Fundamentals of Financial Management

Given:

• Debt, $D = \text{Rs } 24$ million
• Common equity, $E = \text{Rs } 36$ million
• Total capital, $V = \text{Rs } 60$ million
• Interest rate on new debt, $k_d = 10\%$
• Marginal tax rate, $T = 40\%$
• Dividend just paid, $D_0 = \text{Rs } 50$ per share
• Growth rate, $g = 6\%$
• Current market price per share, $P_0 = \text{Rs } 500$

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a. After-tax cost of new debt and cost of common equity

1. After-tax cost of new debt

$$k_d(1-T) = 10\%(1-0.40)$$ $$= 10\% \times 0.60 = 6\%$$

After-tax cost of new debt = 6%.

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2. Cost of common equity from retained earnings

Since new equity comes only from retained earnings, there is no flotation cost. Using the dividend growth model:

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

Where,

$$D_1 = D_0(1+g) = 50(1+0.06) = \text{Rs } 53$$

Now,

$$k_e = \frac{53}{500} + 0.06$$ $$= 0.106 + 0.06 = 0.166 = 16.6\%$$

Cost of common equity = 16.6%.

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b. Weighted Average Cost of Capital (WACC)

The company maintains its present capital structure. So, the weights are:

$$w_d = \frac{24}{60} = 0.40$$ $$w_e = \frac{36}{60} = 0.60$$

WACC formula:

$$\text{WACC} = w_d k_d(1-T) + w_e k_e$$

Substituting the values:

$$\text{WACC} = 0.40 \times 6\% + 0.60 \times 16.6\%$$ $$= 2.4\% + 9.96\%$$ $$= 12.36\%$$

WACC = 12.36%.

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Importance of WACC

1. Capital budgeting decision: WACC is used as the discount rate to evaluate new projects. A project is accepted only if its return is greater than WACC.

2. Hurdle rate: It acts as the minimum required rate of return that a company must earn on its investments.

3. Valuation of the firm: WACC is used to calculate the present value of expected future cash flows of the company.

4. Capital structure decision: It helps management decide the best mix of debt and equity to minimize the overall cost of capital.

5. Performance evaluation: It provides a benchmark to judge whether the company is creating value for shareholders.

6. Investment decision: It helps compare different investment opportunities and select the most profitable one.

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Final Answer:

• After-tax cost of new debt = 6%
• Cost of common equity = 16.6%
• WACC = 12.36%

a. Calculation of required figures

Given:
Cash and marketable securities = Rs 100 ('000)
Sales = Rs 1,000 ('000)
Fixed assets = Rs 283.5 ('000)
Net income = Rs 50 ('000)
Quick ratio = 2.0 times
Current ratio = 3.0 times
DSO = 40 days
ROE = 12%
Days in year = 360

(1) Accounts receivable

$DSO=\frac{\text{Accounts receivable}}{\text{Sales}}\times 360$

$40=\frac{AR}{1000}\times 360$

$AR=\frac{40\times1000}{360}=111.111 \text{ Rs '000}$

Accounts receivable = Rs 111.111 thousand = Rs 111,111.11 approx.

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(2) Current liabilities

Quick assets = Cash and marketable securities + Accounts receivable
= 100 + 111.111 = 211.111 Rs '000

$Quick\ ratio=\frac{\text{Quick assets}}{\text{Current liabilities}}$

$2=\frac{211.111}{CL}$

$CL=\frac{211.111}{2}=105.556 \text{ Rs '000}$

Current liabilities = Rs 105.556 thousand = Rs 105,555.56 approx.

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(3) Current assets

$Current\ ratio=\frac{\text{Current assets}}{\text{Current liabilities}}$

$3=\frac{CA}{105.556}$

$CA=3\times105.556=316.667 \text{ Rs '000}$

Current assets = Rs 316.667 thousand = Rs 316,666.67 approx.

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(4) Total assets

$Total\ assets=Current\ assets+Fixed\ assets$

$=316.667+283.5=600.167 \text{ Rs '000}$

Total assets = Rs 600.167 thousand = Rs 600,166.67 approx.

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(5) Return on assets

$ROA=\frac{\text{Net income}}{\text{Total assets}}\times100$

$=\frac{50}{600.167}\times100=8.33\%$

Return on assets = 8.33% approx.

