Fundamentals of Financial Management

Profit maximization is a traditional business objective asserting that a firm should undertake only those operating actions that maximize its accounting net profit. It assumes that total revenues should exceed total expenses by the widest possible margin. However, it suffers from critical limitations: it ignores the time value of money, overlooks business risk, and relies on easily manipulated accounting book profits.

The annual percentage rate (APR / nominal rate) is the stated annualized contractual rate that ignores intra-year interest compounding. In contrast, the effective annual rate (EAR) reflects the true economic annual rate earned or paid by compounding interest across multiple periods ($m$):

$$\text{EAR} = \left(1 + \frac{r_{\text{Nom}}}{m}\right)^m - 1$$

Whenever compounding occurs semi-annually, quarterly, or monthly ($m > 1$), EAR is strictly higher than the stated annual rate.

The three primary financial statements are:

1. Statement of Financial Position (Balance Sheet): Discloses the firm’s assets, liabilities, and owners’ equity at a specific reporting date.
2. Statement of Profit or Loss (Income Statement): Summarizes operating revenues, expenses, and net profit earned over an accounting period.
3. Statement of Cash Flows: Traces cash inflows and outflows across operating, investing, and financing activities.

A financial asset is a liquid, intangible contractual claim that derives its economic value from a contractual claim to future cash flows rather than from physical tangible properties.

Examples:

• Common stocks (equity shares)
• Corporate debentures and government treasury bonds
• Commercial paper, bank deposits, and treasury bills.

In dividend policy, a stock repurchase (share buyback) is an alternative method of distributing surplus corporate cash to equity holders by repurchasing the company’s own shares from the open market or through a tender offer. By reducing the total number of outstanding shares, it increases future Earnings Per Share (EPS) and book value per share, delivering capital gains to investors instead of cash dividends.

Capital structure refers to the permanent long-term mix of financing utilized by a firm, primarily consisting of long-term debt, preferred stock, and common shareholders’ equity.

Two Key Determinants:

1. Business Risk (Cash Flow Stability): Firms with highly volatile sales and high operating leverage must limit debt financing to avoid bankruptcy.
2. Corporate Tax Rate: Higher corporate income tax rates increase the tax-shield value of interest payments [$k_d = r_d(1 - t)$], encouraging greater use of debt.

The four fundamental elements of a corporate credit policy are:

1. Credit Standards: The minimum financial strength and creditworthiness required of a customer to qualify for trade credit (evaluated via the 5 Cs of credit).
2. Credit Terms: The specification of credit duration and early payment cash discounts (e.g., $2/10, \text{ net } 30$).
3. Credit Period: The total number of days allowed before payment is legally overdue.
4. Collection Policy: The toughness and specific procedures (reminders, legal notices, collection agencies) deployed to collect overdue accounts.

Given:

• $\text{Annual Coupon Payment } (I) = 10\% \times \text{Rs. } 1,000 = \text{Rs. } 100$
• $\text{Current Market Price } (P_0) = \text{Rs. } 900$

Current Yield Formula:

$$\mathbf{\text{Current Yield}} = \frac{\text{Annual Coupon Payment } (I)}{\text{Current Market Price } (P_0)} = \frac{\text{Rs. } 100}{\text{Rs. } 900} = 0.1111 = \mathbf{11.11\%}$$

Given:

• $\text{DOL} = 1.2\text{ times}$, $\text{DFL} = 2.5\text{ times}$
• $\Delta \text{Sales} = +10\%$

Computations:

1. Degree of Total Leverage (DTL):

   $$\mathbf{\text{DTL}} = \text{DOL} \times \text{DFL} = 1.2 \times 2.5 = \mathbf{3.0\text{ times}}$$

2. Percentage Increase in Net Income:

   $$\mathbf{\% \Delta \text{Net Income}} = \text{DTL} \times \% \Delta \text{Sales} = 3.0 \times 10\% = \mathbf{30.00\%}$$

Given:

• $\text{Inventory Conversion Period (ICP)} = 25\text{ days}$
• $\text{Average Collection Period (ACP)} = 50\text{ days}$
• $\text{Payables Deferral Period (PDP)} = 35\text{ days}$

