# Fight Finance

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One formula for calculating a levered firm's free cash flow (FFCF, or CFFA) is to use earnings before interest and tax (EBIT).

\begin{aligned} FFCF &= (EBIT)(1-t_c) + Depr - CapEx -\Delta NWC + IntExp.t_c \\ &= (Rev - COGS - Depr - FC)(1-t_c) + Depr - CapEx -\Delta NWC + IntExp.t_c \\ \end{aligned} \\
Does this annual FFCF or the annual interest tax shield?

One method for calculating a firm's free cash flow (FFCF, or CFFA) is to ignore interest expense. That is, pretend that interest expense $(IntExp)$ is zero:

\begin{aligned} FFCF &= (Rev - COGS - Depr - FC - IntExp)(1-t_c) + Depr - CapEx -\Delta NWC + IntExp \\ &= (Rev - COGS - Depr - FC - 0)(1-t_c) + Depr - CapEx -\Delta NWC - 0\\ \end{aligned}
Does this annual FFCF with zero interest expense or the annual interest tax shield?

A method commonly seen in textbooks for calculating a levered firm's free cash flow (FFCF, or CFFA) is the following:

\begin{aligned} FFCF &= (Rev - COGS - Depr - FC - IntExp)(1-t_c) + \\ &\space\space\space+ Depr - CapEx -\Delta NWC + IntExp(1-t_c) \\ \end{aligned}
Does this annual FFCF or the annual interest tax shield?

There are many ways to calculate a firm's free cash flow (FFCF), also called cash flow from assets (CFFA). Some include the annual interest tax shield in the cash flow and some do not.

Which of the below FFCF formulas include the interest tax shield in the cash flow?

$$(1) \quad FFCF=NI + Depr - CapEx -ΔNWC + IntExp$$ $$(2) \quad FFCF=NI + Depr - CapEx -ΔNWC + IntExp.(1-t_c)$$ $$(3) \quad FFCF=EBIT.(1-t_c )+ Depr- CapEx -ΔNWC+IntExp.t_c$$ $$(4) \quad FFCF=EBIT.(1-t_c) + Depr- CapEx -ΔNWC$$ $$(5) \quad FFCF=EBITDA.(1-t_c )+Depr.t_c- CapEx -ΔNWC+IntExp.t_c$$ $$(6) \quad FFCF=EBITDA.(1-t_c )+Depr.t_c- CapEx -ΔNWC$$ $$(7) \quad FFCF=EBIT-Tax + Depr - CapEx -ΔNWC$$ $$(8) \quad FFCF=EBIT-Tax + Depr - CapEx -ΔNWC-IntExp.t_c$$ $$(9) \quad FFCF=EBITDA-Tax - CapEx -ΔNWC$$ $$(10) \quad FFCF=EBITDA-Tax - CapEx -ΔNWC-IntExp.t_c$$

The formulas for net income (NI also called earnings), EBIT and EBITDA are given below. Assume that depreciation and amortisation are both represented by 'Depr' and that 'FC' represents fixed costs such as rent.

$$NI=(Rev - COGS - Depr - FC - IntExp).(1-t_c )$$ $$EBIT=Rev - COGS - FC-Depr$$ $$EBITDA=Rev - COGS - FC$$ $$Tax =(Rev - COGS - Depr - FC - IntExp).t_c= \dfrac{NI.t_c}{1-t_c}$$

Here are the Net Income (NI) and Cash Flow From Assets (CFFA) equations:

$$NI=(Rev-COGS-FC-Depr-IntExp).(1-t_c)$$

$$CFFA=NI+Depr-CapEx - \varDelta NWC+IntExp$$

What is the formula for calculating annual interest expense (IntExp) which is used in the equations above?

Select one of the following answers. Note that D is the value of debt which is constant through time, and $r_D$ is the cost of debt.

 Project Data Project life 2 yrs Initial investment in equipment $600k Depreciation of equipment per year$250k Expected sale price of equipment at end of project $200k Revenue per job$12k Variable cost per job $4k Quantity of jobs per year 120 Fixed costs per year, paid at the end of each year$100k Interest expense in first year (at t=1) $16.091k Interest expense in second year (at t=2)$9.711k Tax rate 30% Government treasury bond yield 5% Bank loan debt yield 6% Levered cost of equity 12.5% Market portfolio return 10% Beta of assets 1.24 Beta of levered equity 1.5 Firm's and project's debt-to-equity ratio 25%

Notes

1. The project will require an immediate purchase of $50k of inventory, which will all be sold at cost when the project ends. Current liabilities are negligible so they can be ignored. Assumptions • The debt-to-equity ratio will be kept constant throughout the life of the project. The amount of interest expense at the end of each period has been correctly calculated to maintain this constant debt-to-equity ratio. Note that interest expense is different in each year. • Thousands are represented by 'k' (kilo). • All cash flows occur at the start or end of the year as appropriate, not in the middle or throughout the year. • All rates and cash flows are nominal. The inflation rate is 2% pa. • All rates are given as effective annual rates. • The 50% capital gains tax discount is not available since the project is undertaken by a firm, not an individual. What is the net present value (NPV) of the project? A manufacturing company is considering a new project in the more risky services industry. The cash flows from assets (CFFA) are estimated for the new project, with interest expense excluded from the calculations. To get the levered value of the project, what should these unlevered cash flows be discounted by? Assume that the manufacturing firm has a target debt-to-assets ratio that it sticks to. A retail furniture company buys furniture wholesale and distributes it through its retail stores. The owner believes that she has some good ideas for making stylish new furniture. She is considering a project to buy a factory and employ workers to manufacture the new furniture she's designed. Furniture manufacturing has more systematic risk than furniture retailing. Her furniture retailing firm's after-tax WACC is 20%. Furniture manufacturing firms have an after-tax WACC of 30%. Both firms are optimally geared. Assume a classical tax system. Which method(s) will give the correct valuation of the new furniture-making project? Select the most correct answer. The US firm Google operates in the online advertising business. In 2011 Google bought Motorola Mobility which manufactures mobile phones. Assume the following: • Google had a 10% after-tax weighted average cost of capital (WACC) before it bought Motorola. • Motorola had a 20% after-tax WACC before it merged with Google. • Google and Motorola have the same level of gearing. • Both companies operate in a classical tax system. You are a manager at Motorola. You must value a project for making mobile phones. Which method(s) will give the correct valuation of the mobile phone manufacturing project? Select the most correct answer. The mobile phone manufacturing project's: Find Candys Corporation's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.  Candys Corp Income Statement for year ending 30th June 2013$m Sales 200 COGS 50 Operating expense 10 Depreciation 20 Interest expense 10 Income before tax 110 Tax at 30% 33 Net income 77
 Candys Corp Balance Sheet as at 30th June 2013 2012 $m$m Assets Current assets 220 180 PPE Cost 300 340 Accumul. depr. 60 40 Carrying amount 240 300 Total assets 460 480 Liabilities Current liabilities 175 190 Non-current liabilities 135 130 Owners' equity Retained earnings 50 60 Contributed equity 100 100 Total L and OE 460 480

Note: all figures are given in millions of dollars ($m). Why is Capital Expenditure (CapEx) subtracted in the Cash Flow From Assets (CFFA) formula? $$CFFA=NI+Depr-CapEx - \Delta NWC+IntExp$$ Find Trademark Corporation's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.  Trademark Corp Income Statement for year ending 30th June 2013$m Sales 100 COGS 25 Operating expense 5 Depreciation 20 Interest expense 20 Income before tax 30 Tax at 30% 9 Net income 21
 Trademark Corp Balance Sheet as at 30th June 2013 2012 $m$m Assets Current assets 120 80 PPE Cost 150 140 Accumul. depr. 60 40 Carrying amount 90 100 Total assets 210 180 Liabilities Current liabilities 75 65 Non-current liabilities 75 55 Owners' equity Retained earnings 10 10 Contributed equity 50 50 Total L and OE 210 180

