Given

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a. Expected return and standard deviation

Expected return

$E(R)=\sum p_iR_i$

Stock A:

$E(R_A)=0.3(5)+0.4(10)+0.3(15)$ $=1.5+4+4.5=10\%$

Stock B:

$E(R_B)=0.3(30)+0.4(10)+0.3(10)$ $=9+4+3=16\%$

Standard deviation

$\sigma=\sqrt{\sum p_i(R_i-E(R))^2}$

Stock A:

$\sigma_A^2=15$ $\sigma_A=\sqrt{15}=3.87\%$

Stock B:

$\sigma_B^2=84$ $\sigma_B=\sqrt{84}=9.17\%$

Answer:

$E(R_A)=10\%,\quad \sigma_A=3.87\%$ $E(R_B)=16\%,\quad \sigma_B=9.17\%$

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b. Portfolio risk and return

Weights:

$w_A=0.60,\quad w_B=0.40$

Portfolio expected return

$E(R_p)=w_AE(R_A)+w_BE(R_B)$

$E(R_p)=0.60(10)+0.40(16)$ $=6+6.4=12.4\%$

Covariance between A and B

$\text{Cov}_{AB}=\sum p_i(R_A-E(R_A))(R_B-E(R_B))$

$\text{Cov}_{AB}=-30$

Coefficient of correlation

$\rho_{AB}=\frac{\text{Cov}_{AB}}{\sigma_A\sigma_B}$

$\rho_{AB}=\frac{-30}{\sqrt{15}\sqrt{84}}$ $=\frac{-30}{35.50}=-0.845$

Portfolio risk

$\sigma_p^2=w_A^2\sigma_A^2+w_B^2\sigma_B^2+2w_Aw_B\text{Cov}_{AB}$

$\sigma_p^2=(0.60)^2(15)+(0.40)^2(84)+2(0.60)(0.40)(-30)$

$=0.36(15)+0.16(84)-14.4$

$=5.4+13.44-14.4=4.44$

$\sigma_p=\sqrt{4.44}=2.11\%$

Answer:

$E(R_p)=12.4\%,\quad \sigma_p=2.11\%$

Thus, the portfolio has an expected return of 12.4% and risk of 2.11%.

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c. Effect of coefficient of correlation on portfolio return and risk

The coefficient of correlation $\rho$ ranges from $-1$ to $+1$.

Effect on portfolio return

Portfolio expected return is:

$E(R_p)=w_AE(R_A)+w_BE(R_B)$

There is no $\rho$ term in this formula. Therefore, correlation does not affect the expected return of a portfolio. Return depends only on the expected returns of individual stocks and their weights.

Effect on portfolio risk

Portfolio variance is:

$\sigma_p^2=w_A^2\sigma_A^2+w_B^2\sigma_B^2+2w_Aw_B\rho_{AB}\sigma_A\sigma_B$

Correlation affects the third term, i.e. covariance.

• If $\rho=+1$, perfect positive correlation:
  $\sigma_p=w_A\sigma_A+w_B\sigma_B$
  There is no risk reduction from diversification.

• If $\rho=0$, no correlation:
  The covariance term becomes zero, so some risk is reduced.

• If $\rho<0$, negative correlation:
  The covariance term is negative, so portfolio risk falls more sharply.
  If $\rho=-1$, perfect negative correlation, risk can even be reduced to zero with proper weights.

In this problem, $\rho_{AB}=-0.845$. Because of this strong negative correlation, the portfolio risk is only 2.11%, much lower than the weighted average standard deviation:

$0.60(3.87)+0.40(9.17)=5.99\%$

So, correlation does not change portfolio return, but it strongly affects portfolio risk through diversification. Lower or negative correlation reduces risk.

(a) Expected return and standard deviation

Let returns be in percentage terms.

Stock A

$E(R_A)=\sum p_i R_{Ai}$

$=0.3(0)+0.4(10)+0.3(20)=10\%$

Variance:

$\sigma_A^2=\sum p_i(R_{Ai}-E(R_A))^2$

$=0.3(0-10)^2+0.4(10-10)^2+0.3(20-10)^2$

$=0.3(100)+0+0.3(100)=60$

$\sigma_A=\sqrt{60}=7.75\%$

Stock B

$E(R_B)=0.3(35)+0.4(15)+0.3(-5)=15\%$

Variance:

$\sigma_B^2=0.3(35-15)^2+0.4(15-15)^2+0.3(-5-15)^2$

$=0.3(400)+0+0.3(400)=240$

$\sigma_B=\sqrt{240}=15.49\%$

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(b) Covariance and correlation coefficient

Covariance:

$\text{Cov}(A,B)=\sum p_i(R_{Ai}-E(R_A))(R_{Bi}-E(R_B))$

$=0.3(0-10)(35-15)+0.4(10-10)(15-15)+0.3(20-10)(-5-15)$

$=0.3(-10)(20)+0+0.3(10)(-20)$

$=-60-60=-120$

So,

$\text{Cov}(A,B)=-120\ (\%^2)$

Correlation coefficient:

$\rho_{AB}=\frac{\text{Cov}(A,B)}{\sigma_A\sigma_B}$

$=\frac{-120}{\sqrt{60}\sqrt{240}}=\frac{-120}{120}=-1$

Thus,

$\boxed{\text{Cov}(A,B)=-120,\qquad \rho_{AB}=-1}$

Stock A and Stock B are perfectly negatively correlated.

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(c) Portfolio risk and return

Weights:

$w_A=0.70,\qquad w_B=0.30$

Portfolio expected return:

$E(R_p)=w_AE(R_A)+w_BE(R_B)$

$=0.70(10)+0.30(15)$

$=7+4.5=11.5\%$

Portfolio variance:

$\sigma_p^2=w_A^2\sigma_A^2+w_B^2\sigma_B^2+2w_Aw_B\text{Cov}(A,B)$

$=(0.70)^2(60)+(0.30)^2(240)+2(0.70)(0.30)(-120)$

$=29.4+21.6-50.4=0.6$

Portfolio standard deviation:

$\sigma_p=\sqrt{0.6}=0.77\%$

Therefore,

$\boxed{E(R_p)=11.5\%,\qquad \sigma_p=0.77\%}$

Interpretation

The portfolio expected return is 11.5%, which lies between Stock A’s 10% and Stock B’s 15%, but closer to Stock A because 70% of wealth is invested in Stock A.