Computations:

1. Operating Cycle (OC):

   $$\mathbf{\text{Operating Cycle}} = \text{ICP} + \text{ACP} = 25 + 50 = \mathbf{75\text{ days}}$$

2. Cash Conversion Cycle (CCC):

   $$\mathbf{\text{Cash Conversion Cycle}} = \text{Operating Cycle} - \text{PDP} = 75 - 35 = \mathbf{40\text{ days}}$$

Concept and Core Functions of Financial Management

1. Concept of Financial Management

Financial management is an essential branch of managerial administration focused on the efficient planning, raising, deploying, and controlling of corporate funds to maximize shareholder wealth. It bridges operational decision-making with financial markets.

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2. Primary Functions of Financial Management

1. Investment Decision (Capital Budgeting): Determines the allocation of long-term capital toward land, buildings, production equipment, and technological upgrades using DCF criteria (NPV, IRR).

2. Financing Decision (Capital Structure Formulation): Selects the optimal blend of long-term debt, preferred capital, and common equity to minimize the overall Weighted Average Cost of Capital (WACC) while maintaining safe leverage levels.

3. Dividend Decision: Determines the optimal profit retention policy—balancing the reinvestment needs of growing business units against the liquidity and dividend expectations of equity investors.

4. Working Capital Management (Liquidity Planning): Manages day-to-day current assets (cash, receivables, inventories) and current liabilities to safeguard short-term solvency without locking up idle capital.

5. Financial Analysis and Performance Monitoring: Deploys ratio analysis, variance reporting, and financial forecasting to evaluate performance and initiate corrective operational interventions.

Users of Ratio Analysis and Measurement of Liquidity and Profitability

1. Key Users of Financial Ratio Analysis

• Equity Investors & Shareholders: Evaluate growth prospects, dividend sustainability, and return on equity (ROE).
• Short-Term Creditors (Trade Suppliers & Banks): Examine liquidity ratios to verify the firm’s immediate ability to honor maturing bills.
• Long-Term Lenders (Debenture Holders & Bondholders): Scrutinize debt-equity and interest coverage ratios to assess default risk.
• Corporate Management: Monitor operational efficiency across divisions and identify bottlenecks.
• Government & Tax Authorities: Check compliance with tax laws and examine monopolistic pricing.

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2. Measuring Liquidity Position

Liquidity measures the firm’s ability to satisfy immediate short-term obligations as they mature:

1. Current Ratio:
   $$\text{Current Ratio} = \frac{\text{Current Assets}}{\text{Current Liabilities}} \quad (\text{Benchmark standard is } 2 : 1)$$
2. Quick (Acid-Test) Ratio:
   $$\text{Quick Ratio} = \frac{\text{Current Assets} - \text{Inventory}}{\text{Current Liabilities}} \quad (\text{Benchmark standard is } 1 : 1)$$
3. Cash Conversion Cycle (CCC): Evaluates the number of days taken to convert inventory and receivables into cash.

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3. Measuring Profitability Position

Profitability evaluates the firm’s efficiency in generating earnings relative to sales and capital employed:

1. Gross Profit Margin $= \frac{\text{Gross Profit}}{\text{Sales}} \times 100$
2. Net Profit Margin $= \frac{\text{Net Profit After Tax}}{\text{Sales}} \times 100$
3. Return on Assets (ROA) $= \frac{\text{Net Income}}{\text{Total Assets}} \times 100$
4. Return on Equity (ROE) $= \frac{\text{Net Income}}{\text{Common Equity}} \times 100$ (The primary metric of equity shareholder profitability).

