Two identical companies earn the same profit. One is financed wholly by shares. The other has borrowed a third of its capital. Which is worth more? The answer shapes how every board chooses between debt and equity. Economists disagree, and the answers range from “it makes no difference” to “borrow as much as you safely can”. Each theory teaches something and is tested differently in the exam.
This topic covers four theories of how companies choose how to finance an investment (static trade-off, pecking order, market timing and agency effects), the traditional view of gearing and the cost of capital, and the Modigliani and Miller (MM) propositions without and with corporate tax, including their formulae and the idea of arbitrage. The previous topic covered Islamic finance.
The next covers changing gearing, the WACC and asset and equity betas. The May 2014 Pathfinder paper had a question on MM and arbitrage.
In 30 seconds
Static trade-off: there is an optimal gearing where the marginal tax benefit of debt equals the marginal cost of financial distress; profitable firms can borrow more. Pecking order (Myers, 1984): retained profit first, then debt, then new shares; no optimal gearing; profitable firms borrow less. Market timing: issue shares when overvalued, buy back when undervalued. Agency: shareholders, managers and lenders conflict, and the optimum balances agency costs.
Traditional view: WACC falls then rises; there is an optimum. MM without tax: WACC and value are unaffected by gearing (VG = VU); cost of equity rises: keG = keU + (D ÷ E)(keU − kd). MM with tax: VG = VU + D × t; WACCG = WACCU × [1 − Dt ÷ (D + E)]; keG = keU + (1 − t)(D ÷ E)(keU − kd). WACC falls as gearing rises, limited in practice by distress costs.
Key terms in plain English
| Term | What it means |
|---|---|
| Gearing | The proportion of debt in a company’s capital |
| Optimal capital structure | The gearing at which WACC is lowest and value highest |
| Financial distress | The risk and cost of being unable to meet debt payments |
| Asymmetry of information | Managers know more about the company than investors do |
| Tax shield | The value of tax relief on interest, equal to debt times the tax rate |
| Arbitrage | Profiting from a price difference between two equivalent assets |
| Ungeared (all-equity) company | A company with no debt |
Syllabus check
This topic is in syllabus area C (financing decisions). It covers:
- theories of the choice of financing method, including trade-off, pecking order and market timing;
- the effect of gearing on the cost of capital (traditional, and Modigliani and Miller with and without tax);
- the capital structure choice and its agency effects.
CAMA 2020 and capital structure
The Companies and Allied Matters Act 2020 (CAMA 2020) is the company law of Nigeria.
| Section | What it says | Link to this topic |
|---|---|---|
| s. 305 | A director must act in good faith in the best interests of the company | The financing mix should serve the long-term interest of the company |
| s. 308 | A director must use the care, diligence and skill of a reasonably prudent director | Directors should weigh the risk of debt against its benefits |
| s. 377(1) and s. 378 | Directors prepare statements that follow IFRS and give a true and fair view | Decisions later affect reported assets, profit and cash |
| s. 385 | The directors’ report covers performance and risk | Major plans and risks are reported to shareholders |
Choosing how to finance an investment
Static trade-off theory
Each company has an optimal gearing. The benefit of debt is mainly tax relief on interest. The cost is the risk of financial distress, which makes borrowing costlier or unavailable. The optimum is where the marginal benefit of more debt equals its marginal cost. Profitable companies can take more debt before distress costs bite, so profitability and gearing are positively correlated.
Low-profit companies avoid both new debt and new shares and rely on retained profit, and may even reject a positive-NPV project they cannot fund that way.
Pecking order theory
Myers (1984) argued that companies have an order of preference: 1st retained earnings, 2nd debt, 3rd new shares. Retained profit is convenient and cheap; debt is cheaper than a share issue because it is easier to arrange and gets tax relief. Gearing results from a series of such choices, so there is no optimal gearing. Profitable companies can use retained profit, so profitability and gearing are negatively correlated.
Market timing theory
Because managers know more than investors (asymmetry of information), they can tell when shares are over-valued (issue shares) or under-valued (buy back). The gearing level then follows market opportunities, with no target.