The portfolio risk is only 0.77%, which is much lower than the risk of Stock A alone (7.75%) and Stock B alone (15.49%). This happens because the two stocks are perfectly negatively correlated ($\rho=-1$). When one stock performs poorly, the other tends to perform well, so the losses and gains offset each other.

Thus, this portfolio gives a return higher than Stock A and almost eliminates risk through diversification. In fact, with perfect negative correlation, a zero-risk portfolio is possible when about two-thirds of wealth is invested in Stock A and one-third in Stock B. The 70:30 portfolio is very close to that zero-risk combination.

Given: capital structure: debt 30%, preferred stock 10%, common equity 60%. Expected EPS = Rs 30, payout = 40%, tax rate = 30%, growth $g$ = 5%, market price $P_0$ = Rs 120.

(a) Cost of each component

1. Cost of debt (after tax)

$K_d = i(1-t) = 12\% \times (1-0.30) = 8.4\%$

2. Cost of preferred stock

$K_p = \frac{D_p}{P_n} = \frac{11}{95} = 11.58\%$

3. Cost of retained earnings (common equity), Gordon model

Expected dividend: $D_1 = 30 \times 0.40 = \text{Rs } 12$

$K_e = \frac{D_1}{P_0} + g = \frac{12}{120} + 0.05 = 0.10 + 0.05 = 15\%$

4. Cost of new common stock

$K_{ne} = \frac{D_1}{P_n} + g = \frac{12}{110} + 0.05 = 10.91\% + 5\% = 15.91\%$

(b) WACC (equity entirely from retained earnings)

$WACC = 0.30(8.4) + 0.10(11.58) + 0.60(15) \approx 12.68\%$

The company must earn about 12.68% on its new investments to keep its share price unchanged.

Notes on Any Two

a. Financial Leverage

Meaning: Financial leverage refers to the use of fixed-charge sources of funds (debt and preference share capital) in the capital structure to magnify the return to equity shareholders. It is measured by the relationship between EBIT and EPS.

Formula:

$\text{DFL} = \frac{\text{EBIT}}{\text{EBIT} - \text{Interest}} = \frac{\% \text{ change in EPS}}{\% \text{ change in EBIT}}$

Interpretation:

• If DFL > 1, the firm uses debt; a small change in EBIT causes a larger change in EPS.
• Higher DFL means higher financial risk (risk of insolvency and variability of EPS).
• If DFL = 1, the firm is unlevered (no debt).

Illustration: EBIT = Rs 1,00,000; Interest = Rs 20,000.

$\text{DFL} = \frac{1{,}00{,}000}{1{,}00{,}000 - 20{,}000} = 1.25 \text{ times}$

A 10% rise in EBIT will raise EPS by 12.5%.

Advantages: Debt is cheaper (interest is tax-deductible), so leverage can raise EPS and the value of the firm; it also gives owners control without dilution.

Disadvantages: Increases financial risk, fixed interest obligation must be paid even in losses, and excessive leverage raises the cost of capital and may lead to bankruptcy.

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b. Preferred Stock

Meaning: Preferred stock is a hybrid security that carries a fixed rate of dividend and has a prior claim over equity shares on dividend and on assets at the time of liquidation, but has no voting right.

Features:

1. Fixed dividend — paid at a stated rate before any dividend on equity shares.
2. Priority claim — on earnings and on assets at liquidation, but after creditors.
3. Cumulative provision — unpaid dividends (dividends in arrears) must be cleared before equity dividend.
4. Non-voting — normally no voting rights, except on matters affecting their interest.
5. Redeemable/convertible — may be redeemed after a period or converted into equity shares.
6. No fixed maturity — treated as part of capital, not debt.

Advantages: Dividend is not a legal obligation (unlike interest); no dilution of control; helps raise capital from investors who want steady income; improves the borrowing capacity of the firm.

Disadvantages: Dividend is not tax-deductible, so it is costlier than debt; it creates a fixed charge on earnings; excessive use increases financial risk.

Cost of preference share:

$K_p = \frac{D_p}{P_0} \quad \text{(or)} \quad K_p = \frac{D_p}{P_0(1 - f)}$

where $D_p$ = annual preference dividend, $P_0$ = net proceeds, $f$ = flotation cost.

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c. Dividend Policy

Meaning: Dividend policy is the decision of the management regarding how much of the profit is to be distributed to shareholders as dividend and how much is to be retained in the business for growth and investment.

Forms of dividend: Cash dividend, stock (bonus) dividend, property dividend and scrip dividend.

Factors affecting dividend policy:

1. Legal and contractual restrictions — provisions of the Companies Act and loan covenants.
2. Liquidity position — cash available to pay dividend.
3. Growth opportunities — firms with profitable investment plans retain more.
4. Stability of earnings — stable earnings allow a steady dividend.
5. Tax position of shareholders — dividend vs. capital gains taxation.
6. Access to capital market — easy access to external funds allows liberal dividend.
7. Control — issuing new shares to pay dividend may dilute control.
8. Age and size of the firm — mature firms pay more dividend.

Theories of dividend policy:

• Walter's Model: $P = \dfrac{D + \frac{r}{k}(E - D)}{k}$, where $r$ = return on investment, $k$ = cost of capital. If $r > k$, retain all; if $r < k$, distribute all.
• Gordon's Model: $P = \dfrac{E(1 - b)}{k - br}$, where $b$ = retention ratio. Value rises with retention when $r > k$.
• MM Hypothesis: Under perfect markets, dividend policy is irrelevant; the value of the firm depends only on investment policy.
• Residual Theory: Dividend is paid only from earnings left after financing all positive-NPV projects.

Importance: A sound dividend policy maximises shareholders' wealth, maintains the firm's image, stabilises the market price of shares and helps in long-term financing and growth.

