cost)

Profit or (loss) _(30X 35,000) - (3,60,000 + 21 x35,000) 3

Profit or (loss) = 10,50,000) - (3,60,000 + 7,35,000)

Profit or (loss) = - 45,000.

So, the loss is Tk. 45,000.

Required ii:

New variable cost = Tk. 19.50

New fixed expense = (3,60,000+90,000)

= Tk. 4,50,000.

New selling price = 30- (30X 0.05)

= Tk.28.50

So, BEP in units = Fixed Cost/(Selling price per Unit - Variable cost per unit)

= 4,50,000/(28.50 - 19.50)

= 50,000 units

The required BEP in units 50,000.

The required BEP in sales volume =Total unitsx Sales price

= 5O,OOOX 28.50

= Tk. 14,25,000

Required iii:

New, variable cost = Tk. (19.50 + 1.50 + 0.50)

= Tk. 21.50

New selling price = 30 +(30X 0.50)

= Tk. 31.50

So, BEP in units = Fixed Cost/(Selling price per Unit - Variable cost per unit)

= 3,60,000/(31.50 - 21.50)

= 36,000 units

New REP in sale volume = 36,OOOX31.50

= Tk. 11, 34,000

Required iv:

Particulars	Amount	Total Amount TK.
Sales revenue (5O,OOOX30)		15,00,000
Less,
Variable commission Tk. 0.30 is imposed in excess BEP
40,000 units X 21.00	Tk. 8,40,000
Excess, 10,000 units X 21.30	TK. 2,13,000	(10,33,000)

Excess, 10,000 units X21.30

Tk. 2,13,000

(10,53,000)

Commission margin 4,47,000

Less, fixed cost (3,60,000)

Profit 87,000

Problem 2-Nov'08: Atiqul Company sells a product for TK. 60.00 per unit and has a contribution margin ratio of 40%. The company's fixed expenses are Tk. 3,60,000.00 per year.

Required:

(i) What are the variable expenses per unit?

(ii) What is Break even point in unit and in sales amount?

(iii) What sales level in unit and in amount is required to earn an annual before tax profit of Tk. 90,000.00?

(iv)Assume that through negotiation with the manufacturer the company is able to reduce its variable costs by Tk. 3 per unit. What is the company's new Break even point in units and in sales amount?

Solution:

Given information:

Selling price- Tk. 60/Unit Contribution margin ratio-40% Fixed cost-3, 60,000

Required-i:

We know,

Contribution margin/sales = 40%

So, Variable expenses/sales=(100% - 40%)= 60%

So, Variable expenses per unit= (Selling price per unit x variable expenses rate)

=60 X60%

= Tk.36/unit

Required-ii:

Contribution margin per unit=Selling price per unit)-(Variable Cost per unit) =60-36=24 Taka.

So, BEP in unit = FC/ Unit Contribution = 36,000/24 = 15,000 units

Therefore BEP in sales = BEP in unitsx selling price per unit _ (1 5,000 X60)=Tk. 9, 00,000

Required-iii:

Expected profit: Tk. 90,000

a) To earn expected profit of Tk. 90,000 sales level requirement in units _ (FC+expected profit)/Contribution margin per unit) _ (3, 60,000+90,000)/24 = 45,000/24

= 18,750 units

b) So, sales level in taka= 18,750X60=11,25,000 Taka

Required-iv:

Given, Variable expenses= 36 taka

Revised Variable expenses= (36-3) taka=33 taka per unit

So, Contribution margin per unit=Selling price per unit)-(Variable Cost per unit)

=60-33=27 Taka.
Now, new BEP in units = Fixed Cost/ Contribution Margin
=	36,000/27
=	13,333.33 units
New BEP in sales = BEP in unitsx selling price per unit

= 13,333.33X60 = Tk. 7, 99,999.98 = Tk. 8,00,000

Problem 3- May'08:The Shirin International Ltd. is the distributor for a certain product. The product sells in the market for TK. 300.00 per unit with a variable procurement cost of Tk. 210.00 and a variable selling expense of Tk. 25.00. The Company's other variable

cost is Tk. 15. Fixed selling and administrative expenses are Tk. 2,00,000.00 per year.

Required:

(i) What is Break even point in unit and taka;

(ii) What sales level in unit is required to earn an annual before tax profit of "I'k. 1,50,000.00

(iii) What sales level must be achieved to have the same level of after tax profit of Tk. 2,00,000.1f tax rate is 50%.

(iv) What sales level must be achieved to have the after tax target profit Tk. 2.40.000. It' tax rate i s 40%.

(v) What is the Margin of safety (MS) and after tax profit for sales level of 10,000 units. if tax rate is 40%.

Solution:

Variable cost of the product/unit:

Procurement cost :	210.00
Sales expenses :	25.00
Other variable cost :	15.00

Total Variable Cost= Tk. 250 Selling price per unit =Tk. 300

So, Unit Contribution = Selling price per unit - Variable Cost per unit = 300-250= Tk. 50.00

Required i:

BEP in units = FC/Contribution per unit = 2, 00,000/50 = 4,000 units

Therefore BEP in sales = 4,OOOX300

= 12, 00,000 Taka

Required ii:

Level of sales unit to earn an annually profit before tax of Taka 1,50,000

Level of sales = (Fixed Cost+expected profit)/Contribution margin per unit) = (2,00,000+1,50,000)/50

= 3,50,000/50

= 7000 units

Required iii:

Protit after tax

Fixed Cost + 1- Tax rate

Required sales Level=

Contribution Margin per unit

	2,00,000
2,00,000	+ 1-0.50
	50
	2,00,000
2,00,000	+ 0.50
	50
2,00,000	+ 4,00,000
	50

= 12,000 units

Required iv:

Given, Profit after tax= Tk. 2,40,000

Profit after tax

Required sales Level=

Fixed Cost + 1- Tax rate

Contribution Margin per unit

	2,40,000
2,00,000	+ 1-0.40
	50
	2,00,000
2,00,000	+ 0.60
	50
2,00,000	+ 4,00,000
	50

= 12,000 units

Required v:

Marginal safety in units = Sales - BEP

= 10,000 - 4,000 = 6,000 units

Marginal safety in Tk. = 6,OOOX300

= 18, 00,000 Taka

Profit of marginal safety 6,OOOX50 = 3,00,000

Less,Tax(40%o of 3,00,000)_____ 3,00,OOOX0.40 = 1,20,000

Now, Profit after tax = 1,80,000

So, Marginal safety in units = 6,000 units Marginal safety in Tk =18, 00,000 Taka

Now, Profit after tax = 1,80,000

Problem 4-Nov'08: The Sunmoon Ltd. Is the distributor for a foreign product. The product sells in the market for TK. 200.00 per unit with a variable selling expenses of Tk. 20.00 and a item based commission of Tk. 40.00 per item. The Company's cost of import at its godown is Tk. 90.00. Fixed selling and administrative expenses are Tk.

2,00,000.00 per year. Required:

(i) What is Break even point in unit and taka;

(ii) What sales level in unit is required to earn an annual before tax profit of Tk. I ,50,000.00

(iii) What sales level must be achieved to have the same level of after tax profit as above. If tax rate is 40%.

(iv) What sales level must be achieved to have the after tax target profit Tk. 3,00,000. If tax rate is 30%.

