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Here is a compilation of problems on operating and financial leverage in a business with its relevant solutions.

**Problem 1:**

Given Sales Rs.100 million, Variable cost Rs.40 Million and Fixed Cost Rs.40 Million. Find out the Degree of Operating Leverage.

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**Solution: **

**Problem 1(a):**

(a) Given Sales Rs.100 million, Variable cost Rs.48 Million and Fixed Cost Rs.30 Million. Find out the Degree of Operating Leverage?

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**Solution: **

**Observation:**

When the company reduces its fixed cost by increasing variable cost, it manages to reduce operating leverage.

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High operating leverage produces a situation where a small change in sales can result in a large change in operating income [Sales – Variable cost – Fixed cost]. Illustration 1(b) and 1(c) compare two business situations with high and low operating leverage:

**Problem 1(b):**

**Situation 1:** Given Sales Rs.100 million, Variable cost Rs. 40 Million and Fixed Cost Rs. 40 Million.

**Situation 2:** Sales Rs.80 million, Variable cost Rs.32 Million and Fixed Cost Rs.40 Million. Compare operating income. Degree of Operating Leverage = 3 for the first business situation, which has already been calculated in Illustration 1.

**Solution: **

In situation 1 Operating income is Rs.20 million. In situation 2 is Rs.8 million. Sales declined by 20%, but operating income declined by 60% which is 3 times the change in sales.

**Problem **1(c):

**Situation 1:** Given Sales Rs.100 million, Variable cost Rs.60 Million and Fixed Cost Rs.20 Million.

**Situation 2:** Sales Rs.80 million, Variable cost Rs.48 Million and Fixed Cost Rs.20 Million. Compare operating income.

**Solution: **

Business Situation 1

DOL = 2

Business Situation 2 as compared to Business Situation 1

Change in sales =20%

New operating income = Rs.12 million

Change in operating income = Rs.8 million

% Change in Operating Income = 40%

**What is your ****observation? **

Change in Operating Income = Change in Sales × Degree of Leverage

Therefore, a high operating leverage leads to change operating income heavily which would create low or negative profit in adverse business situation.

This we should keep in the background of all capital structure planning. This is because if a company is already having very high degree of operating leverage, taking financial risk by way of higher borrowing will magnify the risk.

**Financial Leverage: **

It reflects amount of interest costs embedded in a firm’s capital structure. Higher the interest cost higher is the degree of financial leverage.

Of course, the level of interest cost depends upon the debt – equity ratio of the company. In other words, higher interest cost results from the higher level of borrowings.

**Problem 2**:

Given Sales Rs.100 million, Variable cost Rs.40 Million and Fixed Cost Rs.40 Million. Capital employed of the Company Rs.80 million with debt equity ratio 1:1. This means debts = Rs.40 million. Debt carries 10% interest. Find out the Degree of Financial Leverage?

**Solution: **

Interest cost = Rs.4 million.

(Figures are in Rs. Million)

DFL explains change in net profit resulting from change in operating profit. This is explained in Illustration 2(a).

**Problem** 2(a):

Continue with the data given in Illustration 2. Now assume that sales change to Rs.80 million. First prepare a statement showing operating profit and PBT in both the situation and then explain the change in profits using DOL and DFL.

**Solution: **

**Using data of Case 1: **

DOL = 3, DFL = 1.25

% Change in Operating profit = % change in sales × DOL = – 20% × 3 = -60%

**Check: **

Operating income in case 1 Rs.20 million has been reduced by Rs.12 million which is 60% decline.

% Change in PBT = % Change in Operating profit × DFL = -60% × 1.25 = -75%

**Check: **

PBT has been reduced by Rs.12 million from Rs.16 million which 75% decline.

On the basis of the discussion held, we may conclude that –

% Change PBT = % Change in sales × DOL × DFL

**Let us introduce a new term: **

Degree of Combined Leverage (DCL) = DOL × DFL

% Change PBT = % Change in sales × DOL × DFL

= % Change in sales × DCL

Application of Operating and Financial Leverage in Capital Structure Planning: A newly established company should look into the issue of creating operating facilities and cost structure planning together with the financial structure planning. An existing company should attempt to re-structure its cost and financial structure in the light of market demand.

**Problem **3:

Jambo Chemicals Ltd. is newly formed company.

**The promoters has planned two different cost structures: **

(i) Variable cost 50%, Fixed Cost Rs.30 lacs or

(ii) Variable cost 60%, Fixed cost Rs.20 lacs. Projected average sales Rs.150 lacs. The pessimistic projection of sales is Rs.120 lacs and optimistic projection is Rs.180 lacs. Its total investment has been worked out as Rs.150 lacs of which Rs.120 lacs is in fixed assets and Rs.30 lacs for working capital.

**The company is considering two financing alternatives: **

(i) Equity Rs.100 lacs and Debt Rs.50 Lacs, Debt – equity ratio of 1:2 or

(ii) Equity Rs.50 lacs, Debt Rs.100 lacs, Debt – Equity ratio of 2:1.

For the first alternative, interest rate is worked out to be 8% and for the second alternative it is 10%. Tax Rate is 35% and surcharge 5%. Depreciation component in the fixed costs is Rs.6 lacs.

Since there is now-a-days a provision for deferred tax liability is to be created as per Accounting Standard -22, there is no need to take care of tax depreciation. The company wants to carry out the analysis using accounting depreciation and tax benefit arising out of that.

Find out degree of operating leverage, financial leverage and combined leverage for the possible alternatives. Work out PAT, EPS and expected share value for these alternatives. Take that market return is 14%, Risk free rate 6%, Unlevered beta of the company is 0.60.

**Solution: **

Presented below are twelve alternative EPS for different cost structure and given debt -equity ratio of 1:2 and 2:1. Financial leverage reduces on the impact of cost structure given a particular level of debt – equity ratio.

**Conclusion: **

At each level of sales there are four alternative EPS. In case the company wants to maximize EPS, it is found that Variable cost of 50%, Fixed Cost Rs.30 million with D/E 1:1 is acceptable level of operational and financial mix which maximizes EPS at all different level of sales.

**Now let us look into the value of equity given EPS and unlevered beta:**

β_{1} = Beta of levered firm with D/E = 1:2

β_{2} = Beta of levered firm with D/E = 2:1

Ke_{1} = Cost of equity with D/E = 1:2

Ke_{2} = Cost of equity with D/E = 2:1

**Conclusion: **

Earlier we have observed that EPS with D/E 1:2 is maximum in all three different level of sales. But now we find that value of equity is maximum with D/E 2:1 at all three different level of sales. Also there is differing decision as regards cost structuring.

At sales level of Rs.120 lacs variable cost of 60% with lower fixed cost of Rs.20 million is preferred. But at higher level of sales at Rs.150 million and Rs.180 million lower level of variable cost 50% and higher level of fixed cost Rs.30 million is preferred.

**What should the company finally plan? **

1. A debt – equity ratio of 2:1

2. Cost structuring would depend on level of sales. It can start with 60% variable cost and low fixed cost. Once the sales level is achieved, it can shift to higher level of fixed cost.