Loan Amortization Analysis for Mountain Resort

Parameters:

• Principal ($P$) $= \text{Rs. } 100,000$
• Interest Rate ($i$) $= 10\% = 0.10$
• Term ($n$) $= 3\text{ years}$

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a. Amount of Annual Payment (PMT)

$$\text{PVIFA}_{10\%, 3} = \frac{1 - (1 + 0.10)^{-3}}{0.10} = 2.48685$$

$$\mathbf{PMT} = \frac{\text{Loan Amount}}{\text{PVIFA}_{10\%, 3}} = \frac{\text{Rs. } 100,000}{2.48685} = \mathbf{\text{Rs. } 40,211.48}$$

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b. Loan Amortization Schedule

Year	Beginning Balance (Rs.)	Total Payment (Rs.)	Interest Paid (10%) (Rs.)	Principal Repayment (Rs.)	Ending Balance (Rs.)
1	100,000.00	40,211.48	10,000.00	30,211.48	69,788.52
2	69,788.52	40,211.48	6,978.85	33,232.63	36,555.89
3	36,555.89	40,211.48	3,655.59	36,555.89	0.00
Total		120,634.44	20,634.44	100,000.00

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c. Equation to Calculate Equal Monthly Installments (EMI)

For monthly installments, the annual interest rate is divided by 12, and the number of periods is multiplied by 12:

$$\mathbf{\text{EMI}} = \frac{P \times r \times (1 + r)^N}{(1 + r)^N - 1}$$

Where:

• $P = \text{Principal Loan Amount (Rs. 100,000)}$
• $r = \text{Monthly Interest Rate} = \frac{i}{12} = \frac{0.10}{12} = 0.008333$
• $N = \text{Total Monthly Periods} = n \times 12 = 3 \times 12 = 36\text{ months}$

Supernormal Growth Stock Valuation

Given:

• $D_0 = \text{Rs. } 40$, $k_s = 18\% = 0.18$.
• Growth rates: $g_1 = g_2 = g_3 = 10\% = 0.10$; Normal growth $g_n = 3\% = 0.03\text{ thereafter}$.

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Step 1: Project Dividends

• $D_1 = 40 \times (1 + 0.10) = \text{Rs. } 44.00$
• $D_2 = 44 \times (1 + 0.10) = \text{Rs. } 48.40$
• $D_3 = 48.40 \times (1 + 0.10) = \text{Rs. } 53.24$
• $D_4 = 53.24 \times (1 + 0.03) = \text{Rs. } 54.8372$

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a. Stock’s Intrinsic Value Today ($P_0$)

1. Horizon Value at End of Year 3 ($\hat{P}_3$):

   $$\hat{P}_3 = \frac{D_4}{k_s - g_n} = \frac{\text{Rs. } 54.8372}{0.18 - 0.03} = \frac{54.8372}{0.15} = \text{Rs. } 365.581$$

2. Present Value of Cash Flows:

   • $PV(D_1) = \frac{44.00}{1.18} = \text{Rs. } 37.288$
   • $PV(D_2) = \frac{48.40}{(1.18)^2} = \frac{48.40}{1.3924} = \text{Rs. } 34.760$
   • $PV(D_3 + \hat{P}_3) = \frac{53.24 + 365.581}{(1.18)^3} = \frac{418.821}{1.643032} = \text{Rs. } 254.907$

$$\mathbf{P_0} = 37.288 + 34.760 + 254.907 = \mathbf{\text{Rs. } 326.96}$$

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b. Dividend Yield and Capital Gains Yield for Year 1

• Dividend Yield $= \frac{D_1}{P_0} = \frac{\text{Rs. } 44.00}{\text{Rs. } 326.96} = \mathbf{13.46\%}$
• Capital Gains Yield $= k_s - \text{Dividend Yield} = 18.00\% - 13.46\% = \mathbf{4.54\%}$

Cost of Capital Analysis for Lumbini Hotel

Capital Weights: $w_d = 0.40$, $w_p = 0.10$, $w_e = 0.50$. Parameters: Tax rate $t = 30\%$, Pre-tax debt rate $r_d = 10\%$, Preferred dividend $D_p = \text{Rs. } 12$, Preferred price $P_p = \text{Rs. } 92$, Common dividend $D_0 = \text{Rs. } 30$, Growth $g = 5\%$, Current price $P_0 = \text{Rs. } 300$, New issue price $P_n = \text{Rs. } 250$.

