**Question 69** interest tax shield, capital structure, leverage, WACC

Which statement about risk, required return and capital structure is the most correct?

Your friend just bought a house for $400,000. He financed it using a $320,000 mortgage loan and a deposit of $80,000.

In the context of residential housing and mortgages, the 'equity' tied up in the value of a person's house is the value of the house less the value of the mortgage. So the initial equity your friend has in his house is $80,000. Let this amount be E, let the value of the mortgage be D and the value of the house be V. So ##V=D+E##.

If house prices suddenly fall by **10**%, what would be your friend's percentage change in equity (E)? Assume that the value of the mortgage is unchanged and that no income (rent) was received from the house during the short time over which house prices fell.

Remember:

### r_{0\rightarrow1}=\frac{p_1-p_0+c_1}{p_0} ###

where ##r_{0-1}## is the return (percentage change) of an asset with price ##p_0## initially, ##p_1## one period later, and paying a cash flow of ##c_1## at time ##t=1##.

A firm has a debt-to-assets ratio of 50%. The firm then issues a large amount of debt to raise money for new projects of similar market risk to the company's existing projects. Assume a classical tax system. Which statement is correct?

**Question 121** capital structure, leverage, financial distress, interest tax shield

Fill in the missing words in the following sentence:

All things remaining equal, as a firm's amount of debt funding falls, benefits of interest tax shields __________ and the costs of financial distress __________.

A company increases the proportion of debt funding it uses to finance its assets by issuing bonds and using the cash to repurchase stock, leaving assets unchanged.

Ignoring the costs of financial distress, which of the following statements is **NOT** correct:

**Question 241** Miller and Modigliani, leverage, payout policy, diversification, NPV

One of Miller and Modigliani's (M&M's) important insights is that a firm's managers should not try to achieve a particular level of leverage or interest tax shields under certain assumptions. So the firm's capital structure is irrelevant. This is because investors can make their own *personal* leverage and interest tax shields, so there's no need for managers to try to make *corporate* leverage and interest tax shields. This is true under the assumptions of equal tax rates, interest rates and debt availability for the person and the corporation, no transaction costs and symmetric information.

This principal of 'home-made' or 'do-it-yourself' leverage can also be applied to other topics. Read the following statements to decide which are true:

(I) Payout policy: a firm's managers should not try to achieve a particular pattern of equity payout.

(II) Agency costs: a firm's managers should not try to minimise agency costs.

(III) Diversification: a firm's managers should not try to diversify across industries.

(IV) Shareholder wealth: a firm's managers should not try to maximise shareholders' wealth.

Which of the above statement(s) are true?

Your friend just bought a house for $**1,000,000**. He financed it using a $**900,000** mortgage loan and a deposit of $**100,000**.

In the context of residential housing and mortgages, the 'equity' or 'net wealth' tied up in a house is the value of the house less the value of the mortgage loan. Assuming that your friend's only asset is his house, his net wealth is $100,000.

If house prices suddenly fall by **15%**, what would be your friend's percentage change in net wealth?

Assume that:

- No income (rent) was received from the house during the short time over which house prices fell.
- Your friend will not declare bankruptcy, he will always pay off his debts.

**Question 337** capital structure, interest tax shield, leverage, real and nominal returns and cash flows, multi stage growth model

A fast-growing firm is suitable for valuation using a multi-stage growth model.

It's **nominal** unlevered cash flow from assets (##CFFA_U##) at the end of this year (**t=1**) is expected to be $**1** million. After that it is expected to grow at a rate of:

**12**% pa for the next two years (from t=1 to 3),**5**% over the fourth year (from t=3 to 4), and**-1**% forever after that (from t=4 onwards). Note that this is a negative one percent growth rate.

Assume that:

- The nominal WACC
**after**tax is**9.5**% pa and is not expected to change. - The nominal WACC
**before**tax is**10**% pa and is not expected to change. - The firm has a target debt-to-
**equity**ratio that it plans to maintain. - The inflation rate is
**3**% pa. - All rates are given as
**nominal**effective annual rates.

What is the levered value of this fast growing firm's assets?

**Question 397** financial distress, leverage, capital structure, NPV

A levered firm has a market value of assets of $**10**m. Its debt is all comprised of zero-coupon bonds which mature in one year and have a combined face value of $**9.9**m.

Investors are risk-neutral and therefore all debt and equity holders demand the same required return of **10**% pa.

Therefore the current market capitalisation of debt ##(D_0)## is $**9**m and equity ##(E_0)## is $**1**m.

A new project presents itself which requires an investment of $**2**m and will provide a:

- $
**6.6**m cash flow with probability 0.5 in the good state of the world, and a **-**$**4.4**m (notice the negative sign) cash flow with probability 0.5 in the bad state of the world.

The project can be funded using the company's excess cash, no debt or equity raisings are required.

What would be the new market capitalisation of equity ##(E_\text{0, with project})## if shareholders vote to proceed with the project, and therefore should shareholders proceed with the project?

**Question 398** financial distress, capital raising, leverage, capital structure, NPV

A levered firm has zero-coupon bonds which mature in one year and have a combined face value of $**9.9**m.

Investors are risk-neutral and therefore all debt and equity holders demand the same required return of **10**% pa.

