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Explain what target and optimal capital structures mean

CFA® Level I · Corporate Finance · Capital Structure · CI.1.e

The idea

The static trade-off theory extends MM with taxes by recognising the expected costs of financial distress: V_L = V_U + tD - PV(costs of financial distress). As debt rises the tax shield adds value, but the probability and cost of distress rise too. The optimal capital structure is where the marginal tax benefit equals the marginal distress cost, which is also where the WACC is lowest and firm value highest. The target capital structure is the mix management aims to maintain over time; actual weights drift around it as market values move and financing is raised in lumps. Target weights are expressed as proportions of total capital, D/(D + E). Without a stated target, analysts use current market-value weights, trends or peer averages.

Formulas

Trade-off theory of capital structure

V_L = V_U + PV_shield − PV_distress

V_L
the value of the firm with debt
V_U
the value of the firm with no debt
PV_shield
the present value of the tax saved on interest
PV_distress
the present value of the costs of financial distress

Add debt until the extra tax saving is just matched by the extra expected distress cost; that point is the best mix.

A practice question

From the question bank, with the reason each wrong option is wrong.

A company's target capital structure is best described as the:

  1. mix management aims for over time - correct
  2. mix recorded on its latest balance sheetWhy not: The current book mix can drift away from the target as earnings are retained and debt is repaid.
  3. mix that has no debt at allWhy not: Most firms target some debt to benefit from the tax shield, so a zero-debt target is not the definition.

The target is the proportion of debt and equity management seeks to maintain, often chosen with the optimum in mind. Actual proportions fluctuate around it because of market value changes and the timing of financing.

A harder one

Under the static trade-off theory, the value of a levered firm is best expressed as:

  1. V_U + tD, with no deduction for distressWhy not: This is MM with taxes, which ignores distress costs and so implies all-debt financing.
  2. V_U + tD - PV(costs of financial distress) - correct
  3. V_U, whatever the level of debtWhy not: This is MM without taxes, which ignores both the tax shield and distress costs.

The trade-off theory starts from MM with taxes and subtracts the present value of expected financial distress costs. Value rises with debt while the marginal tax benefit exceeds the marginal distress cost, then falls.

The hardest tier

An unlevered firm is worth 1,000 and faces a 25% tax rate. The present value of financial distress costs is 5 at debt of 100, 20 at debt of 200 and 50 at debt of 300. Under the static trade-off theory, the value-maximising debt level is:

  1. 200 - correct
  2. 300Why not: Choosing the largest tax shield ignores that distress costs rise faster than the shield beyond 200.
  3. 100Why not: Minimising distress costs gives up tax shield value that exceeds the extra cost at 200.

V_L = V_U + tD - PV(distress): 1,000 + 25 - 5 = 1,020 at 100; 1,000 + 50 - 20 = 1,030 at 200; 1,000 + 75 - 50 = 1,025 at 300. Value peaks at 1,030 with debt of 200.

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