Solution:
Calculation of unit contribution: Variable cost of the product/unit:
Variable Selling expenses :	20.00
Commission :	40.00
Cost of import :	90.00
Variable Cost per unit= 150 Taka
Selling price per unit = Tk.200

So, Unit Contribution = Selling price per unit - Variable Cost per unit = 200-150= Tk. 50.00

Required i:

BEP in units = FC/Contribution per unit = 2, 00,000/50 = 4,000 units

Therefore BEP in sales = 4,OOOX200

= 8, 00,000 Taka

Required ii:

Level of sales unit to earn an annually profit before tax of Taka 1,50,000

Level of sales = (Fixed Cost+expected profit)/Contribution margin per unit) = (2,00,000+1,50,000)/50

= 3,50,000/50

= 7000 units

Required iii:

Profit after tax

Fixed Cost + 1- Tax rate

Required sales Level=

Contribution Margin per unit

	1, 50,000
2,00,000	+ 1-0.40
	50
	1,50,000
2,00,000	+ 0.60
	50
2,00,000	+ 2,50,000
	50

= 9,000 units

Required iv:

Given, Profit after tax= Th. 3,00,000

Required sales Level= Profit after tax

Fixed Cost + 1- Tax rate

Contribution Margin per unit

3,00,000

2,00,000 + 1-0.30

3,00,000

2,00,000 + 0.70

2,00,000 + 4,28,571.42

50 6,28,571.42

Problem: 5

Philips Company manufactures and sells its own brand of cameras. It sells each camera for Tk. 28. The company's account shows the following data:

Manufacturing cost:

Variable Tk. 12 per unit

Fixed Tk. 1,00,000 per year

Selling and Administrative cost:

Variable Tk. 4 per unit

Fixed Tk. 44,000 per year

Required:

(i) Use the per unit Contribution Margin (CM) approach to determine the Break even point in unit and in Taka.

(ii) Use the per unit Contribution Margin (CM) approach to determine the level of sales in units and in Taka required to obtain a Tk. 84,000 profit.

(iii) Suppose that variable selling and administrative cost could be eliminated by having a salaried sales force. If the company could sale 20,000 units, how much could it pay in salaries for the sales people and still have a profit of Tk. 84.000.

Solution:

Total VC= Tk.12+4=Tk. 16 Total FC = Tk. 1,44,000 Sell price =Tk. 28

Contribution margin=28-16=12

Required i:

BEP in unit = TFC/CM per unit = 1,44,000/12 = 12,000 units

BEP in sales volume = Tk. 12,OOOX28 = Tk. 3,36,000

Required ii:

BEP in unit = TFC/CM per unit

= 1,44,000+84,000/12 = 19,000 units

BEP in sales volume = Tk. 19,OOOX28 = Tk. 5,32,000

Required iii:

New VC = Tk.12/unit

Total sell price= 20,OOOX28 = Tk. 5,60,000

New CM = 28-12 =16

Target profit = Tk.84,000 Target sales = 20,000 units

Suppose salaries = `X' So, FC=(1,44,OOO+X)

Target sales = (FC+ Profit)/CM per unit

Or 20,000 = (1,44,000+X+84,000)/16

Or 20,OOOX 16 = 2,28,000+X

Or X = 3,20,000-2,28,000

X = 92,000.

So, Salaries will be stand = Tk. 92,000

Problem 6-May'20ll, 2012: Lisa Company is the executive distributor of an automative product. The product sells for Tk. 40 per unit and has a CM ratio 30%. The company's fixed expenses are Tk. 1,80,000 per year.

Required:

(i) What is the variable expenses per unit? (ii) Using the equation method:

(1) What is the Break even point in units and sales taka.

(2) What sales level in units and in sales taka is required to earn an annual profit of Tk. 60,000? .

(3) Assume that by using a more efficient shipper, the company is able to reduce its variable expenses by Tk. 4 per unit. What is the Company's new Break even point in units and sales taka?

(iii) Repeat (ii) above using the unit contribution method.

Solution:

Given,

Sales price= Tk. 40

Contribution Margin = 30%= 40X30%= Tk. 12 Fixed Cost = 1,80,000

Required i:

Variable Cost per unit

We know, Contribution=Sales-Variable cost per unit

Variable cost per unit = Sales - Contribution

=40-12

= 28 Taka

Required ii:

BI--,P in units = Fixed Cost/Contribution Margin per unit = 1,80,000/12 = 15,000 units

BEP in sales volume = 15,OOOX40

= 6,00,000 Taka

Required iii:

Expected profit: Tk. 60,000

a) To earn expected profit of Tk. 90,000 sales level requirement in units _(Fixed Cost+expected profit)/Contribution margin per unit) _ (1,80,000+60,000)/12

= 2,40,000/12

= 20,000 units

BEP in sales volume = 20,OOOX40

= 8,00,000 Taka

Required iii:

By equation method,

Suppose BEP in unit = `X' So, Sales price 40X So, Variable cost 28X

Now,

40X = FC+28X

12X = 1,80,000

= 15,000 units

So, BEP in sales= 15,OOOX40

= 6,00,000 Taka

(2) Target profit Tk. 60,000

Target profit= Sales-(Fixed Coct+Variable Cost per unit) Or, 60,000 = 40X- 1,80,000 -28X Or, 12X = 2,40,000

X = 20,000 units

So, sales in Tk. 20,OOOX40 Tk. 8,00,000

(3) New Variable Cost per unit= (28-4)X = 24X

Now, 40X = 1,80,000+24X 16X = 1,80,000 X = 11,250 units

Sales in Taka= 1 1,250X40

= 4,50,000 Taka.

Target sales = (FC+ Profit)/CM per unit

Or 20,000 = (1,44,000+X+84,000)/ 16

Or 20,OOOX 16 = 2,28,000+X

Or X = 3,20,000-2,28,000

X = 92,000.

So, Salaries = Tk. 92,000

New VC = Tk. 28-4 =Tk. 24

New REP in units = FC/CM per unit

= 1,80,000/40-24 = 11,250 units

BEP in sales volume= Tk. 1 1,250X40 = Tk. 4,50,000

Ch. Capital Budgeting

Problem-1: The Azad Int. Ltd. is contemplating to invest in a new project that would require procurement of a machine costing Tk. 25,50,000; and a working capital of Tk. 1,00,000. The project is expected provide benefits for five years. The expected profit before depreciation and tax from the project is as below:

Year	Profit before Tax & Depreciation
l^s`year	8,50,000
2"^a year	7,00,000
3`^d year	6,50,000
4"' year	6,00,000
5`^h year	4,50,000

(The policy of the company is to depreciate fixed assets on straight line basis over the period of the asset. Salvage value of the machine is expected to be Tk. 50,000. Assume a 40% tax rate and cost of capital of 10%.)

Required: Determine the acceptability of the project on the basis of

(i) Payback period; (ii) ARR; (iii) NPV; (iv) IRR; (v) Profitability Index.

(The present values of Tk.1 for five years at 10% are 0.9091; 0.8264; 0.7513; 0.6830; 0.6209)

Solution:

Depreciation= Cost-Salvage value/No. of year in lifetime = 25,50,000-50,000/5 = 5,00,000

Total investment= 25,50,000 (Machine price)+1,00,000(Working capital) = 26,50,000

Statement of cash inflow:

Particular

I^styear

2"^d year

3`^d year

4`^h year

5`^h year

Profit before Tax & Depreciation

Less Depreciation

8,50,000

5,00,000

7,00,000

5,00,000

6,50,000

5,00,000

6,00,000

5,00,000

4,50,000

5,00,000

Profit before Tax

Less Tax(~,40%

3,50,000

1,40,000

2,00,000

80,000

1,50,000

60,000

1,00,000

40,000

(50,000)

Profit after tax

Add depreciation

2,10,000

5,00,000

1,20,000

5,00,000

90,000

5,00,000

60,000

5,00,000

(50,000)

5,00,000

Cash before Terminal cash inflow

Add Salvage value at 5'^h year

Add Working capital

7,10,000

6,20,000

5,90,000

5,60,000

4,50,000

50,000

1,00,000

7,10,000

6,20,000

5,90,000

5,60,000

6,00,000

Required 1:

