Math Solutions- AIBB: Credit Operation and Management

 

AIBB · Credit Operations & Management

All Math Questions from COM Past Papers — Fully Solved

A complete, exam-oriented collection of every numerical problem from the IBB Banking Professional Examination (COM) papers, with concept notes, formulas, step-by-step workings and final answers.

16 Solved Problems CVP · NPV · IRR · BCR Working Capital · Ratio Analysis Provision & Eligible Collateral

What's inside

Click any topic to jump straight to the question, concept note and solution.

1. Eligible Collateral & Provision Base (Adit Enterprise)
2. CVP Analysis — ABC Seating
3. Capital Budgeting — ABO Enterprise
4. Working Capital — XYZ Company
5. Financial Ratio Analysis — Shakib & Afif
6. Capital Budgeting — TMJ Corporation
7. Break-Even Point (Graphical)
8. CVP Analysis — ABC Company
9. Working Capital — XYZ Company (70,000 units)
10. CVP Analysis — XYZ Enterprise
11. Capital Budgeting — XYZ Company Ltd.
12. CVP Analysis — ABC Company (2025)
13. Benefit Cost Ratio — Project X
14. Future Value of Deposit
15. Capital Budgeting — Delta Company Ltd.
16. Provision — Faruk Enterprise

Solved Problems

1

Eligible Collateral & Base for Provision — Adit Enterprise

96th Banking Professional Examination, 2023 · COM-6, Q4(c) · 8 marks

Question

Adit Enterprise took a loan from Loyal Bank Ltd. The present loan outstanding is Tk 50 lac. There is Tk 10 lac unrealized interest in the Interest Suspense Account. Other collaterals:

• Mortgaged land — Tk 30 lac
• Tin shed — Tk 10 lac
• Pledged goods — Tk 10 lac
• Deposit kept lien against the loan — Tk 10 lac

What is the total value of eligible collateral and base for provision?

Understanding Note

Eligible collateral is the value of security that Bangladesh Bank allows to be deducted from the loan outstanding before computing the base for provision. Banks cannot claim the full market value of every asset.

Bangladesh Bank approved eligibility percentages:

• Deposit under lien with the same bank — 100%
• Government bond / savings certificate under lien — 100%
• Government or Bangladesh Bank guarantee — 100%
• Gold / gold ornaments pledged — 100% of market value
• Easily marketable commodities under bank control — 50%
• Land & building mortgaged with bank — 50% max
• Listed shares — 50% (lower of 6-month average market value or 50% face value)

The base for provision is the greater of:

1. Outstanding − Interest Suspense − Eligible Collateral
2. 15% of outstanding

Solution

Step 1 — Compute eligible collateral:

Collateral	Value (lac)	Eligibility	Eligible (lac)
Deposit under lien	10	100%	10.00
Pledged goods	10	50%	5.00
Land + Tin shed	40	50%	20.00
Total eligible collateral	—	—	35.00

Step 2 — Compute base for provision:

Option 1 = 50 − 10 − 35 = Tk 5 lac Option 2 = 15% × 50 = Tk 7.5 lac

Base for provision = greater of the two = Tk 7.5 lac

Final Answer

• Total eligible collateralTk 35 lac
• Base for provisionTk 7.5 lac

2

CVP Analysis — ABC Seating

96th Banking Professional Examination, 2023 · COM-6, Q5(c)

Question

ABC Seating, a manufacturer of chairs, had the following information for 2020:

Sales	2,400 units
Sales price	Tk 40 per unit
Variable costs	Tk 15 per unit
Fixed costs	Tk 19,500

Calculate:

1. Contribution margin ratio
2. Break-even point in sales
3. Margin of safety in units and sales
4. If the company wishes to increase its contribution margin by 40% in 2021, by how much will it need to increase its sales, if all other factors remain constant?

Understanding Note

CVP (Cost-Volume-Profit) analysis studies how total revenue, total cost and operating income behave as output, selling price, variable cost per unit and fixed costs change. Its key assumptions are: selling price is constant, costs are linear, sales mix is constant, and production equals sales.