Agency effects
Jensen and Meckling (1976): owners, managers and lenders have conflicting interests. Shareholders may prefer debt, because a share issue dilutes managers’ holdings and debt reduces free cash for managers to spend on benefits. Lenders worry that debt lets shareholders back risky projects, so they may oppose new borrowing. The optimal structure balances the agency costs of debt against those of equity, as well as the marginal tax benefit and distress cost.
| Static trade-off | Pecking order | Market timing | |
|---|---|---|---|
| Optimal gearing? | Yes | No | No |
| Driver | Tax benefit against distress cost | Ease and cost of each source | Share price over- or under-valuation |
| Profitability and gearing | Positive | Negative | Not specified |
The traditional view
As gearing rises, the cost of equity rises, but at first the cheaper debt has the bigger effect and WACC falls. At higher gearing the cost of equity rises faster, and WACC begins to rise. There is an optimum gearing where WACC is lowest and company value highest.
Modigliani and Miller
Without tax
MM started with a simplified world: perfect capital markets, no tax, no bankruptcy risk, and investors indifferent between borrowing themselves and investing in companies that borrow. They did not claim the real world is like this. Their results:
- Proposition 1: WACC is the same at all levels of gearing, so the total value of a company is the same: WACCG = WACCU and VG = VU. Gearing is irrelevant.
- Proposition 2: the cost of equity rises with gearing just enough to hold WACC constant: keG = keU + (D ÷ E)(keU − kd).
ICAN’s example. An all-equity company worth ₦150m with a cost of equity of 10% borrows ₦50m at 6% and buys back ₦50m of shares. Ignore tax.
- WACC stays at 10% and total value stays at ₦150m (debt 50, equity 100).
- keG = 10% + (50 ÷ 100) × (10% − 6%) = 12.0%.
- The reverse works too.
with ke 14%, kd 8% and D ÷ E = 100 ÷ 500, the ungeared cost of equity is 13.0%.
With tax
Tax relief on interest cheapens debt, so MM revised their results:
- Proposition 1: WACC falls as gearing rises, and value rises. VG = VU + D × t, where D × t is the tax shield.
WACCG = WACCU × [1 − Dt ÷ (D + E)].
In theory the lowest WACC is at 100% debt, but financial distress costs raise the cost of debt at high gearing. - Proposition 2: keG = keU + (1 − t)(D ÷ E)(keU − kd).
ICAN’s example. An all-equity company worth ₦60m with a cost of equity of 8% borrows ₦20m at 5% and buys back ₦20m of shares. Tax is 25%.
- VG = 60 + 20 × 0.25 = ₦65m.
Equity = 65 − 20 = ₦45m. - WACCG = 8% × [1 − (0.25 × 20) ÷ 65] = 8% × 0.9231 = 7.38%.
- keG = 8% + 0.75 × (8% − 5%) × (20 ÷ 45) = 9%.
Check: (45 × 9% + 20 × 3.75%) ÷ 65 = 7.38%.
Arbitrage
MM’s argument rests on arbitrage. If two companies with the same business risk and profit have different values because of gearing, shareholders can profit by selling shares in the over-valued one and buying the under-valued one, using personal borrowing to keep their risk the same. This continues until the values are equal.
ICAN’s May 2014 question applied it: with tax, B Ltd (geared) was expected to be worth ₦280m + ₦62.5m × 30% = ₦298.75m but was priced at ₦312.5m, so it was over-valued. A holder of 4% of B sells that stake for ₦10m, borrows 4% of the after-tax debt (₦1.75m), invests ₦11.75m in A (the all-equity company) and raises his income from ₦1.54m to about ₦1.63m, a gain of about ₦86,000 at the same risk.
The rules in more depth
Why MM without tax says gearing is irrelevant
Investors can borrow personally, so a company’s borrowing adds nothing they cannot do themselves. The cost of equity rises to offset the cheaper debt.
Why tax breaks the result
Interest is deductible, so the government in effect pays part of the interest. That is a real gain, worth D × t, which accrues to the company.
Why the real world has an optimum
Financial distress, agency costs and information asymmetry add costs at high gearing, so the WACC curve turns up again and an interior optimum exists.
Why pecking order and trade-off give opposite predictions
A profitable firm has cash to avoid borrowing (pecking order) or has low distress risk and can borrow more (trade-off).
Effect on analysis
State the theory, give its prediction, and test it on the case facts, for example the firm’s profit, gearing and share price.