Pay Back Period (PBP):

Year	Cash inflow	Cumulative cash inflow
1	7,10,000	7,10,000
2	6,20,000	13,30,000
3	5,90,000	19,20,000
4	5,60,000	24,80,000
5	6,00,000	30,80,000

PBP= 4+ (Total investment-4`^h year cumulative cash inflow)/5`^h year cash inflow = 4+ (26,50,000-24,80,000)/6,00,000 = 4.28 years

Required-2:

Averaj!e rate of return:

ARR= (Average annual profit/Average investment)x 100

_({(2, I 0,000+ I,20,000+90,000+60,000-50,000)/5}/(26,50,000+50,000)/2J x 100 (86,000/13,50,000)x]00

= 6.37%

Required-3:

Net Present Value (NPV) calculation:

Year	Cash flow	Discount factor a,10%	Present value
1	7,10,000	0.9091	6,45,467
2	6,20,000	0.8264	5,12,368
_	5,90,000	0.7513	4,43,267
_	5,60,000	0.6830	3,82,480
5	6,00,000	0.6209	3,72,540
Present value of cash = 23,56,1 16 Less, investment =(26,50,000)
Net Present Value (NPV) (2,93,884)

Required-4:

Internal Rate of Return (IRR):

Since the NPV at 10%, discounting rate is negative Let us take lower discounting rate 5%.

Therefore,

Present value={7,10,000/(1+0.05)+6,20,000/(1+0.05)²+5,90,000/(1+0.05)³ +5,60,000/(1+0.05)⁴+6,00,000/(1+0.05)⁵}-26,50,000(total investment)

=(6,76,190.48+5,62,358.28+5,09,664.18+4,60,713.39+4,70,115.70) - 26,50,000 (total investment)

= 26,77,488-26,50,000(total investment) =27488.

IRR= A+C/C-D(B-A)

= 5%+27488/27488-(-2,93,884)X(10%-5%)

= 5%+27488/321372x5% = 5%+ 0.0855 X 5%

= 0.05+0.0042 =0.0542 -5.42%

Required-5:

Calculation of Profitability Index (PI):

P1=PV of cash inflow/PV of investment cost = 23, 56,116/26, 50,000 = 0.889

= 0.89 (Approximated)

Ans:

i) Pay Back Period 4.28 years

ii) ARR= 6.37%

iii) NPV= (-2,93,884)

iv) PI = 0.89

Here,

A= Lower discounting rate

B= Higher discounting rate

C= NPV of lower discounting rate

D= NPV of higher discounting rate

Comments: Out of 5 years project life, the investment will return within 4.28 years, ARR is 6.37% which is lower than cost of capital, PI is less than I and NPV value negative, So the project is not acceptable.

Problem-2: The Azom Int. Ltd. is contemplating to invest in a new project that would require procurement of a machine costing Tk. 21,00,000; and a working capital of Tk. 1,00,000. The project is expected to provide benefits for five years. The expected profit before depreciation and tax from the project is as below:

Year	Profit before Tax & Depreciation
1 S` year	7,50,000
2"^d year	6,50,000
3`^d year	5,50,000
4`" year	5,00,000
5`" year	4,50,000

(The policy of the company is to depreciate fixed assets on straight line basis over the period of the asset. Salvage value of the machine is expected to be Tk. 1,00,000. Assume a 50% tax rate and cost of capital of 10%.)

Required: Determine the financial viability of the project on the basis of (i) Payback period; (ii) ARR; (iii) NPV; (iv) IRR; (v) Profitability Index.

(The present values of Tk.1 for five years at 10% are 0.9001; 0.8264; 0.7513; 0.6830: 0.6209)

Solution:

Depreciation= Cost-Salvage value/No. of year in lifetime = 21,00,000-1,00,000/5 = 4,00,000

Statement of investment cost

Total investment= 21,00,000 (Cost of project)+1,00,000(Working capital)

= 22,00,000

Statement of cash inflow

Particular	1'` year	2"' year	3`^d year	4`" year	5`" year
Profit before Tax & Depreciation Less Depreciation	7,50,000 4,00,000	6,50,000 4,00,000 _	5,50,000 4,00,000	5,00,000 4,00,000	4,50,000 4,00,000
Profit before Tax	3,50,000	2,50,000	1,50,000	1,00,000	50,000
Less Tax cr,50%	1,75,000	1,25,000	75,000	50,000	25,000
Profit after tax	1,75,000	1,25,000	75,000	50,000	25,000
Add depreciation	4,00,000	4,00,000	4,00,000	4,00,000	4,00,000
Cash before Terminal cash	5,75,000	5,25,000	4,75,000	4,50,000	4,25,000
inflow	-	-	-	-	1,00,000
Add Salvage value at 5`^h year	-	-	-	-	1,00,000
Add Working capital
	5,75,000	5,25,000	4,75,000	4,50,000	6,25,000

Required -1:

Pay Back Period (PBP):

Year	Cash inflow	Cumulative cash inflow
1	5,75,000	5,75,000
2	5,25,000	11,00,000
3	4,75,000	15,75,000
4	4,50,000	20,25,000
5	6,25,000	26,50,000

PBP= 4+ (Total investment-4^th year cumulative cash inflow)/5 ^Ihyear cash inflow = 4+ (22,000,000-20,25,000)/6,25,000 = 4.28 years

Required-2:

Average rate of return:

ARR= (Average annual profit/Average investment)x 100

= [{(I,75,000+1,25,000+75,000+50,000+25,000)/5}/(22,00,000+1,00,000)/2] x100

= (90,000/11,50,000)X100

= 7.83%

Required-3:

Net Present Value(NPV) calculation:

Ye ar	Cash flow	Discount factor@ 10%	Present value
	5,75,000	0.9091	5,22,732
2	5,25,000	0.8264	4,33,860
3	4,75,000	0.7513	3,56,867
4	4,50,000	0.6830	3,07,350
5	6,25,000	0.6209	3,88,062
Present value of cash inflow = 20,08,871 Less, investment =(22,00,000)
Net Present Value (NPV) (1,91,129)

Required-4:

Internal Rate of Return (IRR):

Since the NPV at 10%, discounting rate is negative, let us take lower discounting rate 5%.

Therefore,

Present value= 5,75,000/(1+0.05)+5,25,000/(1+0.05)²+4,75,000/(1+0.05)³

So, NPV

+4,50,000/(1+0.05 )⁴+6,25,000/(1 +0.05)⁵

= (5,47,619+4,76,406+4,10,331+3,70,218+4,89,735) = 22,94,309

= 22,94,309-22,00,000

= 94,309.

IRR= A+C/C-D(B-A)

= 5%+94,309/94,309-(-1,19,129)X(10%-5%)

= 5%+94,309/2,85,138x5% = 0.05+ 0.0165

=6.65%

Here,

A=Lower discounting rate

B= Higher discounting rate

C=NPV of lower discounting rate

D= NPV of higher discounting rate

Required-5:

Calculation of Profitability Index (PI):

P1=PV of cash inflow/PV of investment cost = 20,08,871/22,00,000 = 0.91 (Approximate)

Comments: Out of 5 years project life, the investment will return within 4.28 years, ARR is 7.83% which is lower than cost of capital, P1 is less than I and NPV value negative, So the project is not financially viable.

Problem-3: The `X' Int. Ltd. is contemplating to invest in a new project that would require procurement of a machine costing Tk.10,00,000; and no working capital. The project is expected to provide benefits for ten years. The expected profit before depreciation and tax from the project is as below:

Year	Profit before Tax & Depreciation
1⁵¹year	2,50,000
2"^d year	4,00,000
3^rdyear	4,00,000
4`^h year	4,00,000
5'ⁿ year	3,50,000
6"' year	3,00,000
7`ⁿ year	2,50,000
8th year	2,00,000
9th year	1,50,000
10`^h year	1,00,000

(The policy of the company is to depreciate fixed assets on straight line basis over the period of the asset. No Salvage value of the machine is expected. Assume a 40% tax rate and cost of capital of 15%.)

