Chapter 47: Capital Structure, Payout, and Corporate Finance. The Encyclopedia of Economic Principals, interactive companion

Every example here is a constructed teaching example: it uses the hypothetical numbers of the chapter's worked examples, plus a few values added for comparison and labelled as such in each panel. Nothing here measures a real market, firm or household.

Demonstration 1 of 4

When equity is too expensive to issue

Why would managers turn down a positive NPV project if it must be paid for with new shares?

Selling underpriced shares hands value to new investors. When that transfer exceeds the project's NPV, old shareholders lose. Internal cash and safe debt avoid the transfer, which is why they rank ahead of equity.

$Equation, written in LaTeX: 12-10=2\text{ million dollars}.$

$Equation, written in LaTeX: \frac{10}{0.75}=13.333\ldots\text{ million dollars}.$

$Equation, written in LaTeX: 13.333-10=3.333\text{ million dollars}.$

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The project costs 10 million dollars and is worth 12 million. Outsiders pay a price per dollar of the firm's true equity value; at 0.75 they pay 75 cents per dollar. The transfer is the true value handed to new holders above what they pay.

Predict first. Above what outsider price does the equity-funded project become acceptable to old shareholders?

Your prediction About 0.83 0.75 Only 1.00

Price outsiders pay per dollar of true value

Funding source

Figure: When equity is too expensive to issue. Bars for project NPV 2.00, transfer 3.33 and old holders' net -1.33 million when the project is funded with new equity at an outsider price of 0.75. — Price outsiders pay per dollar of true value: 0.75, Funding source: New equity
Constructed example: the chapter's hypothetical project (cost 10, value 12, price 0.75, retained cash and safe debt); outsider prices of 0.85, 0.90 and 1.00 are added.

Project NPV: 2.00
Claims sold (true value): 13.33
Transfer to new holders: 3.33
Old holders' net: -1.33
Old shareholders: reject

NPV = 12 - 10 = 2.00. Outsiders pay 0.75 per dollar of true value, so raising 10 million means selling claims worth 10 / 0.75 = 13.33 million. The transfer is 13.33 - 10 = 3.33, and old holders net 2.00 - 3.33 = -1.33, so they reject the project. Break-even price: 10 / 12 = 0.83.

Worked steps

NPV = 12 - 10 = 2.00
Claims = 10 / 0.75 = 13.33
Transfer = 13.33 - 10 = 3.33
Net = 2.00 - 3.33 = -1.33: reject

Use the idea

Before issuing stock for a project, compare the project's NPV with the discount you think the market applies to your shares.

Where the conclusion applies

Managers act for existing shareholders, the discount comes only from outsiders' missing information, and safe debt is fairly priced. Large distress costs on debt can reverse the order.

Check your understanding: If the outsider price were 0.85, would managers issue equity for the project?

10 / 0.85 = 11.76, so the transfer is 1.76 < 2 and the net is +0.24: yes.

Chapter 47 source: section "Pecking-order theory".

Demonstration 2 of 4

Finding the debt target at the margin

Should the firm take on a second slice of debt?

Debt is worth adding while its marginal tax benefit exceeds its marginal expected distress cost. The target is where that margin turns negative, not where total value is still above the debt-free figure.

$Equation, written in LaTeX: 100+5-1=104\text{ million dollars}.$

$Equation, written in LaTeX: 104+4-6=102\text{ million dollars}.$

$Equation, written in LaTeX: 104+4-2=106\text{ million dollars}.$

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The debt-free firm is worth 100 million dollars. Each debt increment adds a present value of tax benefits and a present value of expected distress costs.

Predict first. With the book's tax benefit of 4, which distress cost makes the second increment exactly break even?

Your prediction 4 2 6

Expected distress cost of second increment

Tax benefit of second increment

Figure: Finding the debt target at the margin. Firm value at no debt, one and two increments: 100, 104 and 102 million, with the target at one increment. — Expected distress cost of second increment: 6, Tax benefit of second increment: 4
Constructed example: the chapter's hypothetical firm (100, first slice 5 and 1, second slice 4 and 6, guarantee case 2); distress costs of 4 and 8 and tax benefits of 2 and 6 are added.

Value with no debt: 100
Value after one increment: 104
Value after two increments: 102
Change from the second increment: -2
Debt target: one increment

V1 = 100 + 5 - 1 = 104. V2 = 104 + 4 - 6 = 102, a change of -2. The second increment destroys value, so the target is one increment.

Worked steps

V1 = 100 + 5 - 1 = 104
V2 = 104 + 4 - 6 = 102
Marginal effect = 4 - 6 = -2
Target: one increment

Use the idea

Value each extra slice of borrowing on its own: list its tax saving and the extra distress cost it brings, and stop when the second outweighs the first.

Where the conclusion applies

Tax benefits and distress costs are known present values and debt comes in two fixed slices. Agency costs, issue costs and information problems are ignored.

Check your understanding: With tax benefit 6 and distress cost 6, does the target move?

104 + 6 - 6 = 104, so the firm is indifferent between one and two increments.

Chapter 47 source: section "Trade-off theory of capital structure".

Demonstration 3 of 4

Leverage raises the equity return, not firm value

If borrowing raises the return on equity, why does it not raise the value of the firm?

The assets produce 8 million whatever the financing. Debt takes a fixed slice, so the residual is spread over a smaller equity claim and its percentage return rises with risk, while the weighted return stays at 8 percent.