Note: all figures are given in millions of dollars ($m). Interest expense (IntExp) is an important part of a company's income statement (or 'profit and loss' or 'statement of financial performance'). How does an accountant calculate the annual interest expense of a fixed-coupon bond that has a liquid secondary market? Select the most correct answer: Annual interest expense is equal to: Which one of the following will increase the Cash Flow From Assets in this year for a tax-paying firm, all else remaining constant? Cash Flow From Assets (CFFA) can be defined as: A firm has forecast its Cash Flow From Assets (CFFA) for this year and management is worried that it is too low. Which one of the following actions will lead to a higher CFFA for this year (t=0 to 1)? Only consider cash flows this year. Do not consider cash flows after one year, or the change in the NPV of the firm. Consider each action in isolation. 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: Value the following business project to manufacture a new product.  Project Data Project life 2 yrs Initial investment in equipment$6m Depreciation of equipment per year $3m Expected sale price of equipment at end of project$0.6m Unit sales per year 4m Sale price per unit $8 Variable cost per unit$5 Fixed costs per year, paid at the end of each year $1m Interest expense per year 0 Tax rate 30% Weighted average cost of capital after tax per annum 10% Notes 1. The firm's current assets and current liabilities are$3m and $2m respectively right now. This net working capital will not be used in this project, it will be used in other unrelated projects. Due to the project, current assets (mostly inventory) will grow by$2m initially (at t = 0), and then by $0.2m at the end of the first year (t=1). Current liabilities (mostly trade creditors) will increase by$0.1m at the end of the first year (t=1).
At the end of the project, the net working capital accumulated due to the project can be sold for the same price that it was bought.
2. The project cost $0.5m to research which was incurred one year ago. Assumptions • All cash flows occur at the start or end of the year as appropriate, not in the middle or throughout the year. • All rates and cash flows are real. The inflation rate is 3% pa. • All rates are given as effective annual rates. • The business considering the project is run as a 'sole tradership' (run by an individual without a company) and is therefore eligible for a 50% capital gains tax discount when the equipment is sold, as permitted by the Australian Tax Office. What is the expected net present value (NPV) of the project? Find Scubar Corporation's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.  Scubar Corp Income Statement for year ending 30th June 2013$m Sales 200 COGS 60 Depreciation 20 Rent expense 11 Interest expense 19 Taxable Income 90 Taxes at 30% 27 Net income 63
 Scubar Corp Balance Sheet as at 30th June 2013 2012 $m$m Inventory 60 50 Trade debtors 19 6 Rent paid in advance 3 2 PPE 420 400 Total assets 502 458 Trade creditors 10 8 Bond liabilities 200 190 Contributed equity 130 130 Retained profits 162 130 Total L and OE 502 458

Note: All figures are given in millions of dollars ($m). The cash flow from assets was: A new company's Firm Free Cash Flow (FFCF, same as CFFA) is forecast in the graph below. To value the firm's assets, the terminal value needs to be calculated using the perpetuity with growth formula: $$V_{\text{terminal, }t-1} = \dfrac{FFCF_{\text{terminal, }t}}{r-g}$$ Which point corresponds to the best time to calculate the terminal value? Which one of the following will decrease net income (NI) but increase cash flow from assets (CFFA) in this year for a tax-paying firm, all else remaining constant? Remember: $$NI=(Rev-COGS-FC-Depr-IntExp).(1-t_c )$$ $$CFFA=NI+Depr-CapEx - ΔNWC+IntExp$$ An old company's Firm Free Cash Flow (FFCF, same as CFFA) is forecast in the graph below. To value the firm's assets, the terminal value needs to be calculated using the perpetuity with growth formula: $$V_{\text{terminal, }t-1} = \dfrac{FFCF_{\text{terminal, }t}}{r-g}$$ Which point corresponds to the best time to calculate the terminal value? A new company's Firm Free Cash Flow (FFCF, same as CFFA) is forecast in the graph below. To value the firm's assets, the terminal value needs to be calculated using the perpetuity with growth formula: $$V_{\text{terminal, }t-1} = \dfrac{FFCF_{\text{terminal, }t}}{r-g}$$ Which point corresponds to the best time to calculate the terminal value? Which one of the following will decrease net income (NI) but increase cash flow from assets (CFFA) in this year for a tax-paying firm, all else remaining constant? Remember: $$NI = (Rev-COGS-FC-Depr-IntExp).(1-t_c )$$ $$CFFA=NI+Depr-CapEx - \Delta NWC+IntExp$$ Over the next year, the management of an unlevered company plans to: • Achieve firm free cash flow (FFCF or CFFA) of$1m.
• Pay dividends of $1.8m • Complete a$1.3m share buy-back.
• Spend $0.8m on new buildings without buying or selling any other fixed assets. This capital expenditure is included in the CFFA figure quoted above. Assume that: • All amounts are received and paid at the end of the year so you can ignore the time value of money. • The firm has sufficient retained profits to pay the dividend and complete the buy back. • The firm plans to run a very tight ship, with no excess cash above operating requirements currently or over the next year. How much new equity financing will the company need? In other words, what is the value of new shares that will need to be issued? Which one of the following will have no effect on net income (NI) but decrease cash flow from assets (CFFA or FFCF) in this year for a tax-paying firm, all else remaining constant? Remember: $$NI=(Rev-COGS-FC-Depr-IntExp).(1-t_c )$$ $$CFFA=NI+Depr-CapEx - ΔNWC+IntExp$$ Over the next year, the management of an unlevered company plans to: • Make$5m in sales, $1.9m in net income and$2m in equity free cash flow (EFCF).
• Pay dividends of $1m. • Complete a$1.3m share buy-back.

Assume that:

• All amounts are received and paid at the end of the year so you can ignore the time value of money.
• The firm has sufficient retained profits to legally pay the dividend and complete the buy back.
• The firm plans to run a very tight ship, with no excess cash above operating requirements currently or over the next year.

How much new equity financing will the company need? In other words, what is the value of new shares that will need to be issued?

Your friend is trying to find the net present value of a project. The project is expected to last for just one year with:

• a negative cash flow of -$1 million initially (t=0), and • a positive cash flow of$1.1 million in one year (t=1).

The project has a total required return of 10% pa due to its moderate level of undiversifiable risk.

Your friend is aware of the importance of opportunity costs and the time value of money, but he is unsure of how to find the NPV of the project.

He knows that the opportunity cost of investing the $1m in the project is the expected gain from investing the money in shares instead. Like the project, shares also have an expected return of 10% since they have moderate undiversifiable risk. This opportunity cost is$0.1m $(=1m \times 10\%)$ which occurs in one year (t=1).

He knows that the time value of money should be accounted for, and this can be done by finding the present value of the cash flows in one year.

Your friend has listed a few different ways to find the NPV which are written down below.

(I) $-1m + \dfrac{1.1m}{(1+0.1)^1}$

(II) $-1m + \dfrac{1.1m}{(1+0.1)^1} - \dfrac{1m}{(1+0.1)^1} \times 0.1$

(III) $-1m + \dfrac{1.1m}{(1+0.1)^1} - \dfrac{1.1m}{(1+0.1)^1} \times 0.1$

(IV) $-1m + 1.1m - \dfrac{1.1m}{(1+0.1)^1} \times 0.1$

(V) $-1m + 1.1m - 1.1m \times 0.1$

Which of the above calculations give the correct NPV? Select the most correct answer.