• Contribution per unit = Selling price − Variable cost per unit
• CM Ratio = Contribution per unit ÷ Selling price
• BEP (units) = Fixed cost ÷ Contribution per unit
• BEP (sales) = Fixed cost ÷ CM Ratio
• Margin of Safety = Actual sales − BEP sales

Solution

Contribution per unit = 40 − 15 = Tk 25 CM Ratio = 25 ÷ 40 = 62.5%

(i) Contribution margin ratio = 62.5%

(ii) Break-even point in sales

BEP sales = 19,500 ÷ 0.625 = Tk 31,200 BEP units = 19,500 ÷ 25 = 780 units

(iii) Margin of safety

Actual sales = 2,400 × 40 = Tk 96,000 MS (units) = 2,400 − 780 = 1,620 units MS (sales) = 96,000 − 31,200 = Tk 64,800

(iv) Required increase in sales for +40% CM

Current total CM = 2,400 × 25 = Tk 60,000 Target CM = 60,000 × 1.40 = Tk 84,000 Required units = 84,000 ÷ 25 = 3,360 units Increase = 3,360 − 2,400 = 960 units Increase in sales = 960 × 40 = Tk 38,400

Final Answer

• (i) CM Ratio62.5%
• (ii) BEP SalesTk 31,200
• (iii) Margin of Safety1,620 units / Tk 64,800
• (iv) Increase in SalesTk 38,400

3

Capital Budgeting — ABO Enterprise

96th Banking Professional Examination, 2023 · COM-6, Q6(b)

Question

ABO Enterprise is reviewing an investment proposal. The initial cost and estimates of book value, net cash flows and net income for each year are given below. All cash flows take place at the end of the year. Residual value at the end of each year equals its book value; there is no residual value at the end of the investment's life.

Year	Book Value (Tk)	Cash Flows (Tk)	Net Income (Tk)
0	1,05,000	—	—
1	70,000	45,000	16,000
2	42,000	40,000	18,000
3	21,000	35,000	20,000
4	7,000	30,000	22,000
5	0	25,000	24,000

ABO Enterprise uses a 15% target rate of return. Discount factors:

Year	1	2	3	4	5
DF @ 15%	0.86957	0.75614	0.65752	0.57175	0.49718

Calculate: (i) Cash payback period (ii) ARR (iii) NPV.

Understanding Note

Capital budgeting is the process of planning expenditures on assets whose cash flows extend beyond one year. The main techniques are Payback Period, Discounted Payback, NPV, BCR (Profitability Index) and IRR.

• Payback period = time required to recover the original investment from cumulative cash inflows.
• ARR = Average annual net income ÷ Average investment. Average investment = (Initial cost + Salvage) ÷ 2.
• NPV = PV of future cash inflows − Initial investment. Accept if NPV > 0.

Solution

(i) Cash payback period

Cumulative: Y1 = 45,000 → Y2 = 85,000 → Y3 = 1,20,000 Payback = 2 + (1,05,000 − 85,000) ÷ 35,000 = 2 + 0.5714 Payback = 2.57 years

(ii) Annual Rate of Return (ARR)

Average Net Income = (16,000+18,000+20,000+22,000+24,000) ÷ 5 = Tk 20,000 Average Investment = (1,05,000 + 0) ÷ 2 = Tk 52,500 ARR = 20,000 ÷ 52,500 = 38.10%

(iii) Net Present Value (NPV)

Year	Cash Flow	DF @15%	PV
1	45,000	0.86957	39,130.65
2	40,000	0.75614	30,245.60
3	35,000	0.65752	23,013.20
4	30,000	0.57175	17,152.50
5	25,000	0.49718	12,429.50
Total PV of inflows			1,21,971.45

NPV = 1,21,971.45 − 1,05,000 = Tk 16,971.45

NPV is positive → the project is acceptable.