Worked examples
Example 1: MM without tax. An all-equity company is worth ₦200m with a cost of equity of 12%. It borrows ₦50m at 7% to buy back shares.
- WACC stays at 12%. Value stays at ₦200m, with equity ₦150m.
- keG = 12% + (50 ÷ 150)(12% − 7%) = 13.67%.
- Check.
(150 × 13.67% + 50 × 7%) ÷ 200 = 12.0%.
Example 2: MM with tax. An all-equity company is worth ₦120m with a cost of equity of 10%. It borrows ₦40m at 6%. Tax is 30%.
- VG = 120 + 40 × 0.3 = ₦132m
equity = ₦92m. - WACCG = 10% × [1 − (0.3 × 40) ÷ 132] = 9.09%.
- keG = 10% + 0.7 × (10% − 6%) × (40 ÷ 92) = 11.22%.
Example 3: the pecking order. A project needs ₦30m. Retained profit available is ₦12m and debt capacity is ₦14m.
- First use retained profit: ₦12m.
- Next use debt: ₦14m.
- Only the last ₦4m would come from new shares.
Example 4: market timing. The managers believe the shares are trading well above their fair value.
- Market timing says they should issue shares now.
- The extra equity lowers the gearing, but that is a by-product.
- If instead the shares looked cheap, a buy-back would be the logical step.
How to score full marks
- State the theory and its prediction.
- Use the right MM formula for tax or no tax.
- Show value, WACC and cost of equity.
- Check your answer by recomputing WACC from the weights.
- Explain arbitrage when it is asked.
- Comment on the limits of the theory.
Common mistakes in the exam
- Using the no-tax formula when tax is given.
- Forgetting the (1 − t) in the cost of equity formula.
- Using the debt value, not the tax shield, as the gain.
- Using the pre-tax cost of debt in the WACC check.
- Mixing the predictions of pecking order and trade-off.
- Saying MM claim the real world has no tax.
Quick revision
- Trade-off: optimum, positive link to profit. Pecking order: retained, debt, equity; negative link.
- Market timing: issue when over-valued. Agency: balance the agency costs.
- MM no tax: V and WACC constant; keG = keU + (D ÷ E)(keU − kd).
- MM with tax: VG = VU + Dt; WACC falls; (1 − t) in ke.
- Arbitrage keeps values equal.
- CAMA 2020: ss. 305, 308, 377(1), 378, 385.
Practice questions
These are original questions written in the style of the Institute of Chartered Accountants of Nigeria (ICAN) exam. Try each one before you open the answer. Full model answers follow the written questions.
Recall check: multiple choice
Recent ICAN papers are written, although older papers such as May 2014 included multiple-choice questions. These questions are for quick recall. The written questions that follow are closer to the exam.
Question 1. Static trade-off theory says there is:
- An optimal gearing
- No optimal gearing
- Only equity
- Only debt
Show the answer
A. Tax benefit against distress cost.
Question 2. The pecking order of finance is:
- Retained profit, debt, new equity
- Equity, debt, retained profit
- Debt, equity, retained profit
- Retained profit, equity, debt
Show the answer
A. Myers, 1984.
Question 3. Pecking order predicts profitability and gearing are:
- Negatively correlated
- Positively correlated
- Unrelated
- Equal
Show the answer
A. Profitable firms use retained profit.
Question 4. Market timing says issue shares when they are:
- Over-valued
- Under-valued
- Fairly valued only
- Never
Show the answer
A. Buy back when under-valued.
Question 5. MM without tax conclude that gearing:
- Does not change WACC or value
- Lowers WACC
- Raises value
- Is illegal
Show the answer
A. Cost of equity rises to offset.
Question 6. With tax, V_G equals:
- V_U + D × t
- V_U − D × t
- V_U × D
- D + E
Show the answer
A. The tax shield.
Question 7. The tax shield is:
- Debt times the tax rate
- Equity times tax
- Interest only
- Zero
Show the answer
A. Value of the interest relief.
Question 8. In the traditional view, WACC:
- Falls then rises with gearing
- Always rises
- Is constant
- Always falls
Show the answer
A. There is an optimum.
Question 9. Arbitrage brings two equivalent companies’ values:
- Equal
- Further apart
- To zero
- To double
Show the answer
A. Until the gain disappears.
Question 10. Which section of CAMA 2020 sets the director’s duty of care and skill?
