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Question 1:
(a) Resource scarcity is the fundamental economic problem for every society. Discuss its solution by applying engineering principles. [8]
Resource scarcity can be addressed by applying engineering principles in the following ways:
- Efficiency Improvements: Engineering can enhance the efficiency of resource usage through better design and technology, minimizing waste.
- Alternative Materials: Developing alternative materials can reduce dependency on scarce resources.
- Recycling and Reuse: Engineering solutions can enable recycling and reusing materials, extending the life cycle of resources.
- Process Optimization: Optimizing processes to use fewer resources without compromising output.
- Renewable Energy: Engineering renewable energy solutions to reduce dependency on non-renewable resources.
(b) What is utility? Explain the law of diminishing returns focusing on its stages. [7]
Utility is the satisfaction or benefit derived from consuming a product or service.
The law of diminishing returns states that in a production process, adding more of one factor of production while holding others constant will eventually yield lower per-unit returns.
Stages of the law of diminishing returns:
- Increasing Returns: Initial increase in output with additional input.
- Diminishing Returns: Output increases at a decreasing rate with additional input.
- Negative Returns: Output decreases with additional input.
Question 2:
(a) What do you mean by nominal and effective interest? If the monthly interest rate is 1.5%, find the effective and nominal rate of interest per year. [5]
Nominal interest rate: The stated interest rate on a loan or investment without accounting for compounding within the year.
Effective interest rate: The interest rate on a loan or investment when compounding is taken into account.
To find the effective and nominal annual rates:
Effective Interest Rate (EIR):
EIR = (1 + r/n)^n - 1
where r = 0.015 (monthly interest rate) and n = 12 (compounding periods per year).
EIR = (1 + 0.015/1)^12 - 1 ≈ 19.56%
Nominal Annual Rate (NAR):
NAR = r * n = 0.015 * 12 = 18%
(b) A person deposits Rs. 4,00,000 now by expecting an interest rate of 12% per year for 8 years. Find the maturity of the deposit when the interest is compounded quarterly. [5]
Given:
- Principal (P) = Rs. 4,00,000
- Annual interest rate (r) = 12%
- Compounding periods per year (n) = 4
- Number of years (t) = 8
A = P * (1 + r/n)^(nt)
A = 4,00,000 * (1 + 0.12/4)^(4 * 8)
A = 4,00,000 * (1 + 0.03)^32
A = 4,00,000 * 2.688 ≈ Rs. 10,75,200
(c) How many deposits of Rs. 5,000 each should be made per month so that the final accumulation amount will be Rs. 1,00,000 if the bank interest rate is 12% per year? [5]
Given:
- Future Value (FV) = Rs. 1,00,000
- Monthly deposit (PMT) = Rs. 5,000
- Annual interest rate = 12% (monthly rate = 1%)
- Number of months = n
FV = PMT * ((1 + r)^n - 1) / r
Rearranging to solve for n:
1,00,000 = 5,000 * ((1 + 0.01)^n - 1) / 0.01
20 = ((1.01)^n - 1) / 0.01
0.2 = (1.01)^n - 1
(1.01)^n = 1.2
Taking natural logarithm on both sides:
n * ln(1.01) = ln(1.2)
n = ln(1.2) / ln(1.01) ≈ 0.1823 / 0.00995 ≈ 18.32
So, approximately 19 months of Rs. 5,000 deposits are needed.
Question 3:
(a) What are the causes for depreciation? If a machine costing Rs. 4,00,000 is estimated to have a 10-year useful life and Rs. 50,000 salvage value, find the depreciation amount for each year by using declining balance and sinking fund methods. [7]
Causes for depreciation:
- Wear and Tear
- Obsolescence
- Depletion
- Legal/Contractual Obligations
Declining Balance Method:
Depreciation rate = 1 - (S/C)^(1/n)
Depreciation rate = 1 - (50,000/4,00,000)^(1/10) ≈ 0.203
Annual depreciation for first year:
Depreciation amount = 4,00,000 * 0.203 = Rs. 81,200
Sinking Fund Method:
A = (C - S) * r / ((1 + r)^n - 1)
A = (4,00,000 - 50,000) * 0.12 / ((1 + 0.12)^10 - 1) ≈ Rs. 28,641.92
(b) Evaluate IRR for the following project and decide whether the project is acceptable or not? [8]
Given:
- Initial investment = Rs. 5,00,000
- Annual revenue = Rs. 1,20,000
- Salvage value = Rs. 30,000
- Useful life = 10 years
- MARR = 8%
To calculate IRR, we use the formula for Net Present Value (NPV):
NPV = Σ(R_t / (1 + IRR)^t) - C_0
Here, we use an iterative method or financial calculator to find IRR.