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Summary of answers

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b. Limitations of ratio analysis

1. Based on accounting data: Ratios use historical accounting figures, so they may not reflect current market value or future prospects.
2. Ignores price level changes: Inflation and changing prices reduce the reliability and comparability of ratios.
3. Different accounting policies: Firms may follow different methods of depreciation, inventory valuation, etc., making comparison difficult.
4. Window dressing: Financial statements can be manipulated to show better ratios, so ratios may be misleading.
5. Ignores qualitative factors: Management quality, employee morale, market reputation, and economic conditions are not reflected in ratios.
6. Single ratio is not conclusive: A single ratio cannot give a complete picture; trend and comparative analysis are necessary.
7. No standard definitions: Different analysts use different formulas for the same ratio, causing confusion.
8. Ignores size and risk: A small firm may show high ratios, but that does not necessarily mean it is financially stronger.
9. Seasonal and cyclical effects: Business fluctuations can distort ratios and make them unrepresentative.
10. Time value of money ignored: Ratios do not consider the timing of cash flows or the risk associated with them.

Concept of Working Capital and Working Capital Management

1. Meaning of Working Capital

Working capital refers to the funds invested in current assets of a business, i.e., those assets which are converted into cash within one accounting year or one operating cycle. In a narrow sense, working capital is the excess of current assets over current liabilities:

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

• Gross Working Capital = Total investment in current assets (cash, marketable securities, bills receivable, debtors, inventory, prepaid expenses).
• Net Working Capital = Current Assets − Current Liabilities. A positive figure indicates liquidity; a negative figure indicates technical insolvency.

Current assets are also called floating or circulating assets because they keep revolving — cash is used to buy raw materials, raw materials are converted into finished goods, finished goods into debtors, and debtors back into cash. This continuous cycle is called the operating cycle or working capital cycle.

2. Concept of Working Capital Management

Working capital management is the process of planning, organising, directing and controlling the current assets and current liabilities of a firm so as to:

1. Maintain an adequate level of working capital to meet day-to-day obligations.
2. Avoid excessive investment in current assets (which reduces profitability).
3. Avoid inadequate investment (which creates liquidity risk and loss of creditworthiness).
4. Minimise the length of the operating cycle and the cost of funds.

It involves decisions on three broad areas:

The central objective is to strike a trade-off between liquidity and profitability — the two conflicting goals of working capital management. Holding more current assets improves liquidity but lowers return on investment; holding fewer improves profitability but increases the risk of insolvency. The finance manager must find the optimum level.

3. Importance of Working Capital Management in the Manufacturing Industry

1. Large investment in inventory: A manufacturing firm must hold raw materials, work-in-progress and finished goods. Poor inventory control blocks funds and raises carrying cost (storage, insurance, obsolescence). Effective management releases funds for productive use.
2. Long operating cycle: Manufacturing involves production time, so the cycle from cash to cash is longer than in trading. Adequate working capital is essential to pay wages, power, fuel and suppliers continuously without interruption in production.
3. Smooth production and capacity utilisation: Shortage of working capital means inability to buy raw materials on time, causing idle plant, idle labour and loss of output. Thus it directly affects production efficiency.
4. Credit sales and receivables: Manufacturers usually sell on credit to wholesalers and dealers. Sound receivables management ensures prompt collection and reduces bad debts and the cost of financing debtors.
5. Meeting seasonal and cyclical demand: Many manufacturing lines (sugar, textiles, cement, beverages) are seasonal. Working capital must be arranged in advance to build up stock before the peak season.
6. Fixed cost absorption and profitability: Since fixed costs are high in manufacturing, continuous operation is necessary to reduce per-unit cost. Adequate working capital keeps operations running and improves profit.
7. Cash for operating expenses: Regular payment of wages, salaries, electricity, repairs and taxes maintains employee morale, credit standing and uninterrupted operations.

4. Importance of Working Capital Management in the Trading Industry

1. Inventory is the core asset: For a trader, merchandise inventory is the principal current asset. Over-stocking blocks capital and invites losses from price fall and deterioration; under-stocking means lost sales and dissatisfied customers. Hence inventory management is the very heart of a trading concern.
2. Short operating cycle but high turnover: Trading firms buy and sell quickly. Since the cycle is short, small errors in credit or stock policy quickly affect cash flow. Efficient management keeps the cycle short and cash flowing.
3. Dependence on trade credit: Traders rely heavily on suppliers' credit and bank overdrafts. Managing current liabilities — payment periods, discounts and timing — is crucial to profitability.
4. Thin profit margin: Trading margins are usually narrow, so the firm cannot afford high interest cost or bad debts. Careful control of debtors and cash is vital for survival.
5. Seasonal stocking: Traders dealing in garments, fertilizers, stationery and festive goods must build stock before the season and liquidate it afterwards. Working capital planning prevents over-financing and distress sales.
6. Liquidity for creditworthiness: A trader's ability to pay suppliers on time determines the credit terms available. Good working capital management protects reputation and bargaining power.
7. Avoidance of insolvency: Since trading firms have few fixed assets to pledge, an imbalance between current assets and current liabilities can quickly lead to technical insolvency.