The following equation is called the Dividend Discount Model (DDM), Gordon Growth Model or the perpetuity with growth formula: $$P_0 = \frac{ C_1 }{ r - g }$$

What is $g$? The value $g$ is the long term expected:

For a price of $13, Carla will sell you a share which will pay a dividend of$1 in one year and every year after that forever. The required return of the stock is 10% pa.

Would you like to Carla's share or politely ?

For a price of $6, Carlos will sell you a share which will pay a dividend of$1 in one year and every year after that forever. The required return of the stock is 10% pa.

Would you like to his share or politely ?

For a price of $102, Andrea will sell you a share which just paid a dividend of$10 yesterday, and is expected to pay dividends every year forever, growing at a rate of 5% pa.

So the next dividend will be $10(1+0.05)^1=10.50$ in one year from now, and the year after it will be $10(1+0.05)^2=11.025$ and so on.

The required return of the stock is 15% pa.

Would you like to the share or politely ?

In the dividend discount model:

$$P_0 = \dfrac{C_1}{r-g}$$

The return $r$ is supposed to be the:

In the dividend discount model:

$$P_0= \frac{d_1}{r-g}$$

The pronumeral $g$ is supposed to be the:

For a price of $1040, Camille will sell you a share which just paid a dividend of$100, and is expected to pay dividends every year forever, growing at a rate of 5% pa.

So the next dividend will be $100(1+0.05)^1=105.00$, and the year after it will be $100(1+0.05)^2=110.25$ and so on.

The required return of the stock is 15% pa.

Would you like to the share or politely ?

For a price of $10.20 each, Renee will sell you 100 shares. Each share is expected to pay dividends in perpetuity, growing at a rate of 5% pa. The next dividend is one year away (t=1) and is expected to be$1 per share.

The required return of the stock is 15% pa.

Would you like to the shares or politely ?

For a price of $129, Joanne will sell you a share which is expected to pay a$30 dividend in one year, and a $10 dividend every year after that forever. So the stock's dividends will be$30 at t=1, $10 at t=2,$10 at t=3, and $10 forever onwards. The required return of the stock is 10% pa. Would you like to the share or politely ? For a price of$95, Sherylanne will sell you a share which is expected to pay its first dividend of $10 in 7 years (t=7), and will continue to pay the same$10 dividend every year after that forever.

The required return of the stock is 10% pa.

Would you like to the share or politely ?

The following equation is the Dividend Discount Model, also known as the 'Gordon Growth Model' or the 'Perpetuity with growth' equation.

$$p_{0} = \frac{c_1}{r_{\text{eff}} - g_{\text{eff}}}$$

What is the discount rate '$r_\text{eff}$' in this equation?

The following equation is the Dividend Discount Model, also known as the 'Gordon Growth Model' or the 'Perpetuity with growth' equation.

$$P_{0} = \frac{C_1}{r_{\text{eff}} - g_{\text{eff}}}$$

What would you call the expression $C_1/P_0$?

What is the NPV of the following series of cash flows when the discount rate is 5% given as an effective annual rate?

The first payment of $10 is in 4 years, followed by payments every 6 months forever after that which shrink by 2% every 6 months. That is, the growth rate every 6 months is actually negative 2%, given as an effective 6 month rate. So the payment at $t=4.5$ years will be $10(1-0.02)^1=9.80$, and so on. The following is the Dividend Discount Model (DDM) used to price stocks: $$P_0 = \frac{d_1}{r-g}$$ Assume that the assumptions of the DDM hold and that the time period is measured in years. Which of the following is equal to the expected dividend in 3 years, $d_3$? A stock is expected to pay the following dividends:  Cash Flows of a Stock Time (yrs) 0 1 2 3 4 ... Dividend ($) 0.00 1.15 1.10 1.05 1.00 ...

After year 4, the annual dividend will grow in perpetuity at -5% pa. Note that this is a negative growth rate, so the dividend will actually shrink. So,

• the dividend at t=5 will be $1(1-0.05) = 0.95$,
• the dividend at t=6 will be $1(1-0.05)^2 = 0.9025$, and so on.

The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates.

What is the current price of the stock?

A stock is expected to pay the following dividends:

 Cash Flows of a Stock Time (yrs) 0 1 2 3 4 ... Dividend ($) 0.00 1.15 1.10 1.05 1.00 ... After year 4, the annual dividend will grow in perpetuity at -5% pa. Note that this is a negative growth rate, so the dividend will actually shrink. So, • the dividend at t=5 will be $1(1-0.05) = 0.95$, • the dividend at t=6 will be $1(1-0.05)^2 = 0.9025$, and so on. The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates. What will be the price of the stock in four and a half years (t = 4.5)? When using the dividend discount model to price a stock: $$p_{0} = \frac{d_1}{r - g}$$ The growth rate of dividends (g): The following equation is the Dividend Discount Model, also known as the 'Gordon Growth Model' or the 'Perpetuity with growth' equation. $$p_0 = \frac{d_1}{r - g}$$ Which expression is NOT equal to the expected dividend yield? The following equation is the Dividend Discount Model, also known as the 'Gordon Growth Model' or the 'Perpetuity with growth' equation. $$p_0=\frac{d_1}{r_\text{eff}-g_\text{eff}}$$ Which expression is NOT equal to the expected capital return? For certain shares, the forward-looking Price-Earnings Ratio ($P_0/EPS_1$) is equal to the inverse of the share's total expected return ($1/r_\text{total}$). For what shares is this true? Assume: • The general accounting definition of 'payout ratio' which is dividends per share (DPS) divided by earnings per share (EPS). • All cash flows, earnings and rates are real. A stock is expected to pay the following dividends:  Cash Flows of a Stock Time (yrs) 0 1 2 3 4 ... Dividend ($) 8 8 8 20 8 ...

After year 4, the dividend will grow in perpetuity at 4% pa. The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates.

What is the current price of the stock?

A stock is expected to pay the following dividends:

 Cash Flows of a Stock Time (yrs) 0 1 2 3 4 ... Dividend ($) 8 8 8 20 8 ... After year 4, the dividend will grow in perpetuity at 4% pa. The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates. What will be the price of the stock in 5 years (t = 5), just after the dividend at that time has been paid? The following is the Dividend Discount Model used to price stocks: $$p_0=\frac{d_1}{r-g}$$ Which of the following statements about the Dividend Discount Model is NOT correct? The following is the Dividend Discount Model (DDM) used to price stocks: $$P_0=\dfrac{C_1}{r-g}$$ If the assumptions of the DDM hold, which one of the following statements is NOT correct? The long term expected: A very low-risk stock just paid its semi-annual dividend of$0.14, as it has for the last 5 years. You conservatively estimate that from now on the dividend will fall at a rate of 1% every 6 months.

If the stock currently sells for $3 per share, what must be its required total return as an effective annual rate? If risk free government bonds are trading at a yield of 4% pa, given as an effective annual rate, would you consider buying or selling the stock? The stock's required total return is: A stock has a beta of 0.5. Its next dividend is expected to be$3, paid one year from now. Dividends are expected to be paid annually and grow by 2% pa forever. Treasury bonds yield 5% pa and the market portfolio's expected return is 10% pa. All returns are effective annual rates.