Working capital management is the management of a firm's current assets (cash, marketable securities, accounts receivable, inventory) and current liabilities (accounts payable, accruals, short-term loans) so as to maintain a balance between liquidity and profitability. It involves deciding the level and mix of current assets and the way they are financed — the goal being to keep the firm able to meet its short-term obligations while not tying up excessive funds in idle assets. It is also called short-term financial management or management of liquidity.

Importance to Nepalese manufacturing firms:

1. Large share of total assets — In Nepalese manufacturing firms, current assets typically form a very high proportion (often more than half) of total assets. Inventory (raw materials, work-in-progress, finished goods) and receivables dominate, so their efficient management directly determines the firm's return on investment.

2. Liquidity and solvency — Manufacturing firms must pay for raw materials, wages, fuel, electricity and interest regularly. A shortage of working capital can cause delays in production, inability to pay suppliers, default on bank loans and even technical insolvency. Nepal's frequent power cuts, transport strikes (bandhs) and supply disruptions make adequate liquidity essential.

3. Smooth production and sales cycle — Manufacturing involves a long operating cycle: purchase of raw materials → production → storage → credit sales → collection. Working capital keeps this cycle uninterrupted. Poor management causes stock-outs, idle plant and lost sales.

4. Profitability — Excess working capital means idle cash and overstocked inventory earning nothing, while too little means lost sales and costly emergency borrowing. Optimal working capital management directly improves profit.

5. Financing constraints in Nepal — Nepalese firms depend heavily on bank overdrafts and short-term loans because the capital market is thin and long-term funds are scarce and costly. Managing current liabilities well reduces interest burden and dependence on costly borrowing.

6. Credit policy and receivables — In Nepal, trade credit is widely used; poor collection of receivables leads to bad debts and cash crunch. Effective receivables management improves cash inflow.

7. Coping with inflation and price fluctuations — Nepal faces high import dependence and price volatility of raw materials. Sound inventory management helps avoid losses from price rises and obsolescence.

8. Meeting seasonal and cyclical demand — Demand for many manufactured goods (e.g., during festivals like Dashain–Tihar) is seasonal. Firms need extra working capital in peak seasons and must plan for it in advance.

9. Reduces risk of business failure — Studies of Nepalese manufacturing firms show that inadequate working capital and poor management of inventory and receivables are major causes of sickness and closure. Hence, working capital management is vital for survival and growth.

Conclusion: For Nepalese manufacturing firms — operating with limited long-term funds, uncertain supply and seasonal demand — working capital management is not merely a routine task but a key determinant of liquidity, profitability and long-term survival.

All returns are in percent. Variance is therefore in percent-squared.

a. Expected return and standard deviation

Stock A

$E(R_A)=\sum p_iR_{Ai}$

$E(R_A)=0.3(0)+0.4(15)+0.3(30)=0+6+9=15\%$

Variance of A:

$\sigma_A^2=\sum p_i(R_{Ai}-E(R_A))^2$

$=0.3(0-15)^2+0.4(15-15)^2+0.3(30-15)^2$

$=0.3(225)+0+0.3(225)=67.5+67.5=135$

$\sigma_A=\sqrt{135}=11.62\%$

So, Stock A: expected return = 15%, standard deviation = 11.62%.

Stock B

$E(R_B)=0.3(20)+0.4(10)+0.3(10)=6+4+3=13\%$

Variance of B:

$\sigma_B^2=0.3(20-13)^2+0.4(10-13)^2+0.3(10-13)^2$

$=0.3(49)+0.4(9)+0.3(9)$

$=14.7+3.6+2.7=21$

$\sigma_B=\sqrt{21}=4.58\%$

So, Stock B: expected return = 13%, standard deviation = 4.58%.

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b. Covariance and correlation coefficient

Covariance

$\text{Cov}(A,B)=\sum p_i(R_{Ai}-E(R_A))(R_{Bi}-E(R_B))$

$=0.3(0-15)(20-13)+0.4(15-15)(10-13)+0.3(30-15)(10-13)$

$=0.3(-15)(7)+0+0.3(15)(-3)$

$=-31.5+0-13.5=-45$

$\boxed{\text{Cov}(A,B)=-45\%^2}$

Correlation coefficient

$r_{AB}=\frac{\text{Cov}(A,B)}{\sigma_A\sigma_B}$

$r_{AB}=\frac{-45}{11.62\times4.58}$

$r_{AB}=\frac{-45}{53.24}=-0.845$

$\boxed{r_{AB}\approx -0.845}$

The negative correlation means the returns of A and B tend to move in opposite directions.

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c. Portfolio expected return and standard deviation

Weights:

$w_A=0.50,\qquad w_B=0.50$

Portfolio expected return

$E(R_p)=w_AE(R_A)+w_BE(R_B)$

$=0.50(15)+0.50(13)=7.5+6.5=14\%$

$\boxed{E(R_p)=14\%}$

Portfolio standard deviation

$\sigma_p^2=w_A^2\sigma_A^2+w_B^2\sigma_B^2+2w_Aw_B\text{Cov}(A,B)$

$=(0.50)^2(135)+(0.50)^2(21)+2(0.50)(0.50)(-45)$

$=33.75+5.25-22.5=16.5$

$\sigma_p=\sqrt{16.5}=4.06\%$

$\boxed{\sigma_p\approx 4.06\%}$

So, the portfolio has expected return 14% and standard deviation 4.06%.

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d. Preference of a risk-averse investor

A risk-averse investor prefers higher expected return and lower risk. The coefficient of variation is useful here:

$CV=\frac{\sigma}{E(R)}$

The portfolio has the lowest coefficient of variation, meaning it gives the best return per unit of risk. It also has a higher expected return than Stock B and a much lower standard deviation than Stock A. Because A and B are negatively correlated, combining them reduces risk through diversification.

Therefore, a risk-averse investor would prefer to hold the portfolio of 50% Stock A and 50% Stock B.

Given: initial investment (IIC) = Rs 900,000; life = 5 years; required return = 10%; maximum payback period = 3 years.

a. Payback period

Rs 800,000 is recovered by the end of Year 2; the balance Rs 100,000 is recovered in Year 3 (inflow Rs 400,000).

