Question 3
MM as the justification of NOI; NOI valuation as debt rises
18.75 marks
- Time to write
- About 38 minutes
From an older CBCS paper
Question
Question 3 · 18.75 marksExplain: for the NOI approach to Capital Structure theory, the 'Modigliani-Miller model' is the behavioral justification.
A company's annual net operating income is Rs.10.8 lakhs, and it has Rs.48 lakhs 8% debentures. Its overall capitalization rate is 10%. According to the Net Operating Income Approach, calculate the firm's value and its equity capitalization rate. If the debenture debt is increased to Rs.72 lakhs, what will the effect be on the firm's value and on the equity capitalization rate?
Reworded from the university paper: names and figures differ, the task is the same. The original paper belongs to the University of Delhi. See DU's question bank.
Before you write
Read off the question and its marks
Read from the question
- Explain…Is…?Two asks in one question: answer both.
- calculateFormula first, then the working, then the answer with its unit (₹, %, units).
What the paper leaves open
No mark is printed for the question; the paper asks for any four of six, equal marks.
Write it in this order
- Read the data; note exactly what is asked 2 min
- 1 NOI and the MM hypothesis 3 marks 5 min
- 2 Arbitrage as the behavioural justification, with assumptions 6 marks 11 min
- 3 Value of the firm and ke lakh debt 5 marks 9 min
- 4 Effect of raising debt to lakh 4.8 marks 9 min
- Check: arithmetic, units (₹, %), final answer underlined 2 min
Try it first. About 38 minutes for 18.75 marks. Write it out, then open the solution.
Solution
Hover or tap a marked figure, like 72,000, to see how it is made and where else it appears.
MM as the behavioural justification of the NOI approach
The NOI approach holds that the overall cost of capital and the value of the firm are independent of the capital structure, but it simply assumes that the cost of equity rises with leverage just enough to offset cheaper debt. MM reach the same conclusion and supply the reason for it: they support the NOI approach but provide its behavioural justification.
The MM hypothesis. Without taxes, MM hold that the value of a firm and its overall cost of capital do not depend on its capital structure: the cheaper debt is exactly offset by the rise in the cost of equity as leverage increases.
The behavioural justification: arbitrage. Where the NOI approach simply assumes this, MM explain it by how investors behave. Two firms identical in all respects except capital structure cannot have different market values, because if they did, arbitrage would take place:
- Investors in the overvalued firm (usually the levered one) sell their shares.
- They borrow on their own account in proportion to their share of that firm's debt, substituting personal leverage for corporate leverage.
- They buy the shares of the undervalued firm, earning the same income for a smaller outlay and with the same risk.
- The selling depresses the price of the overvalued firm and the buying raises that of the undervalued firm, until the two total values are equal; then no further gain is possible.
Assumptions behind it: no corporate taxes, a perfect market, rational investors, firms in identical risk classes, and all earnings distributed. Personal borrowing must also be possible on the same terms as corporate borrowing.
So the arbitrage process is the behavioural mechanism that keeps the overall cost of capital constant, which the NOI approach only asserts.
NOI approach: value and equity capitalisation rate
Under NOI the value of the firm is NOI ÷ ko whatever the debt; equity is the residual and ke = earnings for equity ÷ value of equity.
| Particulars (₹) | Debt ₹48 lakh | Debt ₹72 lakh |
|---|---|---|
| Net operating income | 10,80,000 | 10,80,000 |
| Overall capitalisation rate (ko) | 10% | 10% |
| Value of the firm (V = NOI ÷ ko) | 1,08,00,000 | 1,08,00,000 |
| Less: debt | 48,00,000 | 72,00,000 |
| Value of equity (S) | 60,00,000 | 36,00,000 |
| Net operating income | 10,80,000 | 10,80,000 |
| Less: interest @ 8% | 3,84,000 | 5,76,000 |
| Earnings for equity | 6,96,000 | 5,04,000 |
| Equity capitalisation rate (ke) | 11.60% | 14.00% |
Effect of raising debt to ₹72 lakh. The value of the firm is unchanged at ₹1.08 crore; the value of equity falls to ₹36 lakh and the equity capitalisation rate rises from 11.60% to 14.00%, because the shareholders bear more financial risk. The benefit of the cheaper debt is exactly offset by the higher ke, so ko stays 10%.
Where the 18.75 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | NOI and the MM hypothesis | 3 |
| 2 | Arbitrage as the behavioural justification, with assumptions | 6 |
| 3 | Value of the firm and ke at ₹48 lakh debt | 5 |
| 4 | Effect of raising debt to ₹72 lakh | 4.75 |
| Total | 18.75 |
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