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a. Component Costs of Capital

1. After-Tax Cost of Debt ($k_d$):

   $$\mathbf{k_d} = r_d(1 - t) = 10\%(1 - 0.30) = \mathbf{7.00\%}$$

2. Cost of Preferred Stock ($k_p$):

   $$\mathbf{k_p} = \frac{D_p}{P_p} = \frac{\text{Rs. } 12}{\text{Rs. } 92} = 0.13043 = \mathbf{13.04\%}$$

3. Cost of Internal Equity / Retained Earnings ($k_s$):

   $$D_1 = D_0(1 + g) = 30 \times (1 + 0.05) = \text{Rs. } 31.50$$
   $$\mathbf{k_s} = \frac{D_1}{P_0} + g = \frac{\text{Rs. } 31.50}{\text{Rs. } 300} + 0.05 = 0.1050 + 0.05 = \mathbf{15.50\%}$$

4. Cost of External New Common Equity ($k_e$):

   $$\mathbf{k_e} = \frac{D_1}{P_n} + g = \frac{\text{Rs. } 31.50}{\text{Rs. } 250} + 0.05 = 0.1260 + 0.05 = \mathbf{17.60\%}$$

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b. Weighted Average Cost of Capital (WACC - Retained Earnings)

$$\text{WACC} = [w_d \times k_d] + [w_p \times k_p] + [w_e \times k_s]$$

$$\mathbf{\text{WACC}} = [0.40 \times 7.00\%] + [0.10 \times 13.04\%] + [0.50 \times 15.50\%]$$

$$\text{WACC} = 2.80\% + 1.304\% + 7.75\% = \mathbf{11.85\%}$$

(a) Himalaya Company Residual Dividend Payout

• $\text{Capital Budget} = \text{Rs. } 15\text{ million}$. Target Debt $= 60\% \implies \text{Target Equity Ratio} = 40\%$.
• $\text{Equity Required} = 40\% \times \text{Rs. } 15\text{ million} = \text{Rs. } 6.0\text{ million}$.
• $\text{Net Income} = \text{Rs. } 12\text{ million}$.
• $\text{Residual Dividend} = 12.0\text{M} - 6.0\text{M} = \text{Rs. } 6.0\text{ million}$.
  $$\mathbf{\text{Dividend Payout Ratio}} = \frac{\text{Rs. } 6.0\text{ million}}{\text{Rs. } 12.0\text{ million}} \times 100 = \mathbf{50.00\%}$$

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(b) Sahara Company 20% Stock Dividend Impact

Parameters:

• Current Shares $= 100,000\text{ shares}$ @ Par Rs. 100; Market Price $= \text{Rs. } 300$.
• $20\%$ Stock Dividend adds: $20\% \times 100,000 = \mathbf{20,000\text{ new shares}}$.
• $\mathbf{\text{New Total Shares Outstanding}} = 100,000 + 20,000 = \mathbf{120,000\text{ shares}}$.

Accounting Entries (Capitalization at Market Price Rs. 300):

• Total Value of Stock Dividend $= 20,000 \times \text{Rs. } 300 = \text{Rs. } 6,000,000$ deducted from Retained Earnings.
• Par Value transferred to Common Stock $= 20,000 \times \text{Rs. } 100 = \text{Rs. } 2,000,000$.
• Excess transferred to Additional Paid-in Capital $= 20,000 \times \text{Rs. } 200 = \text{Rs. } 4,000,000$.

Revised Shareholders’ Equity Account:

Particulars	Before (Rs.)	Adjustment	After (Rs.)
Common Stock (120,000 shares @ Rs. 100)	10,000,000	+2,000,000	12,000,000
Additional Paid-in Capital	5,000,000	+4,000,000	9,000,000
Retained Earnings	15,000,000	(6,000,000)	9,000,000
Total Shareholders’ Equity	Rs. 30,000,000	Rs. 0	Rs. 30,000,000

New Selling Price of Common Stock:

$$\mathbf{P_{\text{new}}} = \frac{P_0}{1 + \% \text{Stock Dividend}} = \frac{\text{Rs. } 300}{1 + 0.20} = \mathbf{\text{Rs. } 250.00\text{ per share}}$$

Working Capital Management and Determinants of Working Capital Requirements

1. Concept of Working Capital

Working capital is the investment required in short-term operating assets to finance the operational cycle from raw material procurement to cash collection.

• Gross Working Capital: The aggregate book value of all Current Assets.
• Net Working Capital (NWC): $CA - CL$. Reflects financial liquidity and the margin of safety provided to short-term creditors.