$\text{Payback} = 2 + \frac{100{,}000}{400{,}000} = 2.25 \text{ years}$

Decision: 2.25 years is less than the maximum 3 years, so the equipment should be installed.

b. NPV at 10%

$NPV = \sum \frac{CF_t}{(1+k)^t} - IIC$

$NPV = 1{,}530{,}760 - 900{,}000 = \text{Rs } 630{,}760$

Decision: NPV is positive, so the equipment should be installed.

c. IRR

IRR is the rate at which the PV of inflows equals Rs 900,000.

At 25%: PV = 400,000 + 192,000 + 204,800 + 204,800 + 98,310 = 1,099,910, so NPV = +199,910.

At 40%: PV = 357,150 + 153,060 + 145,760 + 130,150 + 55,770 = 841,890, so NPV = -58,110.

The IRR lies between 25% and 40%, but closer to 40%, and this wide gap makes straight-line interpolation inaccurate. Trying nearer rates:

NPV changes sign at about 36%, so

$IRR \approx 36\%$

Decision: IRR (about 36%) is far above the required return of 10%, so the equipment should be installed.

d. NPV or IRR: which is superior?

NPV is generally considered superior because:

1. Wealth maximisation: it gives the absolute rupee addition to shareholders' wealth, while IRR gives only a percentage.
2. Reinvestment assumption: NPV assumes cash flows are reinvested at the cost of capital (realistic); IRR assumes reinvestment at the IRR itself, which may be unrealistically high.
3. Unique answer: projects with non-conventional cash flows can have multiple IRRs or none; NPV is always a single value.
4. Mutually exclusive projects: IRR ignores project size and timing, so it may rank projects differently from NPV and mislead; NPV ranks them correctly.
5. Additivity: NPVs of projects can be added; IRRs cannot.

Hence NPV is the superior technique, although IRR is popular because it is easy to compare with the cost of capital.

Given:

• Selling price per bottle, $P = \text{Rs }20$
• Variable cost per bottle, $V = \text{Rs }10$
• Fixed operating cost, $FC = \text{Rs }800{,}000$
• Depreciation included in fixed cost $= \text{Rs }200{,}000$
• Contribution per bottle, $C = P - V = 20 - 10 = \text{Rs }10$

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a. Operating breakeven point and cash breakeven point

Operating BEP (units):

$$\text{Operating BEP} = \frac{FC}{P - V} = \frac{800{,}000}{20 - 10} = \frac{800{,}000}{10} = 80{,}000 \text{ bottles}$$

Cash BEP (units):

Cash fixed cost excludes depreciation.

$$\text{Cash fixed cost} = 800{,}000 - 200{,}000 = \text{Rs }600{,}000$$ $$\text{Cash BEP} = \frac{\text{Cash fixed cost}}{P - V} = \frac{600{,}000}{10} = 60{,}000 \text{ bottles}$$

Answer:

• Operating BEP = 80,000 bottles
• Cash BEP = 60,000 bottles

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b. Sales volume for after-tax profit of Rs 120,000

Corporate tax rate $= 30\%$.

Required before-tax profit:

$$\text{Before-tax profit} = \frac{\text{After-tax profit}}{1 - t} = \frac{120{,}000}{1 - 0.30} = \frac{120{,}000}{0.70} = \text{Rs }171{,}428.57$$

Required sales volume in units:

$$Q = \frac{FC + \text{Before-tax profit}}{P - V} = \frac{800{,}000 + 171{,}428.57}{10} = \frac{971{,}428.57}{10} = 97{,}142.86 \text{ bottles}$$

Since bottles must be sold in whole units:

$$Q \approx 97{,}143 \text{ bottles}$$

Required sales revenue:

$$97{,}143 \times 20 = \text{Rs }1{,}942{,}860$$

Answer: Required sales volume = 97,143 bottles approximately, or Rs 1,942,860 in sales revenue.

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c. Operating leverage at sales volume of 100,000 bottles

Degree of Operating Leverage:

$$DOL = \frac{Q(P - V)}{Q(P - V) - FC}$$

At $Q = 100{,}000$:

$$DOL = \frac{100{,}000(20 - 10)}{100{,}000(20 - 10) - 800{,}000}$$ $$= \frac{1{,}000{,}000}{1{,}000{,}000 - 800{,}000} = \frac{1{,}000{,}000}{200{,}000} = 5 \text{ times}$$

Interpretation:
At a sales volume of 100,000 bottles, the degree of operating leverage is 5 times. This means a 1% change in sales will cause a 5% change in EBIT in the same direction. The company has relatively high operating risk because fixed operating costs are large.

Concept of Working Capital

Working capital refers to the funds required by a business to finance its day-to-day operations. In simple terms, it is the excess of current assets over current liabilities.

$\text{Working Capital} = \text{Current Assets} - \text{Current Liabilities}$

Where:

• Current Assets include cash, marketable securities, accounts receivable, inventory, and prepaid expenses — assets that are convertible into cash within one year or one operating cycle.
• Current Liabilities include accounts payable, bills payable, accrued expenses, short-term loans, and bank overdrafts — obligations payable within one year.

Types of Working Capital

1. Gross Working Capital: The total investment in current assets. It focuses on the total funds tied up in current assets.

2. Net Working Capital: The excess of current assets over current liabilities. It measures the firm's liquidity position. Net working capital may be positive or negative.

3. Permanent (Fixed) Working Capital: The minimum level of current assets a firm must always maintain to carry on operations smoothly. It is the irreducible core of working capital.

4. Temporary (Variable) Working Capital: The additional working capital required to meet seasonal or special demands, such as during festive seasons or peak production periods.

Operating Cycle Concept

Working capital is closely related to the operating cycle — the time taken to convert raw materials into finished goods, sell them, and collect cash from customers.

$\text{Operating Cycle} = \text{Raw Material Period} + \text{WIP Period} + \text{Finished Goods Period} + \text{Receivable Collection Period} - \text{Payable Deferral Period}$

A longer operating cycle requires more working capital; a shorter cycle requires less.

Importance of Working Capital Management in a Manufacturing Firm

Working capital management involves managing current assets and current liabilities to ensure adequate liquidity while maximizing profitability. Its importance in a manufacturing firm is as follows:

1. Ensures Smooth Production: A manufacturing firm must continuously purchase raw materials, pay wages, and meet overhead costs. Adequate working capital ensures uninterrupted production and avoids production stoppages.