Final Answer

• Payback Period2.57 years
• ARR38.10%
• NPVTk 16,971.45 (Accept)

4

Working Capital Assessment — XYZ Company

96th Banking Professional Examination, 2023 · COM-6, Q7(b) · 15 marks

Question

XYZ Company provides the following per-unit particulars:

Particulars	Amount per unit (Tk)
Raw materials	80
Direct labour	30
Overhead	60
Total cost	170
Profit	30
Selling price	200

Additional information:

• Raw materials in stock, on average, one month
• Materials in process (50% complete), on average, half a month
• Finished goods in stock, on average, one month
• Credit allowed by suppliers: one month
• Credit allowed to debtors: two months
• Average time-lag in payment of wages: 1.5 weeks
• Time-lag in payment of overhead: one month
• One-fourth of the output is sold against cash
• Cash in hand and at bank: Tk 3,65,000

Prepare a statement showing the working capital needed for a level of activity of 1,04,000 units of production. Production is carried on evenly throughout the year; wages and overheads accrue similarly. Assume 4 weeks = 1 month and 52 weeks = 1 year.

Understanding Note

Working capital is the capital required to complete the operating cycle — maintaining inventories, receivables and cash for day-to-day operations.

Working Capital = Current Assets − Current Liabilities

• Current Assets: Raw material stock, WIP, finished goods, debtors, cash & bank.
• Current Liabilities: Creditors for raw materials, outstanding wages, outstanding overheads.
• WIP is valued at the stated completion stage (here 50%).
• Only credit sales go into debtors — ¾ of output here since ¼ is cash.

Solution

Production = 1,04,000 units

Current Assets

Item	Working	Amount (Tk)
Raw material stock (1 month)	1,04,000 × 80 ÷ 12	6,93,333.33
Work-in-process (½ month, 50%)	(1,04,000 ÷ 12 × 0.5) × 170 × 50%	3,68,333.33
Finished goods (1 month)	1,04,000 × 170 ÷ 12	14,73,333.33
Debtors (2 months)	¾ × 1,04,000 × 200 × 2/12	26,00,000.00
Cash in hand & bank	—	3,65,000.00
Total Current Assets		55,00,000.00

Current Liabilities

Item	Working	Amount (Tk)
Creditors for raw materials (1 month)	1,04,000 × 80 ÷ 12	6,93,333.33
Outstanding wages (1.5 weeks)	(1,04,000 × 30 ÷ 52) × 1.5	90,000.00
Outstanding overhead (1 month)	1,04,000 × 60 ÷ 12	5,20,000.00
Total Current Liabilities		13,03,333.33

Net Working Capital = 55,00,000 − 13,03,333.33 = Tk 41,96,666.67

Final Answer

• Working Capital RequiredTk 41,96,666.67

5

Financial Ratio Analysis — Shakib & Afif Sportswear Ltd.

COM-5, Q6(c) · 10 marks

Question

Compute the following ratios for 2022:

1. Current Ratio
2. Quick Ratio
3. Accounts Receivable Turnover
4. Inventory Turnover
5. Asset Turnover
6. Profit Margin
7. Return on Equity (ROE)
8. Return on Asset (ROA)
9. Debt to Asset

Balance Sheet — Shakib and Afif Sportswear Ltd. (December 31)

Assets	2022 (Tk)	2021 (Tk)
Cash	5,300	3,700
Accounts Receivable	21,200	23,400
Inventory	9,000	7,000
Land	20,000	26,000
Buildings	70,000	70,000
Total	1,25,500	1,30,100

Liabilities & Owner's Equity	2022 (Tk)	2021 (Tk)
Accounts Payable	10,370	31,100
Accumulated Depreciation — Buildings	15,000	10,000
Capital	75,000	69,000
Retained Earnings	25,130	20,000
Total	1,25,500	1,30,100

Income Statement (year ended 2022): Net Sales = Tk 1,20,000 · COGS = Tk 70,000 · Net Income = Tk 14,000.

Understanding Note

• Current Ratio = Current Assets ÷ Current Liabilities (ideal ≈ 2:1)
• Quick Ratio = (Cash + Receivables) ÷ Current Liabilities (ideal ≈ 1:1)
• Turnover ratios use average balances of the opening and closing figures.
• Profitability ratios relate Net Income to Sales, Assets or Equity.
• Debt to Asset = Total Liabilities ÷ Total Assets. Here liabilities = Accounts Payable + Accumulated Depreciation.