Required: Determine the financial viability of the project on the basis of (i) Payback period; (ii) ARR; (iii) NPV; (iv) Profitability Index.

(The present values of Tk.l for five years at 15% are 0.87; 0.756; 0.658; 0.572; 0.497; 0.376; 0.432; 0.327; 0.284; 0.247.

Solution:

Depreciation= Cost-Salvage value/No. of year in lifetime

= 10,00,000-0/10

= 1,00,000

Statement of investment cost

Total investment= 10,00,000 (Cost of project)+0 (Working Capital)= 10,00,000

(Fi ure in Lac)

¹Particulars	1 st year	' 2nd year	3rd year	' 4th year	5th year	6th year	' 7th year	8th year	' 9th year	1Oth year
Profit before Tax &	2.50	4.00	4.00	4.00	3.50	3.00	2.50	2.00	1.50	1.00
Depreciation Less Depreciation	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00
Profit before Tax	1.50	3.00	3.00	3.00	2.50	2.00	1.50	1.00	0.50	-
Less Tax(a^-b,40%	0.525	1.05	1.05	1.05	0.875	0.70	0.525	0.35	0.175
Profit after tax	0.975	1.95	1.95	1.95	1.625	1.30	0.975	0.65	0.325	-
Add des reciation	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00
Cash before Terminal	-	-	-	-	-	-	-	-	-	-
cash inflow
Add Salvage value	-	-	-	-	-	-	-	-	-	-
Add working capital	-	-	-	-	-	-	-	-	-	-
Net cash inflow	1.975	2.95	2.95	2.95	2.625	2.30	1.975	1.65	1.325	1.00

Note- Please write full fiaure at exam script Required 1:

Pay Back Period (PBP):

Year	Cash inflow	Cumulative cash inflow
	1 ,97,500	1,97,000
	2,95,000	4,92,500
3	2,95,000	7,87,500
4	2,95,000	10,82,500
	2,62,500	13,45,000
	2,30,000	15,75,000

PBP = 3 year+ (Total investment-3`^d year cumulative cash inflow)/4`^h year cash inflow

= 3 year+ (10,00,000-7,87,500)/2,95,000

= 3 year+0.72 = 3.72 years

Required-2:

Avera2e rate of return

ARR = (Average annual profit/Average investment)x100

= [{(97,500+1,95,000+1,95,000+1,95,000+1,62,500+1,30,000+97,500+65,000+32,500)/10} /(10,00,000/2)] x 100

=(1,17,000/5,00,000)x]00

=23.4%

Required-3:

Net Present Value (NPV) calculation

NPV =(1,97,SOOX0.87)+ (2,95,OOOX0.756)+ (2,95,OOOX0.658)+ (2,95,OOOX0.572)+ (2,62,SOOX0.497)+ (2,30,OOOX0.376)+ (1,97,SOOX0.432)+ (1,65,OOOX0.327)+ (I,32,SOOX0.284)+ (1,00,OOOX0.247)] -10,00,000 (total Investment)

= {( l ,71,825+2,23,020+1,94,110+1,68,740+ I ,30,463+99,360+74,260+53,955+3 7,630+24,700)

=11,78,460.50}-10,00,000 (total Investment)

So, NPV =1 1,78,460.50-10,00,000 (total Investment)

= 1,78,460.50

Reg u ired-4:

Calculation of Profitability Index (PI)

P(=PV of cash inflow/PV of investment cost

= 11,78,460.50/10,00,000

= 1.178486

= 1.18 (Approximate)

Statement of present value of payback period

Year	Cash flow	Discount factoroy 15%	Present value	Cumulative amount of PV~'
1	,97,500	0.87	1 71,825	1,71,825
_	2,95,000	0.756	2,23,020	3,94845
	2,95,000	0.658	1,94,110	5,88,955
	2,95,000	0.57?	1,68,740	7,57,695
	2,62,500	0.497	1,30,463	8,88,158
	2,30,000	0.376	99,360	9,87,518
7	1,97,500	0.432	74,260	10,61,778
~ 8	1 65,000	0.327	53,955	1 1,15,733
9	,32,500	0.284	37,630	11,53,366
10	1,00,000	0.247	__ 24,700	1 1,78,063 ;

PVPE3P= 6 years+(Remaining amount)/PV of 7^1hyear

Total Present value

=1 1,78,063

=	6 years+ (10,00,000-9,87,518)/74,260
=	6 years+ 0.168
=	6.168 years
=	6.17 years (approx)

Ans.:
v)		Pay Back Period 3.72 Years
vi)		ARR= 23.8%
vii)		NPV= 1,78,460.50
viii)		PI = 1.18

Comments: Out of 10 years project life, the investment will return within 3.72 years, ARR is 23.8% which is higher than cost of capital, PI is greater than I and NPV value positive, So the project is acceptable.

Problem-4 (May11,12): The Chad Int. Ltd. is contemplating to invest in a new project that would require procurement of a machine costing Tk. 18,50,000; and a working capital of Tk. 1,50,000. The project is expected to provide benefits for nine years. The expected profit before depreciation and tax from the project is as below:

Year	Profit before Tax & Depreciation
ls year	3,50,000
2~ year	2,50,000
3" year	3,50,000
4`^h year	3,00,000
5 year	2,50,000
6"' year	2,50,000
7^1hyear	3,50,000
8 year	2,00,000
9th year	1,50,000

(The policy of the company is to depreciate fixed assets on straight line basis over the period of the asset. Salvage value of the machine is expected to be Tk50,000. Assume a 40% tax rate and cost of capital of 12%.)

Required: Determine the viability of the project on the basis of

(i) Payback period; (ii) ARR; (iii) NPV; (iv) Profitability Index.

(The present values of Tk.l for five years at 12% are 0.8929; 0.7972; 0.7181; 0.6355; 0.5674: 0.5066; 0.4523; 0.4039; 0.3606.

Solution:

Here. Depreciation= Cost-Salvage value/No. of year in lifetime - 18,50,000-50,000/9 = 2,00,000

Total investment = 18,50,000 (Machine price)+1,50,000(Working capital)

⁼20,00.000

Statement of cash inflow

(Fi ure in Lac)

Particulars	_1styear	₂nd year	3rd year	4th year	5th year	6th year	7^th year	8th year	9th year
Profit before Tax & Depreciation Less Depreciation	3.50 2.00	4.50 2.00	4.50 2.00	3.00 2.00	2.50 2.00	2.50 2.00	3.50 2.00	2.00 2.00	1.50 2.00
Profit before Tax Less Tax(&,40%	1.50 0.60	2.50 1.00	2.50 1.00	1.00 0.40	0.50 0.20	0.50 0.20	1.50 0.60	- -	(0.50) -
Profit after tax Add depreciation	0.90 2.00	1.50 2.00	1.50 2.00	0.60 2.00	0.30 2.00	0.30 2.00	0.90 2.00	- 2.00	(0.50) 2.00
Cash before Terminal cash inflow	2.90	3.50	3.50	2.60	2.30	2.30	2.90	2.00	1.50
Add Salvage value	-	-	-	-	-	-	-	-	0.50
Add working capital	-	-	-	-	-	-		-	1.50
Net cash inflow	2.90	3.50	3.50	2.60	2.30	2.30	2.90	2.00	3.50

Note- Please write full figure at exam script]

Required l:

Pay Back Period (PBP)