2. Maintains Liquidity and Solvency: Proper management of working capital enables the firm to meet short-term obligations promptly. This protects the firm's creditworthiness and prevents insolvency.

3. Inventory Management: Manufacturing firms hold large quantities of raw materials, work-in-progress, and finished goods. Effective working capital management maintains an optimum inventory level — avoiding both overstocking (high holding cost) and understocking (production delays).

4. Efficient Cash Management: It ensures that sufficient cash is available for daily operations while excess idle cash is invested profitably. This balances liquidity and profitability.

5. Receivables Management: Manufacturing firms often sell goods on credit. Sound working capital management sets appropriate credit policies, minimizes bad debts, and accelerates cash collection.

6. Exploits Cash Discounts: With adequate working capital, the firm can pay suppliers promptly and avail cash discounts, reducing the cost of raw materials.

7. Enhances Profitability: By minimizing the cost of holding current assets and avoiding idle funds, working capital management directly contributes to higher profits.

8. Supports Business Expansion: A firm with sound working capital management can take advantage of favorable market opportunities, expand production, and increase sales volume.

9. Reduces Financial Risk: Efficient management of current assets and liabilities reduces the risk of cash shortages and financial distress, which is critical for capital-intensive manufacturing operations.

10. Maintains Goodwill and Credit Standing: Timely payment of dues and smooth operations build the firm's reputation in the market, making it easier to obtain credit and attract investors.

Conclusion

Working capital is the lifeblood of a manufacturing firm. Its efficient management ensures that the firm maintains adequate liquidity to meet short-term obligations while using its resources productively to maximize profitability. A balance between liquidity and profitability is the core objective of working capital management.

a. Payback period

The investment of Rs 5,000,000 is recovered during Year 3.

$\text{Payback period} = 2 + \frac{5{,}000{,}000 - 4{,}000{,}000}{2{,}000{,}000} = 2.5 \text{ years}$

Decision: 2.5 years is less than the maximum cost recovery period of 3 years, so the company should run the tourist bus.

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b. NPV at 10 percent

$NPV = \sum_{t=1}^{n} \frac{CF_t}{(1+k)^t} - I_0$

$NPV = 8{,}350{,}100 - 5{,}000{,}000 = \text{Rs } 3{,}350{,}100$

Decision: NPV is positive, so the company should run the tourist bus.

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c. IRR

Definition: The Internal Rate of Return (IRR) is the discount rate at which the present value of a project's cash inflows equals its initial investment, i.e. the rate at which NPV is zero. It is the maximum rate of return the project can earn on the funds invested in it.

At 20%:

NPV at 20% = +Rs 38,500

At 21%:

NPV at 21% = −Rs 62,600

$IRR = 20\% + \frac{38{,}500}{38{,}500 + 62{,}600} \times 1\% = 20.38\% \approx 20.4\%$

Decision: IRR (about 20.4%) exceeds the required rate of return of 10%, so the company should run the tourist bus.

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d. Merits and demerits

Payback period

Merits:

1. Simple to calculate and easy to understand.
2. Emphasises early recovery of investment, so it is useful when liquidity is a major concern.
3. Less risky, as it favours projects that pay back quickly.
4. A useful supplementary tool for ranking projects when capital is rationed.

Demerits:

1. Ignores the time value of money.
2. Ignores cash flows after the payback period, so profitability is not measured.
3. The maximum acceptable payback period is subjective.
4. It may reject profitable long-term projects and accept less profitable short-term ones.

NPV method

Merits:

1. It recognises the time value of money by discounting cash flows.
2. It considers all cash flows over the entire life of the project.
3. It gives an absolute measure of the wealth added, consistent with maximising shareholders' wealth.
4. NPVs of different projects are additive.

Demerits:

1. It requires an accurate estimate of the discount rate, which is difficult.
2. Cash flow forecasts over the project life may be unreliable.
3. Being an absolute measure, it is not suitable for comparing projects of different sizes unless the profitability index is also used.
4. It is more complex and time-consuming than payback.

a. Liquidity, turnover and profitability ratios of Himalaya Tea Company

All amounts in Rs.

Working notes:

• Current assets = Cash + Marketable securities + Accounts receivable + Inventories
  = 50,000 + 40,000 + 100,000 + 200,000 = Rs 390,000

• Current liabilities = Accounts payable + Notes payable + Other current liabilities
  = 80,000 + 60,000 + 40,000 = Rs 180,000

• Total equity = Common stock + Retained earnings
  = 200,000 + 170,000 = Rs 370,000

Conclusion:
The company has better liquidity, profitability and debt-servicing capacity than the industry average. However, its total assets turnover ratio is lower than the industry average, indicating less efficient utilization of total assets to generate sales.

Concept of Working Capital

Working capital refers to the funds invested in a firm's short-term or current assets — cash, marketable securities, accounts receivable, inventory, and prepaid expenses. In simple terms, it is the capital required to meet the day-to-day operating expenses of a business.

Working capital is studied in two senses:

1. Gross Working Capital — the total investment in all current assets. This is the "total" or "current assets" concept.
2. Net Working Capital — the excess of current assets over current liabilities (CA − CL). This is the "net" concept and indicates the firm's liquidity position.

$\text{Net Working Capital} = \text{Current Assets} - \text{Current Liabilities}$

A firm needs adequate working capital to purchase raw materials, pay wages and salaries, meet operating expenses, extend credit to customers, and maintain a minimum cash balance. Neither too much nor too little working capital is desirable — excess ties up funds idle (reducing profitability), while shortage disrupts operations and risks insolvency. Hence, the goal is to maintain an optimum level of working capital.

Types of Working Capital

Working capital may be classified on two bases:

A. On the Basis of Concept

1. Gross Working Capital — total of all current assets.
2. Net Working Capital — current assets minus current liabilities.

B. On the Basis of Time / Permanence

Temporary working capital is further divided into:

• Seasonal Working Capital — required during peak seasons (e.g., festivals for a retailer).
• Cyclical Working Capital — required during boom periods of the business cycle.
• Special Working Capital — required for special purposes such as strikes, unexpected orders, or price rises.