Solution

Current Assets = 5,300 + 21,200 + 9,000 = Tk 35,500 Current Liabilities = Tk 10,370

Ratio	Working	Result
Current Ratio	35,500 ÷ 10,370	3.42 : 1
Quick Ratio	(5,300 + 21,200) ÷ 10,370	2.56 : 1
AR Turnover	1,20,000 ÷ 22,300	5.38 times
Inventory Turnover	70,000 ÷ 8,000	8.75 times
Asset Turnover	1,20,000 ÷ 1,27,800	0.94 times
Profit Margin	14,000 ÷ 1,20,000	11.67%
ROE	14,000 ÷ 94,565	14.80%
ROA	14,000 ÷ 1,27,800	10.95%
Debt to Asset	25,370 ÷ 1,25,500	20.21%

Final Answer

• Current Ratio3.42 : 1
• Quick Ratio2.56 : 1
• AR Turnover5.38 times
• Inventory Turnover8.75 times
• Asset Turnover0.94 times
• Profit Margin11.67%
• ROE14.80%
• ROA10.95%
• Debt to Asset20.21%

6

Capital Budgeting — TMJ Corporation

COM-5, Q8(c) · 10 marks

Question

Taskin, Muiz and Jahanara formed TMJ Corporation. TMJ is considering a long-term capital investment requiring Tk 2,80,000. The equipment has a useful life of 5 years. Annual net income is expected to be Tk 16,000. Cash flows are computed by adding back depreciation. Depreciation is straight-line with no salvage value. Cost of capital = 10%; discount factor for 5 payments @10% = 3.79079.

Compute:

1. Cash payback period
2. Net Present Value (NPV)
3. Annual Rate of Return (ARR)
4. Should the project be accepted? Why?

Understanding Note

• Depreciation = Investment ÷ Life
• Annual cash flow = Net Income + Depreciation (non-cash charge)
• Payback = Initial investment ÷ Annual cash flow (equal CFs)
• NPV = PV of inflows − Initial investment. Accept if > 0.
• ARR = Average net income ÷ Average investment

Solution

Depreciation = 2,80,000 ÷ 5 = Tk 56,000 Annual Cash Flow = 16,000 + 56,000 = Tk 72,000

(a) Cash payback period

Payback = 2,80,000 ÷ 72,000 = 3.89 years

(b) Net Present Value

PV of inflows = 72,000 × 3.79079 = Tk 2,72,936.88 NPV = 2,72,936.88 − 2,80,000 = − Tk 7,063.12

(c) ARR

Average Investment = 2,80,000 ÷ 2 = Tk 1,40,000 ARR = 16,000 ÷ 1,40,000 = 11.43%

(d) Decision: NPV is negative → the project should be rejected.

Final Answer

• Payback Period3.89 years
• NPV− Tk 7,063.12
• ARR11.43%
• DecisionReject the project

7

Break-Even Point — Graphical Presentation

COM-4, Q5(a) · 5 marks

Question

What do you mean by Break-Even Point? Show it graphically.

Understanding Note

The Break-Even Point (BEP) is the level of output or sales at which Total Revenue equals Total Cost — that is, the firm earns zero profit and incurs zero loss.

• Below BEP → the firm makes a loss.
• Above BEP → the firm makes a profit.
• A bank evaluating a short-term credit application prefers a low BEP because it indicates lower risk.

BEP (units) = Fixed Cost ÷ Contribution per unit BEP (sales) = Fixed Cost ÷ CM Ratio

Solution — Graphical Presentation

To draw the Break-Even Chart:

1. Take output/sales (units) on the X-axis and cost & revenue (Tk) on the Y-axis.
2. Draw the Fixed Cost (FC) line parallel to the X-axis.
3. Draw the Total Cost (TC) line starting from the FC intercept and sloping upward.
4. Draw the Total Revenue (TR) line starting from the origin and sloping upward.
5. The point where the TR line intersects the TC line is the Break-Even Point.
6. Drop a perpendicular from BEP to the X-axis to get BEP units; to the Y-axis to get BEP sales.