What is the price of the stock now?

The total return of any asset can be broken down in different ways. One possible way is to use the dividend discount model (or Gordon growth model):

$$p_0 = \frac{c_1}{r_\text{total}-r_\text{capital}}$$

Which, since $c_1/p_0$ is the income return ($r_\text{income}$), can be expressed as:

$$r_\text{total}=r_\text{income}+r_\text{capital}$$

So the total return of an asset is the income component plus the capital or price growth component.

Another way to break up total return is to use the Capital Asset Pricing Model:

$$r_\text{total}=r_\text{f}+β(r_\text{m}- r_\text{f})$$

$$r_\text{total}=r_\text{time value}+r_\text{risk premium}$$

So the risk free rate is the time value of money and the term $β(r_\text{m}- r_\text{f})$ is the compensation for taking on systematic risk.

Using the above theory and your general knowledge, which of the below equations, if any, are correct?

(I) $r_\text{income}=r_\text{time value}$

(II) $r_\text{income}=r_\text{risk premium}$

(III) $r_\text{capital}=r_\text{time value}$

(IV) $r_\text{capital}=r_\text{risk premium}$

(V) $r_\text{income}+r_\text{capital}=r_\text{time value}+r_\text{risk premium}$

Which of the equations are correct?

The following equation is the Dividend Discount Model, also known as the 'Gordon Growth Model' or the 'Perpetuity with growth' equation.

$$P_0=\frac{d_1}{r-g}$$

A stock pays dividends annually. It just paid a dividend, but the next dividend ($d_1$) will be paid in one year.

According to the DDM, what is the correct formula for the expected price of the stock in 2.5 years?

Three years ago Frederika bought a house for $400,000. Now it's worth$600,000, based on recent similar sales in the area.

Frederika's residential property has an expected total return of 7% pa.

She rents her house out for $2,500 per month, paid in advance. Every 12 months she plans to increase the rental payments. The present value of 12 months of rental payments is$29,089.48.

The future value of 12 months of rental payments one year ahead is $31,125.74. What is the expected annual capital yield of the property? 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 risk to the company's existing projects. Assume a classical tax system. Which statement is correct? Question 121 capital structure, leverage, costs of 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 __________. 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 $100,000. If house prices suddenly fall by 15%, what would be your friend's percentage change in net wealth? Assume that: • No income (rent) was received from the house during the short time over which house prices fell. • Your friend will not declare bankruptcy, he will always pay off his debts. A fast-growing firm is suitable for valuation using a multi-stage growth model. It's nominal unlevered cash flow from assets ($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?

The equations for Net Income (NI, also known as Earnings or Net Profit After Tax) and Cash Flow From Assets (CFFA, also known as Free Cash Flow to the Firm) per year are:

$$NI=(Rev-COGS-FC-Depr-IntExp).(1-t_c)$$

$$CFFA=NI+Depr-CapEx - \varDelta NWC+IntExp$$

For a firm with debt, what is the amount of the interest tax shield per year?

The equations for Net Income (NI, also known as Earnings or Net Profit After Tax) and Cash Flow From Assets (CFFA, also known as Free Cash Flow to the Firm) per year are:

$$NI=(Rev-COGS-FC-Depr-IntExp).(1-t_c)$$

$$CFFA=NI+Depr-CapEx - \varDelta NWC+IntExp$$

For a firm with debt, what is the formula for the present value of interest tax shields if the tax shields occur in perpetuity?

You may assume:

• the value of debt (D) is constant through time,
• The cost of debt and the yield on debt are equal and given by $r_D$.
• the appropriate rate to discount interest tax shields is $r_D$.
• $\text{IntExp}=D.r_D$

Question 99  capital structure, interest tax shield, Miller and Modigliani, trade off theory of capital structure

A firm changes its capital structure by issuing a large amount of debt and using the funds to repurchase shares. Its assets are unchanged.

Assume that:

• The firm and individual investors can borrow at the same rate and have the same tax rates.
• The firm's debt and shares are fairly priced and the shares are repurchased at the market price, not at a premium.
• There are no market frictions relating to debt such as asymmetric information or transaction costs.
• Shareholders wealth is measured in terms of utiliity. Shareholders are wealth-maximising and risk-averse. They have a preferred level of overall leverage. Before the firm's capital restructure all shareholders were optimally levered.

According to Miller and Modigliani's theory, which statement is correct?

Unrestricted negative gearing is allowed in Australia, New Zealand and Japan. Negative gearing laws allow income losses on investment properties to be deducted from a tax-payer's pre-tax personal income. Negatively geared investors benefit from this tax advantage. They also hope to benefit from capital gains which exceed the income losses.

For example, a property investor buys an apartment funded by an interest only mortgage loan. Interest expense is $2,000 per month. The rental payments received from the tenant living on the property are$1,500 per month. The investor can deduct this income loss of $500 per month from his pre-tax personal income. If his personal marginal tax rate is 46.5%, this saves$232.5 per month in personal income tax.

The advantage of negative gearing is an example of the benefits of:

A company selling charting and technical analysis software claims that independent academic studies have shown that its software makes significantly positive abnormal returns. Assuming the claim is true, which statement(s) are correct?

(I) Weak form market efficiency is broken.

(II) Semi-strong form market efficiency is broken.

(III) Strong form market efficiency is broken.

(IV) The asset pricing model used to measure the abnormal returns (such as the CAPM) had mis-specification error so the returns may not be abnormal but rather fair for the level of risk.

Select the most correct response:

A person is thinking about borrowing $100 from the bank at 7% pa and investing it in shares with an expected return of 10% pa. One year later the person will sell the shares and pay back the loan in full. Both the loan and the shares are fairly priced. What is the Net Present Value (NPV) of this one year investment? Note that you are asked to find the present value ($V_0$), not the value in one year ($V_1$). Your friend claims that by reading 'The Economist' magazine's economic news articles, she can identify shares that will have positive abnormal expected returns over the next 2 years. Assuming that her claim is true, which statement(s) are correct? (i) Weak form market efficiency is broken. (ii) Semi-strong form market efficiency is broken. (iii) Strong form market efficiency is broken. (iv) The asset pricing model used to measure the abnormal returns (such as the CAPM) is either wrong (mis-specification error) or is measured using the wrong inputs (data errors) so the returns may not be abnormal but rather fair for the level of risk. Select the most correct response: The US government recently announced that subsidies for fresh milk producers will be gradually phased out over the next year. Newspapers say that there are expectations of a 40% increase in the spot price of fresh milk over the next year. Option prices on fresh milk trading on the Chicago Mercantile Exchange (CME) reflect expectations of this 40% increase in spot prices over the next year. Similarly to the rest of the market, you believe that prices will rise by 40% over the next year. What option trades are likely to be profitable, or to be more specific, result in a positive Net Present Value (NPV)? Assume that: • Only the spot price is expected to increase and there is no change in expected volatility or other variables that affect option prices. • No taxes, transaction costs, information asymmetry, bid-ask spreads or other market frictions. Select the most correct statement from the following. 'Chartists', also known as 'technical traders', believe that: Fundamentalists who analyse company financial reports and news announcements (but who don't have inside information) will make positive abnormal returns if: A man inherits$500,000 worth of shares.

He believes that by learning the secrets of trading, keeping up with the financial news and doing complex trend analysis with charts that he can quit his job and become a self-employed day trader in the equities markets.