Year	Cash inflow	Cumulative cash inflow
I	2,90,000	2,90,000
	3,50,000	6,40,000
	3,50,000	9,90,000
	2,60,000	12,50,000
5	2,30,000	14,80,000
6	2,30,000	17,10,000
	2,90,000	20,00,000
8	2,00,000	22,00,000
	3,50,000	25,50,000

Pay Back Period= 7 Years Required-2:

Averaue rate of return

ARR= (Average annual profit/Average investment)X100

=[{(90,000+1,50,000+1,50,000+60,000+30,000+30,000+90,000-50,000)/9} /20,00,000/2] X100

= (61,1 1 1 / 10,00,000)X 100

= 6.11%

Required-3:

Net Present Value(NPV) calculation

Year	Cash flow	Discount factor@ 12%	Present value
1	2,90,000	0.8929	2,58,941
2	3,50,000	0.7972	2,79,020
3	3,50,000	0.7181	2,51,335
4	2,60,000	0.6355	1,65,230
5	2,30,000	0.5674	1,30,502
6	2,30,000	0.5066	1,16,518
7	2,90,000	0.4523	1,31,167
8	2,00,000	0.4039	80,780
9	3,50,000	0.3606	1,26,210
Present value of cash = 15,39,703 Less, investment =(20,00,000)
Net Present Value (NPV) (4,60,297)

Required-4:

Calculation of Profitability Index (PI) P1=PV of cash inflow/PV of investment cost

= 15,39,703/20,00,000 = 0.7698
Ans.:
ix)		Pay Back Period 7 Year
x)		ARR= 6.11%
x0		NPV= (-460297)
xii)		P1 = 0.7698

Comments: Out of 9 years project life, the investment will return within 7 years, ARR is 6.11% which is lower than cost of capital, Pl is less than I and NPV value negative. So the project is not viable.

Problem-(Nov' 11): A large size Company is considering investment in a project that costs Tk. 4,00,000. The estimated salvage value is zero; tax rate is 35%. The company uses straight line depreciation and the proposed project has cash flows before tax (CFBT) as follows:

Year	Profit before Tax & Depreciation
1" vear	1,00,000
2ⁿ`' year	1,00,000 ,
3"^d year	1 ,50,000
4^th year	1,50,000
5`ⁱ' year	2,50,000

_Required: Determine the following:

(i) Payback period; (ii) ARK; (iii) NPV at 15% ; (iv) Profitability Index; (v) Comments on the basis of result.

PVF at 15% : 0.870; 0.756; 0.658; 0.572; 0.497) Solution:

Depreciation- Cost-Salvage value/No. of year in lifetime

= 4,00.000-0/5 = 80, 000/- Statement of cash inflow:
Particulars	1^st Year	2^nd year	3^rd year 4^th year		^5thyear
I Profit before tax & Depreciation	1_00,000	1.00,000	1.50.000	1.50.000	2.50.000
Less Depreciation	80.000	80,000	80.000	80.000	' 80.000
Profit before tax C Profit beliOrc Tax ~	20.000	20,000	70.000	70.000	} 1.70.000
Less tax @ 35%	7.000	7,000	24.500	24.500	'_ 5 9.5 00
I Profit after tax	13,000	13,000	45,500	45.500	1,10,500
Add depreciation	80.000	80,000 '	80.000	80.000	80,000
cash inflow	93.000	93,000	1.25,500 125.500		1.90.500

Required 1:

Pav Back Period (PBP):

Year	Cash inflow	Cumulative cash inflow
1	93,000	93,000
2	93,000	1,86,000
3	1,25,500	3,11,500
4	1,25,500	4,37,000
5	1,90,500	6,27,500

PBP = 3+ (Total investment-3r^d year cumulative cash inflow)/4th year cash inflow

= 3+ (4,00,000-3,11,500)/1,^;-5,500

= 3+0.705

⁼3.71

So,Pay Back Period = 3.71 years

Required-2:

Average rate of return:

ARR= (Average annual profit/Average investment)X 100

=({(13,000+13,000+45,500+45,500+1,10,500)/5,^1./(4,00,000)/2] x 100

= (45,500/2,00,000)X 100

= 22.75%

Required-3:

Net Present Value (NPV) calculation:

Year	Cash flow	Discount factor( 15%	Present value
1	93,000	0.870	80,910
2	93,000	0.756	70,308 -
3	1,25.500	0.658	82,579
4	1,25,500	0.572 1	71,786
5 1,90,500 _I		0.497 1	94,679
I Present value of cash = 4,00,262
Less investment = (4,00,000
Net present value (NPV) = 262

Required-4:

Calculation of Profitabilitv Index (PI): P1-PV of cash intlo~e/PV of investment cost

-- 4.00?62/4,00,000 = 0.889 = 1.000655
Ans.:
i)		Pay Back Period 3.71 years
ii)		ARR=22.75%
iii)		NPV= 262
iv)		P1 =1.000655

Comments: Out of 5 years project life, the investment will return within 3.71 years, ARR is 22.75% which is higher than cost of capital, P1 is greater than I and NPV value positive. So the project is acceptable.

Problem-5: ABC Company has limited funds available for investment and must ration the funds among five competing projects. Selected information on the five projects are given below:

Project	Investmen t required	Net Present Value(NPV)	Life of the project(years)	Internal Rate of Return (%)
Project C	8,00,000	2,21,615		18
Project B	6,75,000	2,10,000	12	16
Project A	5,00,000	1,75,175	7	20
Project D	7,00,000	1,52,544	3	22
Project E	9,00,000	(52,176)	6	8

[The ABC company's cost of capital is 10% (the net present values above have been computed using a 10% discount rate.) The wants your assistance in determining which project to accept first which to accept second and so forth.]

Solution:

(1) Profitability Index Calculation

We know,

Profitability Index Calculation

PI=PV of cash inflow/PV of cash outflow

For project A:

Present value= NPV+Investment = 2,21,615+8,00,000 = 10,21,615

So, Pl= 10,21,615/8,00,000 = 1.27 > 1

For project B:

Present value= NPV+Investment = 2,10,000+6,75,000 = 8,85,000

So, Pl= 8,85,000/6,75,000 = 1.31> 1

For project C:

Present value= NPV+Investment = 1,75,175+5,00,000 = 6,75,175

So, PI= 6,75,175/5,00,000 = 1.35> 1

For project D:

Present value= NPV+Investment = 1,52,544+7,00,000 = 8,52,544

So, PI= 8,52,544/7,00,000 = 1.22 > 1

For project E:

Present value= NPV+Investment = 9,00,000+(-52,176) = 8,47,824

So, PI= 8,47,824/9,00,000 = 0.94< 1

Since ABC has limited funds. So, we have to choose the best alternative and the ranking of preference are:

Project	Rating
Project A=135	1
Project B=1.31	2
Project C=1.27	_ 3
Project D=1.22	4
Pr~ect E=0.94	5

Project E should not be accepted because PI is than 1(<1)

(2) Net Present Value(NPV)

(i) Ranking of the 5(five) projects in terms of Net Present Value(NPV) are as follows:

Project	NPV	Rating
Project A	2,21,615	1
Project B	2,10,000
Project C	1,75,175
Project D	1,52,544	4
Project E	(52,176)

(3) Profitability Index (PI)

(ii) Ranking of the 5(five) projects in terms of Profitability Index (PI) are as follows:

Project	PI	Rating
Project C	1.35	1
Project B	1.31	2
Project A	1.27	3
Pro'ect D	1.22	4
, Pr~ject E	0.94	5

(i) Ranking of the 5(five) projects in terms of Internal Rate of Return(IRR) are as follows:

Project	NPV	Rating
Project D	_-22%	1
Project C	20%	2
Project A	18%	3
Project B	16%	4
Project E	8%	5

(4) The ranking in terms of Net Present Value (NPV) should be given preference. Because

(i) NPV gives accurate results because of consider all cash flows,

(ii) IRR gives misleading in non conventional investment project.