BEP as a percentage of capacity = (BEP ÷ Total Capacity) × 100.

Final Answer

BEP is the point of zero profit where TR = TC. Graphically it is the intersection of the Total Revenue line and the Total Cost line, with FC drawn as a horizontal line above the X-axis.

8

CVP Analysis — ABC Company

COM-4, Q5(c) · 10 marks

Question

ABC Company's projected information:

	Total (Tk)	Per Unit (Tk)
Sales	2,00,000	20
Variable cost	1,20,000	12
Fixed cost	64,000	—

Compute:

1. Break-Even point in units
2. Units to earn a profit of Tk 30,000
3. Contribution Margin and Contribution Margin Ratio
4. Additional profit if sales were Tk 25,000 more

Understanding Note

• CM per unit = Selling price − Variable cost per unit
• BEP units = Fixed cost ÷ CM per unit
• Target units = (Fixed cost + Target profit) ÷ CM per unit
• Additional profit = Additional sales × CM Ratio

Solution

Units = 2,00,000 ÷ 20 = 10,000 units CM per unit = 20 − 12 = Tk 8 CM Ratio = 8 ÷ 20 = 40%

(i) BEP units = 64,000 ÷ 8 = 8,000 units

(ii) Units for profit Tk 30,000

= (64,000 + 30,000) ÷ 8 = 11,750 units

(iii) Contribution Margin

Total CM = 2,00,000 − 1,20,000 = Tk 80,000 CM Ratio = 40%

(iv) Additional profit

= 25,000 × 40% = Tk 10,000

Final Answer

• BEP in units8,000 units
• Units for profit Tk 30,00011,750 units
• CM & CM RatioTk 80,000 & 40%
• Additional profitTk 10,000

9

Working Capital — XYZ Company (70,000 units)

COM-4, Q9(c) · 15 marks

Question

A Proforma Cost Sheet of XYZ Company provides the following data:

Cost (per unit)	Tk
Raw materials	52.00
Direct labour	19.50
Overheads	39.00
Total cost	110.50
Profit	19.50
Selling price	130.00

Additional information:

• Average raw material in stock: one month
• Average material in process: half a month
• Credit allowed by suppliers: one month
• Credit allowed to debtors: two months
• Time lag in payment of wages: 1.5 weeks
• Time lag in payment of overheads: one month
• One-fourth of sales are on cash basis
• Cash balance expected: Tk 1,20,000

Prepare a statement of working capital needed for a level of activity of 70,000 units. Production is even throughout the year; wages and overheads accrue similarly.

Understanding Note

Same framework as Question 4. Note that no finished goods stock is given here, so it is excluded from current assets.

Working Capital = Current Assets − Current Liabilities

Solution

Production = 70,000 units

Current Assets

Item	Working	Amount (Tk)
Raw material stock (1 month)	70,000 × 52 ÷ 12	3,03,333.33
WIP (½ month)	(70,000 × 110.50 ÷ 12) × 0.5	3,22,291.67
Debtors (2 months)	¾ × 70,000 × 130 × 2/12	11,37,500.00
Cash	—	1,20,000.00
Total Current Assets		18,83,125.00

Current Liabilities

Item	Working	Amount (Tk)
Creditors for raw materials (1 month)	70,000 × 52 ÷ 12	3,03,333.33
Outstanding wages (1.5 weeks)	(70,000 × 19.50 ÷ 52) × 1.5	39,375.00
Outstanding overheads (1 month)	70,000 × 39 ÷ 12	2,27,500.00
Total Current Liabilities		5,70,208.33

Net Working Capital = 18,83,125 − 5,70,208.33 = Tk 13,12,916.67

Final Answer

• Working Capital RequiredTk 13,12,916.67

10

CVP Analysis — XYZ Enterprise

99th Banking Professional Examination, 2024 · COM-3, Q7(f)

Question

XYZ Enterprise had the following information for 2020:

Sales	4,800 units
Sales price	Tk 80 per unit
Variable cost	Tk 30 per unit
Fixed cost	Tk 39,000

Calculate:

1. Contribution Margin and CM Ratio
2. Break-even point in sales
3. Margin of safety in units and sales
4. If the company wishes to increase its CM by 40% in 2021, by how much must sales increase (all other factors constant)?