What is the expected gain from doing this over the first year? Measure the net gain in wealth received at the end of this first year due to the decision to become a day trader. Assume the following:

• He earns $60,000 pa in his current job, paid in a lump sum at the end of each year. • He enjoys examining share price graphs and day trading just as much as he enjoys his current job. • Stock markets are weak form and semi-strong form efficient. • He has no inside information. • He makes 1 trade every day and there are 250 trading days in the year. Trading costs are$20 per trade. His broker invoices him for the trading costs at the end of the year.
• The shares that he currently owns and the shares that he intends to trade have the same level of systematic risk as the market portfolio.
• The market portfolio's expected return is 10% pa.

Measure the net gain over the first year as an expected wealth increase at the end of the year.

Economic statistics released this morning were a surprise: they show a strong chance of consumer price inflation (CPI) reaching 5% pa over the next 2 years.

This is much higher than the previous forecast of 3% pa.

A vanilla fixed-coupon 2-year risk-free government bond was issued at par this morning, just before the economic news was released.

What is the expected change in bond price after the economic news this morning, and in the next 2 years? Assume that:

• Inflation remains at 5% over the next 2 years.
• Investors demand a constant real bond yield.
• The bond price falls by the (after-tax) value of the coupon the night before the ex-coupon date, as in real life.

A managed fund charges fees based on the amount of money that you keep with them. The fee is 2% of the start-of-year amount, but it is paid at the end of every year.

This fee is charged regardless of whether the fund makes gains or losses on your money.

The fund offers to invest your money in shares which have an expected return of 10% pa before fees.

You are thinking of investing $100,000 in the fund and keeping it there for 40 years when you plan to retire. What is the Net Present Value (NPV) of investing your money in the fund? Note that the question is not asking how much money you will have in 40 years, it is asking: what is the NPV of investing in the fund? Assume that: • The fund has no private information. • Markets are weak and semi-strong form efficient. • The fund's transaction costs are negligible. • The cost and trouble of investing your money in shares by yourself, without the managed fund, is negligible. A stock is expected to pay a dividend of$15 in one year (t=1), then $25 for 9 years after that (payments at t=2 ,3,...10), and on the 11th year (t=11) the dividend will be 2% less than at t=10, and will continue to shrink at the same rate every year after that forever. The required return of the stock is 10%. All rates are effective annual rates. What is the price of the stock now? Estimate Microsoft's (MSFT) share price using a price earnings (PE) multiples approach with the following assumptions and figures only: • Apple, Google and Microsoft are comparable companies, • Apple's (AAPL) share price is$526.24 and historical EPS is $40.32. • Google's (GOOG) share price is$1,215.65 and historical EPS is $36.23. • Micrsoft's (MSFT) historical earnings per share (EPS) is$2.71.

Source: Google Finance 28 Feb 2014.

Which of the following investable assets are NOT suitable for valuation using PE multiples techniques?

Estimate the US bank JP Morgan's share price using a price earnings (PE) multiples approach with the following assumptions and figures only:

• The major US banks JP Morgan Chase (JPM), Citi Group (C) and Wells Fargo (WFC) are comparable companies;
• JP Morgan Chase's historical earnings per share (EPS) is $4.37; • Citi Group's share price is$50.05 and historical EPS is $4.26; • Wells Fargo's share price is$48.98 and historical EPS is $3.89. Note: Figures sourced from Google Finance on 24 March 2014. Which firms tend to have low forward-looking price-earnings (PE) ratios? Only consider firms with positive earnings, disregard firms with negative earnings and therefore negative PE ratios. Which of the following investable assets are NOT suitable for valuation using PE multiples techniques? Estimate the Chinese bank ICBC's share price using a backward-looking price earnings (PE) multiples approach with the following assumptions and figures only. Note that the renminbi (RMB) is the Chinese currency, also known as the yuan (CNY). • The 4 major Chinese banks ICBC, China Construction Bank (CCB), Bank of China (BOC) and Agricultural Bank of China (ABC) are comparable companies; • ICBC 's historical earnings per share (EPS) is RMB 0.74; • CCB's backward-looking PE ratio is 4.59; • BOC 's backward-looking PE ratio is 4.78; • ABC's backward-looking PE ratio is also 4.78; Note: Figures sourced from Google Finance on 25 March 2014. Share prices are from the Shanghai stock exchange. Which firms tend to have high forward-looking price-earnings (PE) ratios? In Australia, nominal yields on semi-annual coupon paying Government Bonds with 2 years until maturity are currently 2.83% pa. The inflation rate is currently 2.2% pa, given as an APR compounding per quarter. The inflation rate is not expected to change over the next 2 years. What is the real yield on these bonds, given as an APR compounding every 6 months? Most listed Australian companies pay dividends twice per year, the 'interim' and 'final' dividends, which are roughly 6 months apart. You are an equities analyst trying to value the company BHP. You decide to use the Dividend Discount Model (DDM) as a starting point, so you study BHP's dividend history and you find that BHP tends to pay the same interim and final dividend each year, and that both grow by the same rate. You expect BHP will pay a$0.55 interim dividend in six months and a $0.55 final dividend in one year. You expect each to grow by 4% next year and forever, so the interim and final dividends next year will be$0.572 each, and so on in perpetuity.

Assume BHP's cost of equity is 8% pa. All rates are quoted as nominal effective rates. The dividends are nominal cash flows and the inflation rate is 2.5% pa.

What is the current price of a BHP share?

A project to build a toll bridge will take two years to complete, costing three payments of $100 million at the start of each year for the next three years, that is at t=0, 1 and 2. After completion, the toll bridge will yield a constant$50 million at the end of each year for the next 10 years. So the first payment will be at t=3 and the last at t=12. After the last payment at t=12, the bridge will be given to the government.

The required return of the project is 21% pa given as an effective annual nominal rate.

All cash flows are real and the expected inflation rate is 10% pa given as an effective annual rate. Ignore taxes.

The Net Present Value is:

In Germany, nominal yields on semi-annual coupon paying Government Bonds with 2 years until maturity are currently 0.04% pa.

The inflation rate is currently 1.4% pa, given as an APR compounding per quarter. The inflation rate is not expected to change over the next 2 years.

What is the real yield on these bonds, given as an APR compounding every 6 months?

You are a banker about to grant a 2 year loan to a customer. The loan's principal and interest will be repaid in a single payment at maturity, sometimes called a zero-coupon loan, discount loan or bullet loan.

You require a real return of 6% pa over the two years, given as an effective annual rate. Inflation is expected to be 2% this year and 4% next year, both given as effective annual rates.