Determinants of the Size of Working Capital

The amount of working capital a firm needs depends on several factors:

1. Nature of Business — Trading and service concerns need less working capital; manufacturing concerns need more because of large inventory and production cycle requirements.

2. Scale of Operations — A large firm with high volume of production and sales requires more working capital than a small firm.

3. Production Cycle — The longer the operating cycle (time from purchase of raw material to collection from customers), the larger the working capital requirement. A short cycle needs less.

4. Business Cycle — During boom, sales rise and more working capital is needed; during depression, requirements fall.

5. Seasonal Variations — Firms with seasonal demand (e.g., woollen garments) need more working capital during peak season and less in off-season.

6. Credit Policy — A liberal credit policy to customers increases receivables and hence working capital; a strict policy reduces it. Similarly, liberal credit terms from suppliers reduce the need for working capital.

7. Terms of Purchase and Sale — If raw materials are bought on credit and goods sold for cash, working capital needs are low; the reverse increases them.

8. Operating Efficiency — Efficient use of resources shortens the operating cycle and reduces working capital requirements.

9. Price Level Changes — Rising prices raise the cost of materials, wages, and overheads, thus increasing working capital needs.

10. Availability of Raw Materials — If raw materials are easily available and regular, less inventory is held and less working capital is needed; irregular supply forces larger stock.

11. Growth and Expansion — Expanding firms need more working capital to support increased activity.

12. Profitability and Dividend Policy — High profits and a conservative dividend policy retain funds internally, easing working capital needs; high dividend payout reduces retained funds.

13. Taxation Policy — Heavy taxes reduce retained earnings and increase the need for external working capital.

14. Contingencies — Firms must keep reserves for unforeseen events such as strikes or sudden price rises.

Conclusion

Working capital is the lifeblood of a business. Its size is not determined by any single factor but by a combination of the nature of business, operating cycle, credit policy, business cycle, and internal financial policies. A firm must carefully assess these determinants to maintain an optimum level of working capital that balances liquidity with profitability.

Assumption: Coupon and dividend are paid annually. The bond was sold 5 years ago, so its remaining maturity is (15-5=10) years.

a. Value of bond at present

Given:

• Par value, (M = \text{Rs } 1,000)
• Coupon rate (= 8.5%)
• Annual coupon, (C = 1,000 \times 8.5% = \text{Rs } 85)
• Remaining maturity, (n = 10) years
• Required rate of return, (r = 10%)

Formula:

[ P_0 = C \times PVIFA_{r,n} + M \times PVIF_{r,n} ]

Where:

[ PVIFA_{10%,10} = \frac{1-(1.10)^{-10}}{0.10} = 6.1446 ]

[ PVIF_{10%,10} = (1.10)^{-10} = 0.3855 ]

Substituting:

[ P_0 = 85 \times 6.1446 + 1,000 \times 0.3855 ]

[ P_0 = 522.29 + 385.54 = \text{Rs } 907.83 ]

Therefore, the present value of the bond is approximately Rs 907.83.

Since the required return (10%) is greater than the coupon rate (8.5%), the bond sells at a discount.

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b. Relationship between required rate of return and value of bonds

There is an inverse relationship between the required rate of return and the value of a bond.

• When the required rate of return increases, the present value of future coupon payments and maturity value decreases, so bond value falls.
• When the required rate of return decreases, the present value of future cash flows increases, so bond value rises.
• If required rate (=) coupon rate, bond value (=) par value.
• If required rate (>) coupon rate, bond value (<) par value, i.e. discount bond.
• If required rate (<) coupon rate, bond value (>) par value, i.e. premium bond.

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c. Value of the stock

Given:

• Current dividend, (D_0 = \text{Rs } 20)
• Supernormal growth rate for next 3 years, (g_1 = 10%)
• Normal growth rate after 3 years, (g_2 = 5%)
• Required rate of return, (r = 15%)

First, calculate dividends for the next three years:

[ D_1 = 20(1.10) = \text{Rs } 22 ]

[ D_2 = 22(1.10) = \text{Rs } 24.20 ]

[ D_3 = 24.20(1.10) = \text{Rs } 26.62 ]

Dividend from year 4 onward:

[ D_4 = D_3(1+g_2) = 26.62(1.05) = \text{Rs } 27.951 ]

Terminal value at the end of year 3:

[ P_3 = \frac{D_4}{r-g_2} ]

[ P_3 = \frac{27.951}{0.15-0.05} = \frac{27.951}{0.10} = \text{Rs } 279.51 ]

Now, present value of stock:

[ P_0 = \frac{D_1}{(1+r)^1} + \frac{D_2}{(1+r)^2} + \frac{D_3}{(1+r)^3} + \frac{P_3}{(1+r)^3} ]

[ P_0 = \frac{22}{1.15} + \frac{24.20}{(1.15)^2} + \frac{26.62}{(1.15)^3} + \frac{279.51}{(1.15)^3} ]

[ P_0 = 19.1304 + 18.2987 + 17.5031 + 183.7824 ]

[ P_0 = \text{Rs } 238.71 ]

Therefore, the value of the stock is approximately Rs 238.71.

Given: Initial outlay = Rs 60,00,000; required rate = 10%; cash flows (Rs): Y1 25,00,000, Y2 25,00,000, Y3 15,00,000, Y4 20,00,000, Y5 20,00,000.

(a) Payback period

The outlay is recovered during year 3:

$\text{PBP} = 2 + \frac{60{,}00{,}000 - 50{,}00{,}000}{15{,}00{,}000} = 2.67 \text{ years}$

Since 2.67 years < 3 years (maximum recovery period), NMC should purchase the truck.

(b) NPV at 10%

$\text{NPV} = 80{,}73{,}500 - 60{,}00{,}000 = \text{Rs } 20{,}73{,}500$

NPV is positive, so NMC should purchase the truck.

(c) IRR

IRR is the rate at which NPV = 0. Trying rates by trial and error:

$\text{IRR} = 23\% + \frac{75{,}251}{75{,}251 + 43{,}067} \times 1\% \approx 23.64\%$

IRR (about 23.6%) is greater than the required rate of 10%, so NMC should purchase the truck.