5. Conclusion

Working capital is the life-blood of every business. Its management seeks the optimum balance between liquidity and profitability by controlling cash, receivables, inventory and current liabilities. In manufacturing, it ensures uninterrupted production and full utilisation of plant capacity; in trading, it ensures rapid stock turnover, timely payment to suppliers and protection of thin margins. In both industries, efficient working capital management reduces cost, improves cash flow, strengthens credit standing and maximises the wealth of shareholders.

(a) Payback period

The payback period is the time a project takes to recover its initial investment from its net cash inflows.

After 2 years Rs 4,00,000 of the Rs 16,00,000 is still unrecovered, so

$\text{Payback} = 2 + \frac{4{,}00{,}000}{8{,}00{,}000} = 2.5 \text{ years}$

Since 2.5 years is less than the maximum recovery period of 3 years, the company should run the bus.

(b) Net present value

NPV is the present value of a project's cash inflows minus its initial investment, discounted at the required rate of return.

$\text{NPV} = 19{,}83{,}881 - 16{,}00{,}000 = \text{Rs } 3{,}83{,}881$

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

(c) Internal rate of return

The IRR is the discount rate at which the NPV of the project is zero, that is, the present value of inflows equals the cost.

$\text{IRR} \approx 20 + \frac{20{,}756}{20{,}756 + 9{,}491} \times 1 \approx 20.7\%$

The IRR (about 20.7%) is higher than the required return of 10%, so the company should run the tourist bus.

Let returns be expressed in percent.

a. Expected return and standard deviation

Expected return

[ \bar R_A = \sum p_i R_{Ai} ]

[ \bar R_A = (0.3)(0) + (0.4)(10) + (0.3)(20) = 10% ]

[ \bar R_B = (0.3)(30) + (0.4)(10) + (0.3)(0) = 13% ]

Standard deviation

[ \sigma_A = \sqrt{\sum p_i (R_{Ai}-\bar R_A)^2} ]

[ \sigma_A = \sqrt{(0.3)(0-10)^2 + (0.4)(10-10)^2 + (0.3)(20-10)^2} ]

[ \sigma_A = \sqrt{30+0+30} = \sqrt{60} = 7.75% ]

[ \sigma_B = \sqrt{(0.3)(30-13)^2 + (0.4)(10-13)^2 + (0.3)(0-13)^2} ]

[ \sigma_B = \sqrt{86.7+3.6+50.7} = \sqrt{141} = 11.87% ]

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b. Profitability and risk

• More profitable: Stock B, because its expected return is higher: (13%) against (10%) for Stock A.
• More risky: Stock B, because its standard deviation is higher: (11.87%) against (7.75%) for Stock A.

So Stock B is more profitable in absolute expected return, but it is also more risky. On a risk-adjusted basis, Stock A is better because its coefficient of variation is lower:

[ CV_A = \frac{7.75}{10}=0.775 ]

[ CV_B = \frac{11.87}{13}=0.913 ]

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c. Portfolio risk and return

Weights:

[ w_A = 0.60,\qquad w_B = 0.40 ]

First calculate covariance between A and B:

[ Cov(A,B)=\sum p_i (R_{Ai}-\bar R_A)(R_{Bi}-\bar R_B) ]

[ Cov(A,B)=(0.3)(0-10)(30-13)+(0.4)(10-10)(10-13)+(0.3)(20-10)(0-13) ]

[ Cov(A,B)=-51+0-39=-90 ]

Correlation:

[ \rho_{AB}=\frac{Cov(A,B)}{\sigma_A\sigma_B} ]

[ \rho_{AB}=\frac{-90}{(7.75)(11.87)}=-0.9785 ]

Portfolio expected return

[ \bar R_p = w_A\bar R_A + w_B\bar R_B ]

[ \bar R_p = (0.60)(10) + (0.40)(13) = 11.2% ]

Portfolio risk

[ \sigma_p^2 = w_A^2\sigma_A^2 + w_B^2\sigma_B^2 + 2w_Aw_B Cov(A,B) ]

[ \sigma_p^2 = (0.60)^2(60) + (0.40)^2(141) + 2(0.60)(0.40)(-90) ]

[ \sigma_p^2 = 21.6 + 22.56 - 43.2 = 0.96 ]

[ \sigma_p = \sqrt{0.96} = 0.98% ]

Therefore, the portfolio has:

[ \boxed{\text{Expected return} = 11.2%} ]

[ \boxed{\text{Risk} = 0.98%} ]

The portfolio risk is very low because Stock A and Stock B are almost perfectly negatively correlated.