You judge that the customer can afford to pay back $1,000,000 in 2 years, given as a nominal cash flow. How much should you lend to her right now? Details of two different types of light bulbs are given below: • Low-energy light bulbs cost$3.50, have a life of nine years, and use about $1.60 of electricity a year, paid at the end of each year. • Conventional light bulbs cost only$0.50, but last only about a year and use about $6.60 of energy a year, paid at the end of each year. The real discount rate is 5%, given as an effective annual rate. Assume that all cash flows are real. The inflation rate is 3% given as an effective annual rate. Find the Equivalent Annual Cost (EAC) of the low-energy and conventional light bulbs. The below choices are listed in that order. Assume that the Gordon Growth Model (same as the dividend discount model or perpetuity with growth formula) is an appropriate method to value real estate. The rule of thumb in the real estate industry is that properties should yield a 5% pa rental return. Many investors also regard property to be as risky as the stock market, therefore property is thought to have a required total return of 9% pa which is the average total return on the stock market including dividends. Assume that all returns are effective annual rates and they are nominal (not reduced by inflation). Inflation is expected to be 2% pa. You're considering purchasing an investment property which has a rental yield of 5% pa and you expect it to have the same risk as the stock market. Select the most correct statement about this property. A bank grants a borrower an interest-only residential mortgage loan with a very large 50% deposit and a nominal interest rate of 6% that is not expected to change. Assume that inflation is expected to be a constant 2% pa over the life of the loan. Ignore credit risk. From the bank's point of view, what is the long term expected nominal capital return of the loan asset? Imagine that the interest rate on your savings account was 1% per year and inflation was 2% per year. After one year, would you be able to buy , exactly the as or than today with the money in this account? When valuing assets using discounted cash flow (net present value) methods, it is important to consider inflation. To properly deal with inflation: (I) Discount nominal cash flows by nominal discount rates. (II) Discount nominal cash flows by real discount rates. (III) Discount real cash flows by nominal discount rates. (IV) Discount real cash flows by real discount rates. Which of the above statements is or are correct? A residential investment property has an expected nominal total return of 6% pa and nominal capital return of 3% pa. Inflation is expected to be 2% pa. All rates are given as effective annual rates. What are the property's expected real total, capital and income returns? The answer choices below are given in the same order. A residential investment property has an expected nominal total return of 8% pa and nominal capital return of 3% pa. Inflation is expected to be 2% pa. All rates are given as effective annual rates. What are the property's expected real total, capital and income returns? The answer choices below are given in the same order. A firm is considering a new project of similar risk to the current risk of the firm. This project will expand its existing business. The cash flows of the project have been calculated assuming that there is no interest expense. In other words, the cash flows assume that the project is all-equity financed. In fact the firm has a target debt-to-equity ratio of 1, so the project will be financed with 50% debt and 50% equity. To find the levered value of the firm's assets, what discount rate should be applied to the project's unlevered cash flows? Assume a classical tax system. Question 345 capital budgeting, break even, NPV  Project Data Project life 10 yrs Initial investment in factory$10m Depreciation of factory per year $1m Expected scrap value of factory at end of project$0 Sale price per unit $10 Variable cost per unit$6 Fixed costs per year, paid at the end of each year $2m Interest expense per year 0 Tax rate 30% Cost of capital per annum 10% Notes 1. The firm's current liabilities are forecast to stay at$0.5m. The firm's current assets (mostly inventory) is currently $1m, but is forecast to grow by$0.1m at the end of each year due to the project.
At the end of the project, the current assets accumulated due to the project can be sold for the same price that they were bought.
2. A marketing survey was used to forecast sales. It cost $1.4m which was just paid. The cost has been capitalised by the accountants and is tax-deductible over the life of the project, regardless of whether the project goes ahead or not. This amortisation expense is not included in the depreciation expense listed in the table above. Assumptions • All cash flows occur at the start or end of the year as appropriate, not in the middle or throughout the year. • All rates and cash flows are real. The inflation rate is 3% pa. • All rates are given as effective annual rates. Find the break even unit production (Q) per year to achieve a zero Net Income (NI) and Net Present Value (NPV), respectively. The answers below are listed in the same order. Below are 4 option graphs. Note that the y-axis is payoff at maturity (T). What options do they depict? List them in the order that they are numbered. You have just sold an 'in the money' 6 month European put option on the mining company BHP at an exercise price of$40 for a premium of $3. Which of the following statements best describes your situation? The 'option price' in an option contract is paid at the start when the option contract is agreed to. or ? The 'option strike price' in an option contract, also known as the exercise price, is paid at the start when the option contract is agreed to. or ? Which one of the following is NOT usually considered an 'investable' asset for long-term wealth creation? Which option position has the possibility of unlimited potential losses? All things remaining equal, according to the capital asset pricing model, if the systematic variance of an asset increases, its required return will increase and its price will decrease. If the idiosyncratic variance of an asset increases, its price will be unchanged. What is the relationship between the price of a call or put option and the total, systematic and idiosyncratic variance of the underlying asset that the option is based on? Select the most correct answer. Call and put option prices increase when the: You believe that the price of a share will fall significantly very soon, but the rest of the market does not. The market thinks that the share price will remain the same. Assuming that your prediction will soon be true, which of the following trades is a bad idea? In other words, which trade will NOT make money or prevent losses? Which of the following discount rates should be the highest for a levered company? Ignore the costs of financial distress. Which of the following statements about the weighted average cost of capital (WACC) is NOT correct? There are many different ways to value a firm's assets. Which of the following will NOT give the correct market value of a levered firm's assets $(V_L)$? Assume that: • The firm is financed by listed common stock and vanilla annual fixed coupon bonds, which are both traded in a liquid market. • The bonds' yield is equal to the coupon rate, so the bonds are issued at par. The yield curve is flat and yields are not expected to change. When bonds mature they will be rolled over by issuing the same number of new bonds with the same expected yield and coupon rate, and so on forever. • Tax rates on the dividends and capital gains received by investors are equal, and capital gains tax is paid every year, even on unrealised gains regardless of when the asset is sold. • There is no re-investment of the firm's cash back into the business. All of the firm's excess cash flow is paid out as dividends so real growth is zero. • The firm operates in a mature industry with zero real growth. • All cash flows and rates in the below equations are real (not nominal) and are expected to be stable forever. Therefore the perpetuity equation with no growth is suitable for valuation. Where: $$r_\text{WACC before tax} = r_D.\frac{D}{V_L} + r_{EL}.\frac{E_L}{V_L} = \text{Weighted average cost of capital before tax}$$ $$r_\text{WACC after tax} = r_D.(1-t_c).\frac{D}{V_L} + r_{EL}.\frac{E_L}{V_L} = \text{Weighted average cost of capital after tax}$$ $$NI_L=(Rev-COGS-FC-Depr-\mathbf{IntExp}).(1-t_c) = \text{Net Income Levered}$$ $$CFFA_L=NI_L+Depr-CapEx - \varDelta NWC+\mathbf{IntExp} = \text{Cash Flow From Assets Levered}$$ $$NI_U=(Rev-COGS-FC-Depr).(1-t_c) = \text{Net Income Unlevered}$$ $$CFFA_U=NI_U+Depr-CapEx - \varDelta NWC= \text{Cash Flow From Assets Unlevered}$$ A firm's weighted average cost of capital before tax ($r_\text{WACC before tax}$) would increase due to: A company issues a large amount of bonds to raise money for new projects of similar risk to the company's existing projects. The net present value (NPV) of the new projects is positive but small. Assume a classical tax system. Which statement is NOT correct? A firm has a debt-to-assets ratio of 50%. The firm then issues a large amount of equity to raise money for new projects of similar systematic risk to the company's existing projects. Assume a classical tax system. Which statement is correct? A firm's WACC before tax would decrease due to: A company has: • 50 million shares outstanding. • The market price of one share is currently$6.
• The risk-free rate is 5% and the market return is 10%.
• Market analysts believe that the company's ordinary shares have a beta of 2.
• The company has 1 million preferred stock which have a face (or par) value of $100 and pay a constant dividend of 10% of par. They currently trade for$80 each.
• The company's debentures are publicly traded and their market price is equal to 90% of their face value.
• The debentures have a total face value of $60,000,000 and the current yield to maturity of corporate debentures is 10% per annum. The corporate tax rate is 30%. What is the company's after-tax weighted average cost of capital (WACC)? Assume a classical tax system. A firm can issue 5 year annual coupon bonds at a yield of 8% pa and a coupon rate of 12% pa. The beta of its levered equity is 1. Five year government bonds yield 5% pa with a coupon rate of 6% pa. The market's expected dividend return is 4% pa and its expected capital return is 6% pa. The firm's debt-to-equity ratio is 2:1. The corporate tax rate is 30%. What is the firm's after-tax WACC? Assume a classical tax system. Assume that there exists a perfect world with no transaction costs, no asymmetric information, no taxes, no agency costs, equal borrowing rates for corporations and individual investors, the ability to short the risk free asset, semi-strong form efficient markets, the CAPM holds, investors are rational and risk-averse and there are no other market frictions. For a firm operating in this perfect world, which statement(s) are correct? (i) When a firm changes its capital structure and/or payout policy, share holders' wealth is unaffected. (ii) When the idiosyncratic risk of a firm's assets increases, share holders do not expect higher returns. (iii) When the systematic risk of a firm's assets increases, share holders do not expect higher returns. Select the most correct response: A newly floated farming company is financed with senior bonds, junior bonds, cumulative non-voting preferred stock and common stock. The new company has no retained profits and due to floods it was unable to record any revenues this year, leading to a loss. The firm is not bankrupt yet since it still has substantial contributed equity (same as paid-up capital). On which securities must it pay interest or dividend payments in this terrible financial year? You're advising your superstar client 40-cent who is weighing up buying a private jet or a luxury yacht. 40-cent is just as happy with either, but he wants to go with the more cost-effective option. These are the cash flows of the two options: • The private jet can be bought for$6m now, which will cost $12,000 per month in fuel, piloting and airport costs, payable at the end of each month. The jet will last for 12 years. • Or the luxury yacht can be bought for$4m now, which will cost $20,000 per month in fuel, crew and berthing costs, payable at the end of each month. The yacht will last for 20 years. What's unusual about 40-cent is that he is so famous that he will actually be able to sell his jet or yacht for the same price as it was bought since the next generation of superstar musicians will buy it from him as a status symbol. Bank interest rates are 10% pa, given as an effective annual rate. You can assume that 40-cent will live for another 60 years and that when the jet or yacht's life is at an end, he will buy a new one with the same details as above. Would you advise 40-cent to buy the or the ? Note that the effective monthly rate is $r_\text{eff monthly}=(1+0.1)^{1/12}-1=0.00797414$ You just bought a nice dress which you plan to wear once per month on nights out. You bought it a moment ago for$600 (at t=0). In your experience, dresses used once per month last for 6 years.