In one year the firm's assets will be worth:

- $
**13.2**m with probability 0.5 in the good state of the world, or - $
**6.6**m with probability 0.5 in the bad state of the world.

A new project presents itself which requires an investment of $**2**m and will provide a certain cash flow of $**3.3**m in one year.

The firm doesn't have any excess cash to make the initial $2m investment, but the funds can be raised from shareholders through a fairly priced rights issue. Ignore all transaction costs.

Should shareholders vote to proceed with the project and equity raising? What will be the gain in shareholder **wealth** if they decide to proceed?

One year ago you bought $**100,000** of shares partly funded using a margin loan. The margin loan size was $**70,000** and the other $**30,000** was your own wealth or 'equity' in the share assets.

The interest rate on the margin loan was **7.84**% pa.

Over the year, the shares produced a dividend yield of **4**% pa and a capital gain of **5**% pa.

What was the **total** return on your **wealth**? Ignore taxes, assume that all cash flows (interest payments and dividends) were paid and received at the end of the year, and all rates above are effective annual rates.

Hint: Remember that wealth in this context is your equity (E) in the house asset (V = D+E) which is funded by the loan (D) and your deposit or equity (E).

**Question 408** leverage, portfolio beta, portfolio risk, real estate, CAPM

You just bought a house worth $**1,000,000**. You financed it with an $**800,000** mortgage loan and a deposit of $**200,000**.

You estimate that:

- The house has a beta of
**1**; - The mortgage loan has a beta of
**0.2**.

What is the beta of the equity (the $200,000 deposit) that you have in your house?

Also, if the risk free rate is **5**% pa and the market portfolio's return is **10**% pa, what is the expected return on equity in your house? Ignore taxes, assume that all cash flows (interest payments and rent) were paid and received at the end of the year, and all rates are effective annual rates.

A firm has a debt-to-equity ratio of 25%. What is its debt-to-assets ratio?

A firm has a debt-to-equity ratio of 60%. What is its debt-to-assets ratio?

**Question 536** idiom, bond pricing, capital structure, leverage

The expression 'my word is my bond' is often used in everyday language to make a serious promise.

Why do you think this expression uses the metaphor of a bond rather than a share?

A firm has a debt-to-assets ratio of **20**%. What is its debt-to-**equity** ratio?

**Question 772** interest tax shield, capital structure, leverage

A firm issues debt and uses the funds to buy back equity. Assume that there are no costs of financial distress or transactions costs. Which of the following statements about interest tax shields is **NOT** correct?

One year ago you bought a $**1,000,000** house partly funded using a mortgage loan. The loan size was $**800,000** and the other $**200,000** was your wealth or 'equity' in the house asset.

The interest rate on the home loan was **4**% pa.

Over the year, the house produced a net rental yield of **2**% pa and a capital gain of **2.5**% pa.

Assuming that all cash flows (interest payments and net rental payments) were paid and received at the end of the year, and all rates are given as effective annual rates, what was the **total** return on your **wealth** over the past year?

Hint: Remember that wealth in this context is your equity (E) in the house asset (V = D+E) which is funded by the loan (D) and your deposit or equity (E).

In the home loan market, the acronym LVR stands for Loan to Valuation Ratio. If you bought a house worth one million dollars, partly funded by an $800,000 home loan, then your LVR was 80%. The LVR is equivalent to which of the following ratios?

**Question 800** leverage, portfolio return, risk, portfolio risk, capital structure, no explanation

Which of the following assets would you expect to have the highest required rate of return? All values are current market values.

**Question 801** negative gearing, leverage, capital structure, no explanation

The following steps set out the process of ‘negative gearing’ an investment property in Australia. Which of these steps or statements is **NOT** correct? To successfully achieve negative gearing on an investment property:

**Question 802** negative gearing, leverage, capital structure, no explanation

Which of the following statements about ‘negative gearing’ is **NOT** correct?

**Question 941** negative gearing, leverage, capital structure, interest tax shield, real estate

Last year, two friends Lev and Nolev each bought similar investment properties for $**1 million**. Both earned net rents of $**30,000** pa over the past year. They funded their purchases in different ways:

- Lev used $200,000 of his own money and borrowed $
**800,000**from the bank in the form of an interest-only loan with an interest rate of**5**% pa. - Nolev used $1,000,000 of his own money, he has no mortgage loan on his property.

Both Lev and Nolev also work in high-paying jobs and are subject personal marginal tax rates of **45**%.

Which of the below statements about the past year is **NOT** correct?

**Question 959** negative gearing, leverage, capital structure, interest tax shield, real estate

Last year, two friends Gear and Nogear invested in residential apartments. Each invested $1 million of their own money (their net wealth).

Apartments cost $1,000,000 last year and they earned net rents of $30,000 pa over the last year. Net rents are calculated as rent revenues less the costs of renting such as property maintenance, land tax and council rates. However, interest expense and personal income taxes are not deducted from net rents.

Gear and Nogear funded their purchases in different ways:

- Gear used $
**1,000,000**of her own money and borrowed $**4,000,000**from the bank in the form of an interest-only loan with an interest rate of**5**% pa to buy**5**apartments. - Nogear used $
**1,000,000**of his own money to buy one apartment. He has no mortgage loan on his property.

Both Gear and Nogear also work in high-paying jobs and are subject personal marginal tax rates of **45**%.

Which of the below statements about the past year is **NOT** correct?