Understanding Note

• CM per unit = Price − Variable cost per unit
• Total CM = Units × CM per unit
• BEP = Fixed cost ÷ CM Ratio
• Margin of Safety = Actual sales − BEP sales

Solution

CM per unit = 80 − 30 = Tk 50 Total CM = 4,800 × 50 = Tk 2,40,000 CM Ratio = 50 ÷ 80 = 62.5%

(i) CM and CM Ratio = Tk 2,40,000 and 62.5%

(ii) BEP sales

= 39,000 ÷ 0.625 = Tk 62,400 BEP units = 39,000 ÷ 50 = 780 units

(iii) Margin of safety

Actual sales = 4,800 × 80 = Tk 3,84,000 MS (units) = 4,800 − 780 = 4,020 units MS (sales) = 3,84,000 − 62,400 = Tk 3,21,600

(iv) Required increase in sales for +40% CM

Target CM = 2,40,000 × 1.40 = Tk 3,36,000 Required units = 3,36,000 ÷ 50 = 6,720 units Increase = 6,720 − 4,800 = 1,920 units Increase in sales = 1,920 × 80 = Tk 1,53,600

Final Answer

• (i) CM / CM RatioTk 2,40,000 / 62.5%
• (ii) BEP SalesTk 62,400
• (iii) Margin of Safety4,020 units / Tk 3,21,600
• (iv) Increase in SalesTk 1,53,600

11

Capital Budgeting — XYZ Company Ltd.

COM-2, Q7(c) · 10 marks

Question

XYZ Company Ltd. is considering to invest in a project. It has the following options:

Year	0	1	2	3
Project A	(1,00,000)	40,000	50,000	40,000
Project B	(1,20,000)	60,000	50,000	80,000

Cost of capital for both projects is 10%. PV factors: Y1 = 0.90909, Y2 = 0.82645, Y3 = 0.75131.

Compute:

1. Pay-back period for Project A and Project B
2. NPV for Project A and Project B
3. Which project should be considered according to NPV?

Understanding Note

• Payback = Years before full recovery + (Unrecovered cost ÷ Cash flow in recovery year)
• NPV = Σ (CF × DF) − Initial Investment
• Choose the project with the higher positive NPV.

Solution

Project A

Cumulative CF: 40,000 → 90,000 → 1,30,000 Payback = 2 + (1,00,000 − 90,000) ÷ 40,000 = 2.25 years PV = 40,000×0.90909 + 50,000×0.82645 + 40,000×0.75131 = 1,07,738.50 NPV = 1,07,738.50 − 1,00,000 = Tk 7,738.50

Project B

Cumulative CF: 60,000 → 1,10,000 → 1,90,000 Payback = 2 + (1,20,000 − 1,10,000) ÷ 80,000 = 2.125 years PV = 60,000×0.90909 + 50,000×0.82645 + 80,000×0.75131 = 1,55,972.70 NPV = 1,55,972.70 − 1,20,000 = Tk 35,972.70

(iii) Project B should be considered — its NPV is much higher.

Final Answer

• Payback — A / B2.25 yrs / 2.125 yrs
• NPV — A / BTk 7,738.50 / Tk 35,972.70
• DecisionSelect Project B

12

CVP Analysis — ABC Company (2025)

6th Banking Professional Examination, 2025 · COM-1, Q5

Question

The ABC Company makes a single product with a sale price of Tk 15 and variable cost of Tk 9 per unit. Fixed costs are Tk 30,000 p.a. Current sales are 6,000 units.

Required:

1. At what level of sales will the company break even? What is the percentage of current margin of safety?
2. What is the current level of profit?
3. What sales are necessary to make a profit of Tk 12,000 given the same revenue and cost structure?