Your younger sister is a student with no money and wants to borrow your dress once a month when she hits the town. With the increased use, your dress will only last for another 3 years rather than 6.

What is the present value of the cost of letting your sister use your current dress for the next 3 years?

Assume: that bank interest rates are 10% pa, given as an effective annual rate; you will buy a new dress when your current one wears out; your sister will only use the current dress, not the next one that you will buy; and the price of a new dress never changes.

The hardest and most important aspect of business project valuation is the estimation of the:

Which of the following companies is most suitable for valuation using PE multiples techniques?

Which of the following investable assets is the LEAST suitable for valuation using PE multiples techniques?

One and a half years ago Frank bought a house for $600,000. Now it's worth only$500,000, based on recent similar sales in the area.

The expected total return on Frank's residential property is 7% pa.

He rents his house out for $1,600 per month, paid in advance. Every 12 months he plans to increase the rental payments. The present value of 12 months of rental payments is$18,617.27.

The future value of 12 months of rental payments one year in the future is $19,920.48. What is the expected annual rental yield of the property? Ignore the costs of renting such as maintenance, real estate agent fees and so on. The perpetuity with growth formula is: $$P_0= \dfrac{C_1}{r-g}$$ Which of the following is NOT equal to the total required return (r)? 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).

A stock has a real expected total return of 7% pa and a real expected capital return of 2% pa.

Inflation is expected to be 2% pa. All rates are given as effective annual rates.

What is the nominal expected total return, capital return and dividend yield? The answers below are given in the same order.

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 pharmaceutical firm has just discovered a valuable new drug. So far the news has been kept a secret.

The net present value of making and commercialising the drug is $200 million, but$600 million of bonds will need to be issued to fund the project and buy the necessary plant and equipment.

The firm will release the news of the discovery and bond raising to shareholders simultaneously in the same announcement. The bonds will be issued shortly after.

Once the announcement is made and the bonds are issued, what is the expected increase in the value of the firm's assets (ΔV), market capitalisation of debt (ΔD) and market cap of equity (ΔE)?

The triangle symbol is the Greek letter capital delta which means change or increase in mathematics.

Ignore the benefit of interest tax shields from having more debt.

Remember: $ΔV = ΔD+ΔE$

The CAPM can be used to find a business's expected opportunity cost of capital:

$$r_i=r_f+β_i (r_m-r_f)$$

What should be used as the risk free rate $r_f$?

A firm plans to issue equity and use the cash raised to pay off its debt. No assets will be bought or sold. Ignore the costs of financial distress.

Which of the following statements is NOT correct, all things remaining equal?

Question 412  enterprise value, no explanation

A large proportion of a levered firm's assets is cash held at the bank. The firm is financed with half equity and half debt.

Which of the following statements about this firm's enterprise value (EV) and total asset value (V) is NOT correct?

There are many ways to calculate a firm's free cash flow (FFCF), also called cash flow from assets (CFFA).

One method is to use the following formulas to transform net income (NI) into FFCF including interest and depreciation tax shields:

$$FFCF=NI + Depr - CapEx -ΔNWC + IntExp$$

$$NI=(Rev - COGS - Depr - FC - IntExp).(1-t_c )$$

Another popular method is to use EBITDA rather than net income. EBITDA is defined as:

$$EBITDA=Rev - COGS - FC$$

One of the below formulas correctly calculates FFCF from EBITDA, including interest and depreciation tax shields, giving an identical answer to that above. Which formula is correct?

A mature firm has constant expected future earnings and dividends. Both amounts are equal. So earnings and dividends are expected to be equal and unchanging.

Which of the following statements is NOT correct?

A residential real estate investor believes that house prices will grow at a rate of 5% pa and that rents will grow by 2% pa forever.

All rates are given as nominal effective annual returns. Assume that:

• His forecast is true.
• Real estate is and always will be fairly priced and the capital asset pricing model (CAPM) is true.
• Ignore all costs such as taxes, agent fees, maintenance and so on.
• All rental income cash flow is paid out to the owner, so there is no re-investment and therefore no additions or improvements made to the property.
• The non-monetary benefits of owning real estate and renting remain constant.

Which one of the following statements is NOT correct? Over time:

A managed fund charges fees based on the amount of money that you keep with them. The fee is 2% of the end-of-year amount, paid at the end of every year.

This fee is charged regardless of whether the fund makes gains or losses on your money.

The fund offers to invest your money in shares which have an expected return of 10% pa before fees.