(iii) IRR also gives multiple rates.

(iv) Profitability Index(PI) is crude way to cope up the rate and it gives misleading if investment made reversal time.

(5) If capital rationing situation prevails in the company with a budget constraints of the 1.5 million, we should prefer project A and Project D

Because

(i) Project A gives higher NPV

(ii) Project D gives highest IRR

(iii) Since Project B gives second highest NPV but it takes 12 years

(iv) In considering PI the Project C is the best but some portion of our investment is

being idle if project C is chosen. SO project A and D would be best preference.

(6) The causes of difference in outcomes of the project under NPV and IRR methods are as follows:

(i) NPV consider cash flows at the cost of capital rate over the year but IRR deals re-investment rate that may not prevail in the market.

(ii) If the outcome or inflows are great in recent year and smaller in later year than IRR gives misleading

(iii) For non conventional project, IRR gives misleading for that reason the difference is made.

Ch-Lease

Problem No.1( May'2011): Y Ltd. is considering an investment project, which will require an equipment costing Tk. 10,00,000. Two options are available to (i) term loan for 5 years. or (ii) to lease such equipment from a leasing company at an annual installment of Tk. 2,00,000 for five years. The asset would be depreciated at straight line method with a salvage value 10% of the asset. The asset will also require an annual repair costs of Tk. 20,000. The company is at 40% tax bracket and its cost of capital (required rate of return) is 10%. Preliminary negotiations with the bank reveal that the company may have a hypothecation loan to be adequate to purchase the asset of Tk. 10,00,000 at 10% interest rate for 5 years to be paid on equal annual installments. The loan is available at 20% compensating balance. As a manager, decide which one is acceptable-leasing or borrow-buy. (The present values of Tk. 1 for five years at 10% are 0.909; 0.826; 0.751; 0.683 and 0.620)

(i ) If the company take lease

Statement of payment procedure in the context of lease perspective

Year	Amount of Rent (Tk.)	Rebate of Tax (c~45%	Cash outflow 3=1-2	PV flow	PV g10%
0	1	2	3	4	5
0	2,00,000	0	2,00,000	1.00	2,00,000
1-4	2,00,000	90,000	1,10,000	3.17	3,48,000
	0	90,000	(90,000)	0.621	(55,890)
Total =4,92,810

(ii) I f the company take loan

First find out the installment size:

Installment size =Principal= [1/R-1/R(1+R)"]

=	10,00,000 = [1/o.lo-vo.lo(l+o.lo)^s]
=	10,00,000 =	[1/0.10-1/0.000016]
=	10,00,000 =	[0.000016-1 /0.000016]

= 10,00,000 = 3.789

= 2,63,922

Table of principal amount & amount of interest for loan perspective

Year	Balance of loan	Amount of installment	Interest @ 10%	Payment of principal amount
0	10,00,000	2,00,000	-	-
1	10,00,000	2.63,922	1,00,000	1,63,922
2	8,36,078	2,63,922	83,608	1,80,314
3	6,55,764	2,63,922	65,576	1,98,346
	4,57,418	2,63,922	45,742	2,18,180
	2,39,238	2,63,922	23,924	2,39,238

[Tk. 2,00,000 adjusted which is paid at the period of loan disbursement]

Depreciation +Maintenance Exp.=1,80,000

Statement of cash inflow and it's present value in the context of loan and purchase a reement

Year	Payment of loan installment	Interest exp.	Depreci ation+ Exp.	Tax shield able exp	Tax shield 4x45%	Net cash outflow	PV factor	PV of 10%
0	1	2	3	4=2+3	5	6=1-5	7	8=6X7
	2,00,000	-	-	-	-	2,00,000	-	2,00,000
1	2,63,922	1,00,000	_ 1,80,000	_ 2,80,000	_ 1,26,000	1,37,922	09	1,25,371
2	2,63,922 _	83,608	1,80,000	2,63,608	1,18624	1,45,298	0.8264	1,20,074 ,
	2,63,922	65,576	1,80,000	2,45,578	_ 1,10,510	1,53,412	_ 0.75131	1,15.260
	2,63,922 _	45,742	1,80,000	2,25,142	1.01.584	1,62,338	0.6830	1 ¹0.877
5	2,63,922	23,924	1,80,000	2,03,924	91,760	(28,604)	0.620q~ ~(17,761)

Total 6,5 3.821

Less-Salvage value (2,00,OOOx0.62092) (1.24,180)

Gross Total PV of net cash flow 5.29.641

Here,

Total cash outflow Tk.4, 92,810 in case of leasing

Total cash outflow Tk.S, 29,641 in case of purchase and loan Amount sho^-vvn less in case of leasing Tk. 36.831

So, in the above circumstances leasing is acceptable.

Problem No.2 ( May'2011): XYZ Builders and Co. needs to acquire the use of a crane for construction business and is considering whether to buy or lease. The crane cost Tk. 10,00,000 and subject to straight line depreciation method to a zero salvage value at the end of 5 years. In contrast, lease rent of Tk. 2,20,000 per year to be paid in advance each year for 5 years. The XYZ Builders can raise debt at 14% payable in 5 equal installments, each installment becoming due at the beginning of the year. It is in 50% tax bracket.

Advice the company which one is will be beneficial.

Solution:

(i ) If the company take lease

Statement of payment procedure in the context of lease perspective

Year	Amount of Rent (Tk.)	Rebate of Tax @50%	Cash outflow 3=1-2	PV flow	PV @10%
0	1	2	3	4	5
0	2,20,000	0	2,20,000	1.00	2,20,000
1-4	2,20,000	1,10,000	1,10,000	3.17	3,48,700
	0	1,10,000	(1,10,000)	0.621	(68,310)
Total
=500,390

(ii) If the company take loan

First find out the installment size:

Installment size =Principal = [1/R-1/R(1+R)"]

= 10,00,000 = [1/0.14-1/0.14(1+0.14)⁵] = 10,00,000 = [1/0.14-1/0.14(1.14) ⁵]= 10.,00,000 = [7.14286-3.70975⁵] = 10,00,000 = 3.43311

=2,91,281

Table of principal amount & amount of interest for loan perspective

Year	Balance of loan	Amount of installment	Interest @14%	Payment of principal amount
0	10,00,000	-	-	-
1	10,00,000	2,91,281	1,40,000	1,51,281
2	8,48,719	2,91,281	1,18,821	1,72,460
3	6,76,259	2,91,281	94,676	1,96,605
4	4,79,654	2,91,281	67,152	2,24,129
	2,55,525	2,91,299	35,774	2,55,525

Depreciation =(10,00,000-0)/5=2,00,000

Statement of cash inflow and it's present value in the context of loan and purchase agreement

Y.	Payment of loan installment	Interest exp.	Depreciat ion+,Vop,	Tax shield able exp	Tax shield 4x50%	Net cash outflow	PV factor	PV of 10%
	1	2	3	4=2+3	5	6=1-5	7	8=6X7
1	2,91,281	1,40,000	2,00,000	3,40,000	1,70,000	1 21,281	0.909	1,10,244
2	2,91,281	1,18,821	2,00,000	3,18,821	159,411	1,31,870	0.8264	1,08,977
3	2,91,281	94,676	2,00,000	2,94,676	1,47,338	1,43,943	0.75131	1,08,146
4	2,91,281	67,152	2,00,000	2,68,152	1,33,576	1,57,705	0.6830	1,07,713
5	2,91,299	35,774	2,00,000	2,35,774	1,17,887	1,73,412	0.62092	10,7,675
Total 5,42,755
Gross Total PV of net cash flow 5,42,755

Here,

Total cash outflow Tk.500,390 in case of leasing

Total cash outflow Tk.5, 42,755 in case of purchase and loan Amount shown less in case of leasing Tk. 42365

So, in the above circumstances leasing is acceptable.