Understanding Note

• CM per unit = Price − VC per unit
• BEP units = Fixed cost ÷ CM per unit
• MS % = (Actual sales − BEP sales) ÷ Actual sales × 100
• Target units = (Fixed cost + Target profit) ÷ CM per unit

Solution

CM per unit = 15 − 9 = Tk 6

(a) BEP and Margin of Safety %

BEP units = 30,000 ÷ 6 = 5,000 units BEP sales = 5,000 × 15 = Tk 75,000 Current sales = 6,000 × 15 = Tk 90,000 MS % = (90,000 − 75,000) ÷ 90,000 × 100 = 16.67%

(b) Current profit

= (6,000 × 6) − 30,000 = Tk 6,000

(c) Sales for target profit Tk 12,000

Units = (30,000 + 12,000) ÷ 6 = 7,000 units Sales = 7,000 × 15 = Tk 1,05,000

Final Answer

• BEP SalesTk 75,000
• Margin of Safety %16.67%
• Current ProfitTk 6,000
• Sales for profit Tk 12,000Tk 1,05,000

13

Benefit Cost Ratio — Project X

6th Banking Professional Examination, 2025 · COM-1, Q6(a)

Question

A project proposal from company 'X' is under review for term loan approval. Total investment is Tk 10,00,000. Expected cash flows over 4 years:

Year	Cash Flow (Tk)	PV Factor @10%
1	2,50,000	0.909
2	3,00,000	0.826
3	3,00,000	0.751
4	2,50,000	0.683

Calculate the Benefit Cost Ratio (BCR). Comment on whether the project qualifies for acceptance.

Understanding Note

The Benefit Cost Ratio (BCR) — also called the Profitability Index — measures value created per taka invested.

BCR = PV of Cash Inflows ÷ Initial Investment

• BCR > 1 → Accept
• BCR < 1 → Reject
• BCR = 1 → Indifferent

Solution

Year	CF	PV Factor	PV
1	2,50,000	0.909	2,27,250
2	3,00,000	0.826	2,47,800
3	3,00,000	0.751	2,25,300
4	2,50,000	0.683	1,70,750
Total PV of inflows			8,71,100

BCR = 8,71,100 ÷ 10,00,000 = 0.8711

Since BCR < 1, the project should not be accepted.

Final Answer

• BCR0.8711
• DecisionReject (BCR < 1)

14

Future Value of a Fixed Deposit

6th Banking Professional Examination, 2025 · COM-1, Q6(b)

Question

A client deposits Tk 8,00,000 for 5 years in a fixed deposit account at an annual compound interest rate of 11.50%. Calculate the future value of the deposit.

Understanding Note

The time value of money concept states that money received sooner is worth more than money received later, because it can be invested to earn a return.

FV = PV × (1 + i)ⁿ

where i = interest rate per period, n = number of periods.

Solution

FV = 8,00,000 × (1.115)⁵ (1.115)⁵ = 1.723354 FV = 8,00,000 × 1.723354 = Tk 13,78,683.20

Final Answer

• Future ValueTk 13,78,683.20

15

Capital Budgeting — Delta Company Ltd.

COM_, Q5 · 10 marks

Question

Delta Company Ltd has decided to invest in a project with the following two alternative options:

Year	0	1	2	3
Project A	(1,30,000)	60,000	55,000	45,000
Project B	(1,50,000)	80,000	60,000	50,000

Cost of capital = 10%. PV factors: Y1 = 0.90909, Y2 = 0.82645, Y3 = 0.75131.

Compute: (i) NPV for A and B (ii) Payback period for A and B (iii) Which project should be considered according to NPV?

Understanding Note

Same framework as Question 11. Apply PV factors to each year's cash flow, then compare against the initial investment.