Working Capital Management is the strategic planning and control of current assets and current liabilities to eliminate the risk of technical insolvency while minimizing the carrying costs of holding idle funds.

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2. Factors Affecting the Size of Working Capital

1. Nature of Business: Trading and retail firms require massive working capital in inventories and receivables but modest fixed assets. Conversely, capital-intensive infrastructure utilities (e.g., hydropower) require massive fixed assets but minimal working capital.

2. Length of Operating Cycle: The longer the span of time required to convert raw materials into finished goods and collect receivables ($RM \to WIP \to FG \to Receivables \to Cash$), the larger the working capital required.

3. Scale of Operations: Larger enterprises handling immense production volumes naturally require higher working capital in absolute rupee terms.

4. Seasonal Fluctuations: Businesses with pronounced seasonal demand (such as woolen garments or beverage makers during festivals) require flexible, peak-season working capital infusions.

5. Credit Policy Extended and Received: Firms extending generous credit terms to customers require large investments in receivables. Conversely, liberal supplier trade credit terms (long payables deferral) reduce net working capital needs.

6. Availability and Lead Time of Raw Materials: If raw materials must be imported from abroad with long, uncertain transit times, the firm must maintain sizable safety buffer stocks, increasing working capital needs.

7. Profit Margin and Cash Retention: High-margin firms generate strong internal operating cash flows, replenishing working capital continuously.

Comprehensive Portfolio Risk and Return Computations

(a) Expected Return and Standard Deviation

1. Expected Returns:

   • $\mathbf{E(R_A)} = (0.3 \times 0\%) + (0.4 \times 10\%) + (0.3 \times 20\%) = 0 + 4.0\% + 6.0\% = \mathbf{10.00\%}$
   • $\mathbf{E(R_B)} = (0.3 \times 35\%) + (0.4 \times 15\%) + (0.3 \times -5\%) = 10.5\% + 6.0\% - 1.5\% = \mathbf{15.00\%}$

2. Standard Deviations:

   • Stock A:
     $$\sigma_A^2 = 0.3(0 - 10)^2 + 0.4(10 - 10)^2 + 0.3(20 - 10)^2 = 0.3(100) + 0 + 0.3(100) = 30 + 30 = 60.0$$
     $$\mathbf{\sigma_A} = \sqrt{60.0} = \mathbf{7.746\%}$$
   • Stock B:
     $$\sigma_B^2 = 0.3(35 - 15)^2 + 0.4(15 - 15)^2 + 0.3(-5 - 15)^2 = 0.3(400) + 0 + 0.3(400) = 120 + 120 = 240.0$$
     $$\mathbf{\sigma_B} = \sqrt{240.0} = \mathbf{15.492\%}$$

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(b) Covariance and Correlation Coefficient

1. Covariance:

   $$\text{Cov}(A, B) = \sum P_i [R_{Ai} - E(R_A)][R_{Bi} - E(R_B)]$$
   • State 1: $0.3(0 - 10)(35 - 15) = 0.3(-10)(+20) = -60.0$
   • State 2: $0.4(10 - 10)(15 - 15) = 0.0$
   • State 3: $0.3(20 - 10)(-5 - 15) = 0.3(+10)(-20) = -60.0$
     $$\mathbf{\text{Cov}(A, B)} = -60.0 + 0 - 60.0 = \mathbf{-120.00}$$

2. Correlation Coefficient ($r_{AB}$):

   $$\mathbf{r_{AB}} = \frac{\text{Cov}(A, B)}{\sigma_A \times \sigma_B} = \frac{-120.00}{7.746 \times 15.492} = \frac{-120.00}{120.00} = \mathbf{-1.00}$$
   (Stock A and Stock B exhibit perfect negative correlation).