(d) NPV or IRR: which is superior?

NPV is generally regarded as the superior method because:

• It measures the absolute addition to shareholders' wealth, which is the aim of financial management.
• It assumes intermediate cash flows are reinvested at the cost of capital (a realistic rate), whereas IRR assumes reinvestment at the IRR itself, which is often unrealistic.
• It gives a single, unambiguous answer, while IRR can give multiple rates or none for non-conventional cash flows.
• For mutually exclusive projects of different size or timing, IRR can rank projects wrongly, whereas NPV always ranks correctly.

IRR is easier to communicate as a percentage, but where the two conflict, NPV should be followed.

The question gives only the interest rate on debt (10%) and the tax rate (30%). The capital structure, preferred dividend, share price, dividend, growth rate and flotation cost come from the data set preceding this item in the paper and are not in the text supplied, so the working is shown by formula, with the cost of debt computed in full and the rest illustrated.

(a) Component costs

1. Cost of debt (after tax)

$K_d = i(1 - t) = 10\%(1 - 0.30) = \mathbf{7\%}$

2. Cost of preferred stock

$K_p = \frac{D_p}{P_p(1 - F)}$

($D_p$ = preferred dividend, $P_p$ = issue price, $F$ = flotation cost; with no flotation cost the denominator is $P_p$.)

3. Cost of internal equity (retained earnings)

$K_e = \frac{D_1}{P_0} + g$

4. Cost of external equity (new shares)

$K_{e}' = \frac{D_1}{P_0(1 - F)} + g$

External equity always costs more than internal equity because of the flotation cost $F$.

Illustration, assumed figures only: $D_p =$ Rs 12 on a Rs 100 preferred share, $D_1 =$ Rs 12, $P_0 =$ Rs 100, $g = 8\%$, $F = 10\%$:

$K_p = \frac{12}{100} = 12\%, \quad K_e = \frac{12}{100} + 0.08 = 20\%, \quad K_e' = \frac{12}{90} + 0.08 = 21.33\%$

(b) WACC with equity from retained earnings only

$WACC = W_dK_d + W_pK_p + W_eK_e$

where the weights are the proportions of debt, preferred stock and retained earnings in the capital structure, and the internal cost $K_e$ is used, not $K_e'$.

Illustration, assumed weights 0.40 debt, 0.20 preferred, 0.40 retained earnings:

$WACC = 0.40(7) + 0.20(12) + 0.40(20) = 2.80 + 2.40 + 8.00 = \mathbf{13.20\%}$

Substitute the weights and figures from the paper's data in the same way to obtain the required answer.

(a) Residual Dividend Model

Given:

• Expected net income = Rs 12,000,000
• Debt ratio = 60%, so equity ratio = 40%
• Profitable investment opportunities = Rs 15,000,000

Step 1: Equity financing required to maintain the debt ratio

$$\text{Equity required} = 15,000,000 \times 40\% = \text{Rs } 6,000,000$$

Step 2: Residual earnings available for dividends

$$\text{Dividends} = \text{Net income} - \text{Equity required}$$ $$= 12,000,000 - 6,000,000 = \text{Rs } 6,000,000$$

Step 3: Dividend payout ratio

$$\text{Payout ratio} = \frac{\text{Dividends}}{\text{Net income}} \times 100$$ $$= \frac{6,000,000}{12,000,000} \times 100 = 50\%$$

Answer: The company’s dividend payout ratio should be 50 percent.

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(b) Effect of 20% Stock Dividend

Current position:

• Shares outstanding = 100,000
• Par value = Rs 100 per share
• Market price = Rs 300 per share
• Common stock = Rs 10,000,000
• Additional paid-in capital = Rs 5,000,000
• Retained earnings = Rs 15,000,000
• Total shareholders’ equity = Rs 30,000,000

Step 1: New shares issued

$$\text{New shares} = 100,000 \times 20\% = 20,000$$ $$\text{Total shares after stock dividend} = 100,000 + 20,000 = 120,000$$

Step 2: Accounting treatment

A 20% stock dividend is normally treated as a small stock dividend and is recorded at market value.

$$\text{Amount transferred from retained earnings} = 20,000 \times 300 = \text{Rs } 6,000,000$$

Of this amount:

$$\text{Increase in common stock} = 20,000 \times 100 = \text{Rs } 2,000,000$$ $$\text{Increase in additional paid-in capital} = 20,000 \times (300 - 100) = \text{Rs } 4,000,000$$

Step 3: New shareholders’ equity account

Step 4: New selling price per share

$$\text{New market price} = \frac{\text{Old market price}}{1 + \text{Stock dividend rate}}$$ $$= \frac{300}{1.20} = \text{Rs } 250$$

Answer:

• Number of shares outstanding increases from 100,000 to 120,000.
• Common stock increases to Rs 12,000,000.
• Additional paid-in capital increases to Rs 9,000,000.
• Retained earnings decrease to Rs 9,000,000.
• Total shareholders’ equity remains Rs 30,000,000.
• The new theoretical selling price of the stock is Rs 250 per share.

Note: If your textbook treats a 20% stock dividend as a large stock dividend, then it is recorded at par value. In that case, retained earnings become Rs 13,000,000 and additional paid-in capital remains Rs 5,000,000; the new price is still Rs 250.

This item is only the section heading of the paper: Analytical Answer Questions, attempt any TWO, 2 × 15 = 30 marks. It carries no question of its own; the individual 15-mark questions that follow it in the paper are answered separately.

How to attempt a 15-mark analytical question in TU BBS second year

1. Read the requirement and list what is asked (for example cost sheet, variances, ratios, WACC, NPV/IRR, or national-income and IS-LM analysis).
2. Write the given data in a short table and state the formula before substituting.
3. Show working notes for every figure that feeds the final answer, so partial marks are earned even if one step slips.
4. Present results in a clean table with units (Rs, %, units) and label variances as Favourable (F) or Adverse (A).
5. Close with a one- or two-line interpretation or decision (accept or reject the project, whether performance is better than standard, and so on).
6. Budget time: about 35 to 40 minutes per question, so that both chosen questions are completed.