Solution

Project A

PV = 60,000×0.90909 + 55,000×0.82645 + 45,000×0.75131 = 1,33,809.10 NPV = 1,33,809.10 − 1,30,000 = Tk 3,809.10 Cumulative CF: 60,000 → 1,15,000 → 1,60,000 Payback = 2 + (1,30,000 − 1,15,000) ÷ 45,000 = 2.33 years

Project B

PV = 80,000×0.90909 + 60,000×0.82645 + 50,000×0.75131 = 1,59,879.70 NPV = 1,59,879.70 − 1,50,000 = Tk 9,879.70 Cumulative CF: 80,000 → 1,40,000 → 1,90,000 Payback = 2 + (1,50,000 − 1,40,000) ÷ 50,000 = 2.20 years

(iii) Project B should be considered — its NPV is higher.

Final Answer

• NPV — A / BTk 3,809.10 / Tk 9,879.70
• Payback — A / B2.33 yrs / 2.20 yrs
• DecisionSelect Project B

16

Eligible Collateral & Provision — Faruk Enterprise

COM_, Q6 · 10 marks

Question

Faruk Enterprise availed a loan from Global Commercial Bank Ltd. The present loan outstanding is Tk 120 lac. There is Tk 6 lac unrealized interest in the Interest Suspense Account. Other information:

• Market value of mortgaged land — Tk 80 lac
• Tin shed structure on the land — Tk 8 lac
• Pledged goods — Tk 50 lac
• FDR value kept lien against the loan — Tk 32 lac
• Present classification status: Substandard (SS)

Required:

1. Calculate eligible collateral and base for provision (per latest BB circular)
2. Compute provision required for this borrower
3. If the loan becomes doubtful next year, what will be the new provision requirement?

Understanding Note

• Eligible collateral percentages: FDR/lien deposit = 100%, pledged goods = 50%, land & building = 50% max.
• Base for provision = greater of (Outstanding − Interest Suspense − Eligible Collateral) and 15% of Outstanding.
• Provision rates: Substandard = 20%, Doubtful = 50%, Bad/Loss = 100%.

Solution

(a) Eligible collateral

Collateral	Value (lac)	Eligibility	Eligible (lac)
FDR under lien	32	100%	32.00
Pledged goods	50	50%	25.00
Land + Tin shed	88	50%	44.00
Total eligible collateral			101.00

Base for provision

Option 1 = 120 − 6 − 101 = Tk 13 lac Option 2 = 15% × 120 = Tk 18 lac Base = Greater = Tk 18 lac

(b) Provision for Substandard (SS)

= 20% × 18 = Tk 3.6 lac

(c) If Doubtful (DF) next year

= 50% × 18 = Tk 9 lac

Final Answer

• Eligible CollateralTk 101 lac
• Base for ProvisionTk 18 lac
• Provision (SS — 20%)Tk 3.6 lac
• Provision if Doubtful (50%)Tk 9 lac

Key Formulas Cheat Sheet

Quick Revision — Formulas You Must Remember

Topic	Formula
Contribution per unit	Selling price − Variable cost per unit
CM Ratio	CM per unit ÷ Selling price
BEP (units)	Fixed cost ÷ CM per unit
BEP (sales)	Fixed cost ÷ CM Ratio
Margin of Safety	Actual sales − BEP sales
Target units	(Fixed cost + Target profit) ÷ CM per unit
Payback period	Initial investment ÷ Annual cash flow
ARR	Average net income ÷ Average investment
NPV	PV of inflows − Initial investment
BCR / PI	PV of inflows ÷ Initial investment
Future Value	PV × (1 + i)n
Working Capital	Current Assets − Current Liabilities
Current Ratio	Current Assets ÷ Current Liabilities
Quick Ratio	(Cash + Receivables) ÷ Current Liabilities
ROE	Net Income ÷ Average Equity
ROA	Net Income ÷ Average Total Assets
Base for Provision	Greater of (Outstanding − IS − Eligible Collateral) and 15% of Outstanding
Eligible Collateral	Deposit/BB Guarantee = 100%; Goods = 50%; Land & Building = 50%

↑ Back to top

Credit Operations & Management (COM) — AIBB Exam Math Solutions Compiled and solved from IBB Banking Professional Examination papers (2023, 2024, 2025).
Based on the official IBB Reading Material on Credit Operations and Management.

For study purposes only. Always cross-check with the latest Bangladesh Bank circulars and IBB syllabus.

```