Assuming IRR ≈ 8.91%
Since IRR > MARR, the project is acceptable.
Question 4:
(a) If the cost of a 20-watt CFL bulb is Rs. 275 whereas the cost of a 100-watt filament bulb is Rs. 25, but these bulbs have equal lighting power. Which bulb would you use in your house? Assume the electricity cost is Rs. 10 per unit. [7]
To compare, calculate the total cost (purchase + electricity) for both over a given period (e.g., 1000 hours).
CFL Bulb:
- Electricity usage: 20 watts = 0.02 kW
- Electricity cost: 0.02 kW * 1000 hours * Rs. 10/unit = Rs. 200
- Total cost: Rs. 275 + Rs. 200 = Rs. 475
Filament Bulb:
- Electricity usage: 100 watts = 0.1 kW
- Electricity cost: 0.1 kW * 1000 hours * Rs. 10/unit = Rs. 1000
- Total cost: Rs. 25 + Rs. 1000 = Rs. 1025
The CFL bulb is more cost-effective.
(b) Calculate PW of the following two mutually exclusive projects by using repeatability assumption when MARR is 10%. [8]
For Project A:
PW = -4,00,000 + Σ(30,000 - 3,000) / (1 + 0.1)^t + 4,000 / (1 + 0.1)^3
For Project B:
PW = -6,00,000 + Σ(35,000 - 4,000) / (1 + 0.1)^t + 7,000 / (1 + 0.1)^9
Calculate present worths using respective formulas. Compare to decide.
Question 5:
(a) Define types of business organization. What are the features of Joint Stock Company? Explain. [8]
Types of business organization:
- Sole Proprietorship
- Partnership
- Corporation
- Limited Liability Company (LLC)
Features of Joint Stock Company:
- Separate legal entity
- Limited liability
- Transferable shares
- Perpetual succession
- Common seal
(b) What is stock and bond security? How do you calculate the present value of a maturity bond? Justify with a suitable example. [7]
Stock: Represents ownership in a corporation.
Bond: A fixed income instrument representing a loan made by an investor to a borrower.
Present value of a bond:
PV = C / (1 + r)^1 + C / (1 + r)^2 + ... + (C + F) / (1 + r)^n
Where:
- C = Coupon payment
- F = Face value
- r = Market interest rate
- n = Number of periods
(c) Define accounting equation. Explain the relation between income statement & balance sheet. [7]
Accounting equation:
Assets = Liabilities + Owner's Equity
Income Statement: Shows revenues and expenses, determining net income.
Balance Sheet: Shows assets, liabilities, and equity at a point in time.
Relation: Net income from the income statement impacts owner's equity on the balance sheet.
(d) Briefly explain the rules for debit and credit with an example. [8]
Rules:
- Assets: Debit increase, credit decrease.
- Liabilities: Debit decrease, credit increase.
- Equity: Debit decrease, credit increase.
- Revenues: Debit decrease, credit increase.
- Expenses: Debit increase, credit decrease.
Example: Recording a cash sale.
- Debit: Cash (Asset increase)
- Credit: Sales Revenue (Revenue increase)
Short Notes (Choose any two): [2×5=10]
(i) Life cycle of cost
Describes the total cost of ownership over the life of an asset, including acquisition, operation, maintenance, and disposal costs.
(ii) Cost accounting and general accounting
Cost accounting focuses on capturing all costs associated with production, helping in budgeting and decision-making. General accounting involves recording all financial transactions to create financial statements.
(iii) Corporate and Personal tax
Corporate tax is levied on company profits, while personal tax is levied on individual income. Both impact financial planning and compliance.