Concept of Working Capital and Working Capital Management

Working capital refers to the funds invested in a firm's current assets — cash, marketable securities, accounts receivable, inventory and prepaid expenses. In a narrow sense, working capital is the excess of current assets over current liabilities, i.e. Net Working Capital = Current Assets − Current Liabilities. In a broad sense, it means the total investment in current assets (gross working capital). It is also called circulating capital or short-term capital because it keeps revolving in the operating cycle — cash → inventory → debtors → cash.

Working capital management is the management of current assets and current liabilities so as to maintain a satisfactory level of working capital. It involves deciding the level of each current asset (cash management, inventory management, receivables management) and the mix of short-term and long-term financing (payables, bank overdraft, commercial paper, etc.). Its two basic aspects are:

1. Determining the optimum level of current assets — balancing liquidity and profitability.
2. Financing the current assets — choosing between long-term and short-term sources.

Its main objectives are: maintaining adequate liquidity to meet short-term obligations, minimising the risk of insolvency, minimising the cost of funds, and maximising the return on investment. The operating cycle (raw materials → work-in-progress → finished goods → debtors → cash) determines how long funds remain tied up; the longer the cycle, the greater the working capital need. A firm must avoid both over-capitalisation in current assets (idle funds, low return) and under-capitalisation (risk of default, lost sales).

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Factors Affecting the Size of Working Capital

The size of working capital varies from firm to firm and from time to time. The main factors are:

1. Nature of business. Trading and service concerns need less working capital; manufacturing concerns need more because funds are tied up in raw materials, WIP and finished goods. Public utilities need very little.

2. Scale of operations. A large firm with high volume of sales and production requires more working capital than a small firm, though the requirement per unit of output may fall due to economies of scale.

3. Production cycle / operating cycle. The longer the time taken to convert raw material into cash, the larger the working capital required. Firms with short cycles (bakeries, dairies) need less.

4. Business cycle fluctuations. During boom, sales rise and stock and debtors increase, so more working capital is needed; during depression, requirements fall.

5. Production policy. A firm producing evenly throughout the year (steady production) needs less working capital than one producing seasonally or in batches.

6. Credit policy. A liberal credit policy (long credit period to customers) increases debtors and hence working capital; a strict cash-sales policy reduces it. Similarly, liberal credit terms from suppliers reduce the need.

7. Terms of purchase and sale. If raw materials are bought on credit and goods sold for cash, working capital need is low; the opposite situation raises it.

8. Seasonal variations. Seasonal industries (sugar, tea, woollen goods) need large working capital in peak season and less in off-season.

9. Cyclical and non-cyclical trends. A growing firm needs more working capital to support higher sales; a declining firm needs less.

10. Availability of raw material. If raw material is easily available throughout the year, less stock need be kept; if it is scarce or seasonal, large stocks must be held, raising working capital.

11. Growth and expansion plans. A firm planning expansion must carry extra working capital for the increased scale of operations.

12. Profit level and dividend policy. Higher profits and retained earnings provide internal funds and reduce dependence on outside working capital; a high dividend payout drains cash and increases the need.

13. Price level changes. Rising prices inflate the cost of inventory and wages, requiring more working capital; falling prices reduce it.

14. Taxation policy. Heavy taxes and advance tax payments reduce cash inflow and increase working capital requirements.

15. Degree of co-ordination in production and distribution. Good co-ordination shortens the operating cycle and lowers the requirement; poor co-ordination lengthens it.

16. Management efficiency. Efficient management of cash, stock and debtors keeps working capital low; inefficient management inflates it.

17. Import policy and government regulations. Restrictions on imports, licensing and price controls affect the level of stock and hence working capital.

Conclusion. The size of working capital is thus the net result of the nature of business, length of the operating cycle, credit and production policies, price and profit conditions, and the efficiency of management. A firm should estimate its requirement carefully and maintain it at the optimum level so that liquidity and profitability are both maximised.

Cost of capital $= 10\%$ for both projects; initial outlay Rs 100,000 each.

(a) Payback period (PBP)

Project X (equal annual flows): $PBP = \dfrac{100{,}000}{40{,}000} = \mathbf{2.5\ years}$

Project Y (unequal flows):

Recovery is complete during year 2: $PBP = 1 + \dfrac{100{,}000 - 50{,}000}{60{,}000} = \mathbf{1.83\ years}$

Both are within the 3-year limit, so both X and Y are accepted (they are independent). Y recovers its cost faster.

(b) Net present value at 10%

Project X: annuity factor for 4 years at 10% = 3.1699

$NPV_X = 40{,}000 \times 3.1699 - 100{,}000 = 126{,}794 - 100{,}000 = \textbf{Rs 26,794}$

Project Y:

$NPV_Y = 137{,}388 - 100{,}000 = \textbf{Rs 37,388}$

Both NPVs are positive, so both projects are accepted (independent projects).

(c) Internal rate of return (IRR)

Project X: required annuity factor $= 100{,}000/40{,}000 = 2.5$. For 4 years, the factor is 2.5887 at 20% and 2.4936 at 22%.

$IRR_X = 20 + \frac{2.5887 - 2.5}{2.5887 - 2.4936} \times 2 \approx \mathbf{21.9\%}$

Project Y: trial and error.

$IRR_Y = 28 + \frac{1{,}463}{1{,}463 + 1{,}526} \times 2 \approx \mathbf{29.0\%}$

Both IRRs exceed the 10% cost of capital, so both projects are accepted. Y has the higher IRR.

(d) Which method is superior?

NPV is superior, because:

1. It measures the absolute addition to shareholders' wealth in rupees, in line with the goal of wealth maximisation.
2. It considers the time value of money and all cash flows, unlike payback, which ignores flows after the payback period.
3. It assumes reinvestment at the cost of capital (realistic), whereas IRR assumes reinvestment at the IRR itself, which can be unrealistic.
4. For mutually exclusive projects or non-conventional cash flows, IRR can rank projects wrongly or give multiple rates, but NPV does not.

Here all methods agree (both projects accepted), but NPV is the more reliable guide when they conflict.