$Equation, written in LaTeX: r_E=8\%+\frac{50}{50}(8\%-4\%)=12\%.$

$Equation, written in LaTeX: \frac{50}{100}(12\%)+\frac{50}{100}(4\%)=8\%.$

$Equation, written in LaTeX: r_E=8\%+3(8\%-4\%)=20\%.$

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The firm is worth 100 million dollars and its assets earn r_A = 8 percent, 8 million a year. D is debt, E = 100 - D is equity, r_D the debt return and r_E the equity return.

Predict first. What equity return does debt of 75 give at a 4 percent debt return?

Your prediction 20% 12% 16%

Debt (million dollars)

Debt return

Figure: Leverage raises the equity return, not firm value. Left: 8 million of income split into debt and equity income at each debt level. Right: equity return rising with D/E; at debt 50 it is 12.00% while the weighted return stays 8.00%. — Debt (million dollars): 50, Debt return: 4%
Constructed example: the chapter's hypothetical firm (value 100, r_A 8%, r_D 4%, debt 0, 50 and 75); debt of 25 and debt returns of 3% and 5% are added.

D/E: 1.00
Equity return: 12.00%
Debt income: 2.00
Equity income: 6.00
WACC: 8.00%

With debt 50 and equity 50, D/E = 50/50 = 1.00. r_E = 8% + 1.00(8% - 4%) = 12.00%. Creditors get 4% x 50 = 2.00, equity gets 8 - 2.00 = 6.00. The weighted return stays 8.00%: leverage shifts the split, not the total.

Worked steps

D/E = 50 / 50 = 1.00
r_E = 8% + 1.00 x (8% - 4%) = 12.00%
Debt income = 0.04 x 50 = 2.00; equity income = 8 - 2.00 = 6.00
WACC = (50/100)(12.00%) + (50/100)(4%) = 8.00%

Use the idea

Do not judge a recapitalization by the higher return on equity; ask whether total cash flows or taxes change.

Where the conclusion applies

No taxes, no distress costs, a fixed debt return by stipulation and unchanged operating assets. Risky debt that demands more would change both returns.

Check your understanding: With debt 25 and r_D = 4%, what is r_E?

D/E = 25/75 = 1/3, so r_E = 8% + (1/3)(4%) = 9.33%; equity income 8 - 1 = 7, and 7/75 = 9.33%.

Chapter 47 source: section "Modigliani-Miller leverage proposition".

Demonstration 4 of 4

NPV of a machine and the reversal

How much lower cash flow or higher discount rate does it take to reverse the machine purchase?

NPV compares discounted incremental cash with the capital it displaces. Lower cash flows or a higher rate shrink the present value until it no longer covers the cost.

$Equation, written in LaTeX: PV=\sum_{t=1}^{4}\frac{350{,}000}{1.10^t} +\frac{100{,}000}{1.10^4} \approx1{,}177{,}754.25\text{ dollars}.$

$Equation, written in LaTeX: NPV\approx1{,}177{,}754.25-1{,}000{,}000 =177{,}754.25\text{ dollars}.$

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The machine costs 1,000,000 dollars today, returns an annual cash flow at the end of years 1 to 4 and 100,000 dollars of salvage at year 4. r is the risk-adjusted discount rate.

Predict first. Does the project survive at 280,000 per year and 10 percent?

Your prediction No, NPV is negative Yes, NPV is still positive

Annual cash flow (dollars)

Discount rate

Figure: NPV of a machine and the reversal. Discounted cash flows for years 1 to 4 and the cumulative present value, which ends at 1,177,754.25 against the 1,000,000 cost line; NPV 177,754.25, accept. — Annual cash flow (dollars): 350,000, Discount rate: 10%
Constructed example: the chapter's hypothetical machine (cost 1,000,000, 350,000 or 280,000 a year, salvage 100,000, 10%); a cash flow of 315,000 and rates of 8%, 12% and 14% are added.

Present value: 1,177,754.25
NPV: 177,754.25
Decision: accept
Annuity factor: 3.1699

The annuity factor at 10% for 4 years is 3.169865446, so the operating flows are worth 350,000 x 3.169865446 = 1,109,452.906. Salvage is worth 100,000 / 1.10^4 = 68,301.346. PV = 1,177,754.25 and NPV = 1,177,754.25 - 1,000,000 = 177,754.25, so accept.

Worked steps

Annuity factor = (1 - 1.10^-4) / 0.10 = 3.169865446
350,000 x 3.169865446 = 1,109,452.906
100,000 / 1.10^4 = 68,301.346
PV = 1,109,452.906 + 68,301.346 = 1,177,754.25
NPV = 1,177,754.25 - 1,000,000 = 177,754.25: accept

Use the idea

List after-tax incremental cash by date, discount at a rate that fits the project's risk, and accept only if the sum beats the outlay.

Where the conclusion applies

Cash flows are known, arrive at year ends and are discounted at one constant rate. The option to wait or abandon is not valued here.

Check your understanding: At 350,000 per year and 14%, accept or reject?

Annuity factor 2.913712: 350,000 x 2.913712 = 1,019,799 plus 100,000 / 1.14^4 = 59,208 gives PV 1,079,007 and NPV 79,007, so accept.

Chapter 47 source: section "Capital Budgeting, NPV, and Real Options".

When equity is too expensive to issue

Choose an example

Calculated values

Worked steps

Use the idea

Where the conclusion applies

Finding the debt target at the margin

Choose an example

Calculated values

Worked steps

Use the idea

Where the conclusion applies

Leverage raises the equity return, not firm value

Choose an example

Calculated values

Worked steps

Use the idea

Where the conclusion applies

NPV of a machine and the reversal

Choose an example

Calculated values

Worked steps

Use the idea

Where the conclusion applies