- Section 308
- Section 400
- Section 405
- Section 409
Show the answer
A. Directors should test the assumptions behind a decision.
Written questions
Question 11 (10 marks). (a) Explain static trade-off theory and pecking order theory. (6 marks) (b) State how each predicts the link between profitability and gearing. (4 marks)
Question 12 (20 marks). An all-equity company is worth ₦300m with a cost of equity of 14%. It borrows ₦90m at 8% and buys back shares. Tax is 25%. (a) Using MM without tax, calculate value, WACC and cost of equity. (6 marks) (b) Using MM with tax, calculate value, WACC and cost of equity. (8 marks) (c) Explain why firms do not use 100% debt.
(3 marks) (d) State one difference between the pecking order and static trade-off theories. (3 marks)
Question 13 (10 marks). (a) Explain arbitrage in the MM context. (5 marks) (b) State four assumptions of MM without tax. (4 marks) (c) State why MM do not claim these hold. (1 mark)
Model answers
Show the model answer to Question 11
(a) Theories (6 marks). Static trade-off: there is an optimal gearing where the marginal tax benefit of debt equals the marginal cost of financial distress. (3) Pecking order: companies prefer retained profit, then debt, then new shares, so there is no optimal gearing. (3)
(b) Predictions (4 marks). Trade-off: positive link, because profitable firms can borrow more before distress costs matter. (2) Pecking order: negative link, because profitable firms fund investment from retained profit. (2)
Show the model answer to Question 12
(a) No tax (6 marks).
- Value stays ₦300m (debt 90, equity 210).
- WACC stays 14%. (3)
- keG = 14% + (90 ÷ 210)(14% − 8%) = 14% + 2.57% = 16.57%. (3)
(b) With tax (8 marks).
- VG = 300 + 90 × 0.25 = ₦322.5m
- equity = ₦232.5m. (3)
- WACCG = 14% × [1 − (0.25 × 90) ÷ 322.5] = 14% × 0.9302 = 13.02%. (2.5)
- keG = 14% + 0.75 × 6% × (90 ÷ 232.5) = 14% + 1.74% = 15.74%. (2.5)
(c) Not 100% debt (3 marks). Financial distress costs and higher interest rates rise at high gearing. (1.5) Lenders will not lend much more except at a high rate, and agency costs also rise. (1.5)
(d) Difference (3 marks). Static trade-off has an optimal gearing the company aims at, while the pecking order has none and gearing results from financing preferences. (3)
Show the model answer to Question 13
(a) Arbitrage (5 marks). If two companies with the same business risk and profit have different values because of gearing, shareholders can sell shares in the over-valued one and buy the under-valued one. (2) They use personal borrowing to keep their risk unchanged. (1.5) This continues until values are equal, so the gain disappears. (1.5)
(b) Assumptions (4 marks). Perfect capital markets; no tax; no bankruptcy risk; investors indifferent between personal borrowing and investing in geared companies. (1 each)
(c) Why not claimed (1 mark). The model is a simplification used to see the effect of each real-world factor. (1)
Pathfinder on Trade-off, pecking order, market timing, agency and MM propositions
These are the ICAN Pathfinder questions that test this topic. ICAN owns the questions and the suggested solutions, so we point you to them and do not copy them. Open your Pathfinder, attempt each question under exam conditions, then check your answer against the notes above.
The 15-mark question gave two identical companies that differ in capital structure and asked what an investor holding 4% of the geared company should do to improve income or keep it, and then the effect of a ₦50m loan on the cost of capital under MM with tax. The model answer uses V = V_U + Dt (₦280m + ₦62.5m × 30% = ₦298.75m against a market value of ₦312.5m), sells the overvalued geared shares, borrows personally and buys the other company’s shares. The examiners noted that fewer than 30% attempted it. Read the section on MM and arbitrage.
Revise first: Modigliani and Miller
Questions ask you to compare theories and their predictions. See the section on choosing how to finance an investment.
Revise first: Choosing how to finance an investment
Source: ICAN Pathfinder, Strategic Financial Management. Diets covered: May 2014 question 2.
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