Ch.-Cost of Goods sold statement

Problem: The following data are from the accounts of M & H Company:

Particulars	July 1, 2011	June 30, 2012
Inventories
	Taka	Taka
Finished goods	20,000	28,000
Work in progress	60,000	25,000
Material	40,000	48,000

Particulars	Taka
Sales discount	8,000
Purchase discount	3,200
Sales	18,00,000
Purchase return and allowances	20,000
Depreciation-factory Machinery	1,60,000 _
Factory Insurance	50,000
Freight-out	8,000
Other Factory Expenses	16,000
Bond Interest Ex.enses	50,000 _
Sales Salaries	1,00,000
Freight-in	12,000
Direct Factory labor	8,00,000
Material Purchases	4,00,000 _
Advertising Expenses	12,000

Required: Prepare a cost of goods Manufactured statement for the year ended June 30, 2012

Solution:

Particulars	Amount	Amount	Amount
Raw Materials:
(1) Beginning Raw materials		40,000
(2) Add-Raw materials purchase (3) Less-Raw materials returns (4) Less-Purchase discount	4,00,000 20,000 3,200
Net purchase Add-Freight in	3,76,800 12,000
Net Raw materials add 3,88,800
Raw Materials available for use 4,28,800
Less- Closing stock of Raw materials 48,000

Raw Materials consumed			3,80,800
Add, Direct labor			8,00,000
Prime cost			11,80,800
Add, Factory overhead	1,60,000 50,000 16,000
Depreciation on Factory machinery Factory Insurance factory expenditure _-Other
Total Factory overhead 2,26,000
manufacturin_ cost _{_}Total		14,06,800
Add- Opening work in process		60,000
		14,66,800
Less- Closing work in process		(25,000)
Cost of goods manufactured		14,41,800
Add- Opening finished goods		20,000
Cost of Goods available for sale		14,61,800
Less-Closing finished goods		(28,000)
Cost of goods sold		14,33,800

Income statement for the ^,ear ended 30`" June 2011

Particulars	Amount	Amount
Sales Less- sales discount		18,00,000 8,000
Net sales		17,92,000
Less-Cost of goods sold		14,33,800 3,58,200
Gross margin		14,33,800 3,58,200
Less- Operating and Administration
Freight out Bond interest Sales salaries Advertising expenses	8,000 50,000 1,00,000 12,000
Total operating expenses _		1,70,000
Net income		1,88,200

Ch-Cash Flow statement

Problem-1: Presented below is the comparative balance sheet for Navana Corporation as of Oct, 3 I^s' :

Assets

Particulars	2012 Taka	2011 Taka
Cash	41,000	45,000
Account receivable	47,500	52,000
Inventory	1,51,450	1,42,000
Prepaid expenses	16,780	21,000
Land	1,00,000	1,30,000
Equipment	2,28,000	1,55,000
Accumulated depreciation-equipment	(45,000)	(35,000)
Building	2,00,000	2,00,000
Accumulated depreciation-building	_ (60,000)	(40,000)
	6,79,730	6,70,000

Liabilities and stockholders' Equity

Particulars	2012 ~ Taka	2011 Taka
Accounts payable	43,730	40,000
Bonds payable	2,50,000	3,00,000
Common Stock, Tk. 10 par	2,00,000	1,50,000
Retained Earnings	1,86,000	1,80,000
	6,79,730	6,70,000

Additional information:

(1) Operating expenses include depreciation expense of Tk. 42,000 and charges from

prepaid expenses of Tk. 4,220;

(2) Land was sold for cash at book value;

(3) Cash dividends of Tk. 32,000 were paid;

(4) Net income for the year was Tk. 38,000;

(5) Equipment was purchased for Tk. 95,000 cash. In addition, equipment costing Tk. 22,000 with a book value of Tk. 10,000 was sold for Tk. 8,100 cash.

(6) Bonds were converted at face value by issuing 5,000 shares of Tk.10 par value common stock.

Instructions: Prepare a statement of Cash flow for the year ended October, 31,2012, using the indirect method.

Net Cash flow from financing activities

(³2.000)

Indirect Method :

Particulars	Taka	Taka
(A) Cash flow from operating activities:
Net Income	38,000
Adjustment to reconcile net income to net cash provided by operating activities:
Decrease in account re eivable	4,500
Increase in inventories
Increase in account pa able
Decrease in prepaid ex crises	4,220
Depreciation expenses	42,000
Capital (Loss on )sale of assets	1 900
Net Cash provided by operating activities		84,900
(B) Cash flow from investing activities:
Purchase of plants and assets:
Sales of land	30,000
Purchase of equipment	(95,000)
Sales of equipment	8,100
Net Cash flow from investing activities		(56.900)
(C) Cash flow from financing activities:		(56.900)
Decrease in bonds payable	(50,000)
Proceed from stock issue	50,000
Paid cash dividend	(32,000)
Change in cash		(4,000)
Opening cash balance in 2010		41,000
_-Closing cash balance at 31^s' October, 2010		37000

Statement of Cost

Problem-1 (Nov.11) : A factory produced and sold 1,000 units of product in the month of June,

2012 for which the following particulars are available: Particulars	Taka
Stock of Raw Materials on I 't June	6,000
Purchase and receipt of Raw Materials during the month of June	1,44,000
Direct wages paid in cash in June(which included Tk. 3,000 on	55,000
account of May and Tk. 2,000 advance for July) Stock of Raw Materials on 30`" June	10,000
Works overhead charges for the month	60,000
Administrative and selling overheads	Tk. 25 per unit
Sales price	Tk. 300 per unit
From the above particulars you are required to prepare:

1. A statement of cost for the month of June,2012;

2. Estimate the sales price of a unit of the same product in July, 2012, assuming(i) 10% increase in the cost of raw materials;

(ii) 10% increase in the direct wages:

(iii) 5% increase in works overhead charges;

(iv) 20% decrease in administrative and selling overhead charges;

(v) Same percentage of profit on sales price as earned during the month of June.

Solution:

1) Statement of cost for the month of June, 2012-

f Particulars		Taka	Taka
Opening stock of RM (1 s` June)			6,000
Add-Purchase and receipt of RM during the month of June			1,44,000
Add- Direct wages		55,000-(3,000+2000)	50,000
Add-Works overhead charges for the month			60,000
Add-Administrative and selling overheads		1000 units x Tk. 25 per unit	25,000
2,85,000
Clsing stock of RM			10,000
Cost of Goods sold			2,75,000

Sales price Tk. 300 per unit
Sales proceed	(Tk. 300 1000 units)		3,00,000
Profit	Tk. 3,00,000-Tk. 2,75,000		25,000
Percentage of profit on sales	Tk. (25,OOOx 100)/3,00,000		8.33%

2) Estimatiniz the sales price:	1,44,000 14,400 1,58,400
(i) RM purchased Add-10% increase	1,44,000 14,400 1,58,400
(ii) Direct wages	50,000
10% increase	5,000
	55,000
(iii) Works overhead	60,000
5% increase	3,000
	63,000
(iv) Administrative and selling expenses	25,000
20% decrease	5,000
	20,000

c) Statement of cost (revised)

_Particulars		Taka	Taka
_Opening stock of RM			6,000
Add-Purchase and recei. of RM			1,58,400
			1,64,400
Clsing stock of RM -			(10,000)
_{_}RM_{_}consumed			1,54,400
_Add- Direct wages			55,000
~ Add-Works overhead charges for the month --- -			63,000 20,000
Add-Administrative and selling overheads
Cost of Goods sold			2,92,400
Add-Profit margin 8.33% (as on June)=2,92,400X8.33%			24,356.92
Sales proceed			3,16,756.92
[Sales_price of a unit	Tk. 3,16,756.92/1000 units		__ 316.76

Inventory Manazement:

Problem-1: Zaved international Ltd. Uses a material as the main component in its production process. Annual usage is 1,60,000 units. Ordering cost per order is Tk. 15,000 and carrying cost is Tk. 15% of the unit cost, which is Tk. 500 per unit for the year.