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(c) Portfolio Return and Risk ($w_A = 0.70, w_B = 0.30$)

1. Portfolio Expected Return ($R_p$):

   $$\mathbf{R_p} = (0.70 \times 10\%) + (0.30 \times 15\%) = 7.0\% + 4.5\% = \mathbf{11.50\%}$$

2. Portfolio Standard Deviation ($\sigma_p$): Since $r_{AB} = -1.00$:

   $$\sigma_p = |w_A \sigma_A - w_B \sigma_B|$$
   $$\mathbf{\sigma_p} = |(0.70 \times 7.746\%) - (0.30 \times 15.492\%)| = |5.4222\% - 4.6476\%| = \mathbf{0.7746\% \approx 0.77\%}$$

3. Interpretation: Combining two perfectly negatively correlated assets achieves near-total elimination of investment risk: individual risks of $7.75\%$ and $15.49\%$ collapse to an extraordinary $0.77\%$ while locking in a solid $11.50\%$ expected return.

Capital Budgeting Analysis for Gaurishanker Herbal Company

Parameters: Initial Outlay ($I_0$) $= \text{Rs. } 100,000$ each. Cost of Capital ($k$) $= 10\% = 0.10$. Projects are Independent.

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(a) Payback Period (PBP)

• Project X (Annuity of Rs. 40,000):
  $$\mathbf{\text{PBP}_X} = \frac{100,000}{40,000} = \mathbf{2.50\text{ years}}$$
• Project Y (Cumulative: Y1=50k, Y2=110k):
  $$\mathbf{\text{PBP}_Y} = 1 + \frac{100,000 - 50,000}{60,000} = 1 + \frac{50,000}{60,000} = \mathbf{1.83\text{ years (1 yr 10 mos)}}$$

Decision: Because both projects recover their initial investment in less than the maximum 3-year cutoff, both Project X and Project Y are acceptable under the PBP rule.

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(b) Net Present Value (NPV @ 10%)

1. Project X:

   $$\text{PVIFA}_{10\%, 4} = 3.1699$$
   $$\mathbf{NPV_X} = (40,000 \times 3.1699) - 100,000 = 126,796 - 100,000 = \mathbf{+\text{Rs. } 26,796}$$

2. Project Y:

   $$PV = \frac{50,000}{1.10} + \frac{60,000}{(1.10)^2} + \frac{40,000}{(1.10)^3} + \frac{18,000}{(1.10)^4}$$
   $$PV = 45,455 + 49,587 + 30,053 + 12,294 = \text{Rs. } 137,389$$
   $$\mathbf{NPV_Y} = 137,389 - 100,000 = \mathbf{+\text{Rs. } 37,389}$$

Decision: Because the projects are independent and both yield positive NPVs ($NPV_X > 0$ and $NPV_Y > 0$), accept both Project X and Project Y.

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(c) Internal Rate of Return (IRR)

1. Project X:

   $$\text{PVIFA}_{IRR, 4} = \frac{100,000}{40,000} = 2.500$$
   From tables: $\text{PVIFA}_{21\%, 4} = 2.5404$, $\text{PVIFA}_{22\%, 4} = 2.4937$.
   $$\mathbf{\text{IRR}_X} = \mathbf{21.86\%}$$

2. Project Y:

   • At $28\%$: $PV = \frac{50,000}{1.28} + \frac{60,000}{(1.28)^2} + \frac{40,000}{(1.28)^3} + \frac{18,000}{(1.28)^4} = 39,063 + 36,621 + 19,073 + 6,706 = \text{Rs. } 101,463 \implies NPV = +1,463$.
   • At $30\%$: $PV = 38,462 + 35,503 + 18,207 + 6,302 = \text{Rs. } 98,474 \implies NPV = -1,526$.
     $$\mathbf{\text{IRR}_Y} = 28\% + \frac{1,463}{1,463 - (-1,526)} \times 2\% = 28\% + 0.98\% = \mathbf{28.98\%}$$

Decision: Because both IRRs exceed the $10\%$ cost of capital, accept both projects.

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(d) Superiority of NPV Method

The Net Present Value (NPV) method is theoretically superior to PBP and IRR because:

1. Direct Measure of Wealth Creation: NPV reflects the actual monetary addition to total equity value.
2. Realistic Reinvestment Rate: Assumes intermediate cash flows are reinvested at the market cost of capital ($10\%$) rather than the artificially high internal rate ($28.98\%$).
3. No Scale or Multiple-Rate Pitfalls: Operates consistently across both independent and mutually exclusive contexts.