Determine:

(1) ECQ;

(2) Minimum Inventory Level, if safety stock is 10,000 units, lead time is ten days; (3) Maximum Inventory Level;

(4) Total Inventory cost.

Solution:

1) ECQ = 2A0/C

=~2X 1,60,OOOX 15,000/7S =~6,40,00,000/75 = 8,000 units

A=Annual Requirement 1,60,000 units

0=0perating Cost 15,000 taka

C=Carrying cost per Unit 500x 15%-75 1 k.

S=Cost per order

2) Minimum Inventory level= Safety stock+Demand during Lead time = 10,000+(1,60,OOOX 10/360) = 10,000+4,444 = 14,444 units

3) Minimum Inventory level= Safety stock+ECQ = 10,000+8,000 = 18,000 units

4) Total Inventory Cost=(EOQ/2) XC +(A/EOQ) XO

= (8,000/2X7S) + (1,60,000/B,OOOX 15,000) = 3,00,000+3,00,000

= Tk. 6,00,000

Ans.

1) ECQ= 8,000 units

2) Minimum Inventory level = 14,444 units 3) Minimum Inventory level = 18,000 units 4) Total Inventory Cost = Tk. 6,00,000

Where,

A=Annual Requirement 1,60,000 units 0=0perating Cost 15,000 taka

C=Carrying cost per Unit 500x 15%-75 1 k. S=Cost per order

Problem-2: Zaed international Ltd. Uses a material as the main component in its production process. Annual usage is 2,40,000 units. Ordering cost per order is Tk. 10,000 and carrying cost is Tk. 15% of the unit cost, which is Tk. 600 per unit for the year.

Determine:

(1) ECQ;

(2) Minimum Inventory Level, if safety stock is 20,000 units, lead time is ten days; (3) Maximum Inventory Level;

(4) Total Inventory cost.

Solution:

	1) ECQ = ~2A0/C =~2X2,40,OOOX 1,000/90 =~480,00,00,000/90		Where, A=Annual Requirement 2,40,000 units 0=0perating Cost 10,000 taka C=Carrying cost per Unit 600x 15%=90'1 i.. S=Cost per order
	= 7,303 units
2) Minimum Inventory level = Safety stock+Demand during Lead time
= = =		20,000+(2,40,000X 10/360) 20,000+6,667 26,667 units
3) Minimum Inventory level= Safety stock+ECQ = 20,000+7,303 = 27,303 units
4) Total Inventory Cost =(EOQ/2) xH + (A/EOQ) XS = (7,303/2X90) + (2,40,000/7,303X				10,000)
= 3,28,635+3,28,635 = Tk. 6,57,267
Ans.
1) ECQ =			7,303 units
2) Minimum Inventory level =			26,667 units
3) Minimum Inventory level =			27,303 units
4) Total Inventory Cost = 6,			57,267 Tk.

Ch.-Working Capital Requirement

Problem-1: A newly formed company has applied for a short-term loan to a commercial bank for financing its working capital requirements. You are requested by the bank to prepare an estimate of the requirements of working capital for that company. The information about the company is as under:

Estimated cost per unit of production is:

Particulars	Taka
Raw materials	80
Direct labor	30
Overheads (exclusive of depreciation)	60
Total cost = 170

Additional information:

Selling price	Tk. 200 per unit
Level of activity	1,04,000 units of production per annum
Raw materials in stock	average 4 weeks
Work in progress (assume gD% completion stage in respect of conversion costs)	average 2 weeks
Finished goods in stock	average 4 weeks
Credit allowed by suppliers	average 4 weeks
Credit allowed by debtors	average 8 weeks
Lag in payment of wages	average 1.50 weeks
Cash at bank expected to be	Tk. 25,000

You may assume that production is carried on evenly throughout the year (52 weeks) and wages and overheads accrue similarly. All sales are on credit basis only.

Required: Estimate the net working capital required for the company.

Solution:

Estimation of working capital requirements

(A) Investment in Inventory
(i) Investment in Raw materials=RM consumption x RM consumption Period/No. of week (ii) Investment in WIP=Cost of goods sold X WIP consumption Period/No. of week (iii) Investment in Finished goods=Cost of production x FG consumption Period/No. of week	(80X 1,04,OOOX4)/52 (170X 1,04,OOOXO.SX2)/52 (170X 1,04,OOOX4)/52	6,40,000 3,40,000 13,60,000
Total investment in inventory	(i+ii+iii)	23,40.000 27.20,000
(B) Investment in debtors= (Credit sale at costx8)/ No. of week	(170X 1,04,OOOx8)/52	23,40.000 27.20,000
Cash balance required _(C)		25,000
(D) Total investment in current assets (A+Q-+-C)			50,85,000
(E) Current liabilities
(i) Creditors=(Purchase of RMxCP)/No. of week (ii) Deferred wages=Labor costXCP)/No. of week	(80X 1,04,OOOX4)/52 (30x 1,04,OOOX 1.5)/52	6₁40,000 90,000	7,30,000
(E) Total Current liabilities			7,30,000
(F) Net working capital requirements (D - E)			43,55,000

Problem-2(Nov' 11): A proforma cost sheet of a company provides the following data:

Fstimated cost per unit of production is:

Costs (per unit)		Taka
Raw materials		52.00
Direct labor		19.50
Overheads		39.00
	Total cost (per unit )	110.50
Profits		19.50
Selling price		130.00

The following is the additional information available:

Average raw material and finished goods in stock	one month
average material in process	half a month
credit allowed by supplier	one month
credit allowed by debtors	two month
Time lag in payment of wages	one and half week
Overheads	one month
Cash balance is expected	Tk. 1,20,000
One fourth of the sales are on cash basis

You are required to prepare a statement showing the working capital needed to finance a level of activity of 70,000 units of output. You may assume that production is carried on evenly throughout the year (52 weeks) and wages and overheads accrue similarly.

Solution:

Estimation of working capital requirements

(A) Investment in Inventory
(i) Investment in Raw materials=RM consumption x RM consumption Period/No. of week (ii) [nvestment in WIP=Cost of goods sold x WIP consumption Period/No. of week (iii) Investment in Finished goods=Cost of production x FG I consumption Period/No. of ~ Week	(52X70,OOOX4)/52 (l 10.50X70,000X2)/52 (1 10.50X70,000X4)/52	2,80,000 2,97,500 5,95,000
~ Total investment in inventory (i+ii+iii) r---- --		1,72,500 10,50,000	I
I (B) Investment in debtors-(Credit sale at ~(130X70,OOOX0.75X8)/52 costx8)/ No. of week
(C) Cash balance required		1,20.000	I, -,
(D) Total investment in current assets (A+B)			23,42,500 i
(F) Current liabilities			I
(i) Creditors=(Purchase of RMxCP)/No. of week (ii) Deferred wages=Labor costxCP)/No. of week tti Deferred overheads	(52X70,OOOX4)/52 (19.5x-,':),000x 1.5)/52 (39X70,OOOX4)/52	2,80,000 39,375 2 ,10,000	5,29,375
(E) Total Current liabilities (i+ii+iii)
(F) Net working capital requirements (D - E)			18,13,125

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10 March, 2022

Management Accounting Math

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