You are thinking of investing $100,000 in the fund and keeping it there for 40 years when you plan to retire. How much money do you expect to have in the fund in 40 years? Also, what is the future value of the fees that the fund expects to earn from you? Give both amounts as future values in 40 years. Assume that: • The fund has no private information. • Markets are weak and semi-strong form efficient. • The fund's transaction costs are negligible. • The cost and trouble of investing your money in shares by yourself, without the managed fund, is negligible. • The fund invests its fees in the same companies as it invests your funds in, but with no fees. The below answer choices list your expected wealth in 40 years and then the fund's expected wealth in 40 years.  Project Data Project life 1 year Initial investment in equipment$8m Depreciation of equipment per year $8m Expected sale price of equipment at end of project 0 Unit sales per year 4m Sale price per unit$10 Variable cost per unit $5 Fixed costs per year, paid at the end of each year$2m Interest expense in first year (at t=1) $0.562m Corporate tax rate 30% Government treasury bond yield 5% Bank loan debt yield 9% Market portfolio return 10% Covariance of levered equity returns with market 0.32 Variance of market portfolio returns 0.16 Firm's and project's debt-to-equity ratio 50% Notes 1. Due to the project, current assets will increase by$6m now (t=0) and fall by $6m at the end (t=1). Current liabilities will not be affected. Assumptions • The debt-to-equity ratio will be kept constant throughout the life of the project. The amount of interest expense at the end of each period has been correctly calculated to maintain this constant debt-to-equity ratio. • Millions are represented by 'm'. • All cash flows occur at the start or end of the year as appropriate, not in the middle or throughout the year. • All rates and cash flows are real. The inflation rate is 2% pa. All rates are given as effective annual rates. • The project is undertaken by a firm, not an individual. What is the net present value (NPV) of the project?  Project Data Project life 1 year Initial investment in equipment$6m Depreciation of equipment per year $6m Expected sale price of equipment at end of project 0 Unit sales per year 9m Sale price per unit$8 Variable cost per unit $6 Fixed costs per year, paid at the end of each year$1m Interest expense in first year (at t=1) $0.53m Tax rate 30% Government treasury bond yield 5% Bank loan debt yield 6% Market portfolio return 10% Covariance of levered equity returns with market 0.08 Variance of market portfolio returns 0.16 Firm's and project's debt-to-assets ratio 50% Notes 1. Due to the project, current assets will increase by$5m now (t=0) and fall by $5m at the end (t=1). Current liabilities will not be affected. Assumptions • The debt-to-assets ratio will be kept constant throughout the life of the project. The amount of interest expense at the end of each period has been correctly calculated to maintain this constant debt-to-equity ratio. • Millions are represented by 'm'. • All cash flows occur at the start or end of the year as appropriate, not in the middle or throughout the year. • All rates and cash flows are real. The inflation rate is 2% pa. • All rates are given as effective annual rates. • The 50% capital gains tax discount is not available since the project is undertaken by a firm, not an individual. What is the net present value (NPV) of the project? You just bought a residential apartment as an investment property for$500,000.

You intend to rent it out to tenants. They are ready to move in, they would just like to know how much the monthly rental payments will be, then they will sign a twelve-month lease.

You require a total return of 8% pa and a rental yield of 5% pa.

What would the monthly paid-in-advance rental payments have to be this year to receive that 5% annual rental yield?

Also, if monthly rental payments can be increased each year when a new lease agreement is signed, by how much must you increase rents per year to realise the 8% pa total return on the property?

Ignore all taxes and the costs of renting such as maintenance costs, real estate agent fees, utilities and so on. Assume that there will be no periods of vacancy and that tenants will promptly pay the rental prices you charge.

Note that the first rental payment will be received at t=0. The first lease agreement specifies the first 12 equal payments from t=0 to 11. The next lease agreement can have a rental increase, so the next twelve equal payments from t=12 to 23 can be higher than previously, and so on forever.

Suppose you had $100 in a savings account and the interest rate was 2% per year. After 5 years, how much do you think you would have in the account if you left the money to grow? than$102, $102 or than$102?

Do you think that the following statement is or ? “Buying a single company stock usually provides a safer return than a stock mutual fund.”

Jan asks you for a loan. He wants $100 now and offers to pay you back$120 in 1 year. You can borrow and lend from the bank at an interest rate of 10% pa, given as an effective annual rate.

Ignore credit risk. Remember:

$$V_0 = \frac{V_t}{(1+r_\text{eff})^t}$$

Will you or Jan's deal?

Katya offers to pay you $10 at the end of every year for the next 5 years (t=1,2,3,4,5) if you pay her$50 now (t=0). You can borrow and lend from the bank at an interest rate of 10% pa, given as an effective annual rate.

Ignore credit risk.

Will you or Katya's deal?

Which of the following statements is NOT correct? Borrowers:

Which of the following statements is NOT correct? Lenders:

Which of the following statements is NOT equivalent to the yield on debt?

Assume that the debt being referred to is fairly priced, but do not assume that it's priced at par.

Question 109  credit rating, credit risk

Bonds with lower (worse) credit ratings tend to have:

A highly leveraged risky firm is trying to raise more debt. The types of debt being considered, in no particular order, are senior bonds, junior bonds, bank accepted bills, promissory notes and bank loans.

Which of these forms of debt is the safest from the perspective of the debt investors who are thinking of investing in the firm's new debt?

You're considering making an investment in a particular company. They have preference shares, ordinary shares, senior debt and junior debt.

Which is the safest investment? Which will give the highest returns?

An 'interest rate' is the same thing as a 'coupon rate'. or ?

An 'interest payment' is the same thing as a 'coupon payment'. or ?

An 'interest rate' is the same thing as a 'yield'. or ?

Which of the following statements about effective rates and annualised percentage rates (APR's) is NOT correct?

In the Merton model of corporate debt, buying a levered company's debt is equivalent to buying risk free government bonds and:

In the Merton model of corporate debt, buying a levered company's shares is equivalent to:

In the Merton model of corporate debt, buying a levered company's debt is equivalent to buying the company's assets and:

Which of the following is the least useful method or model to calculate the value of a real option in a project?

A risky firm will last for one period only (t=0 to 1), then it will be liquidated. So it's assets will be sold and the debt holders and equity holders will be paid out in that order. The firm has the following quantities:

$V$ = Market value of assets.

$E$ = Market value of (levered) equity.

$D$ = Market value of zero coupon bonds.

$F_1$ = Total face value of zero coupon bonds which is promised to be paid in one year.

The levered equity graph above contains bold labels a to e. Which of the following statements about those labels is NOT correct?

A risky firm will last for one period only (t=0 to 1), then it will be liquidated. So it's assets will be sold and the debt holders and equity holders will be paid out in that order. The firm has the following quantities:

$V$ = Market value of assets.

$E$ = Market value of (levered) equity.

$D$ = Market value of zero coupon bonds.

$F_1$ = Total face value of zero coupon bonds which is promised to be paid in one year.

The risky corporate debt graph above contains bold labels a to e. Which of the following statements about those labels is NOT correct?

One of the reasons why firms may not begin projects with relatively small positive net present values (NPV's) is because they wish to maximise the value of their:

A moped is a bicycle with pedals and a little motor that can be switched on to assist the rider. Mopeds offer the rider:

You're thinking of starting a new cafe business, but you're not sure if it will be profitable.

You have to decide what type of cups, mugs and glasses you wish to buy. You can have your cafe's name printed on them, or plain un-marked ones. For marketing reasons it's better to have the cafe name printed, but the plain un-marked cups, mugs and glasses maximise your:

Some financially minded people insist on a prenuptial agreement before committing to marry their partner. This agreement states how the couple's assets should be divided in case they divorce. Prenuptial agreements are designed to give the richer partner more of the couples' assets if they divorce, thus maximising the richer partner's:

An expansion option is best modeled as a or option?

An abandonment option is best modeled as a or option?

A timing option is best modeled as a or option?

According to option theory, it's rational for students to submit their assignments as or as possible?

The cheapest mobile phones available tend to be those that are 'locked' into a cell phone operator's network. Locked phones can not be used with other cell phone operators' networks.

Locked mobile phones are cheaper than unlocked phones because the locked-in network operator helps create a monopoly by:

Your firm's research scientists can begin an exciting new project at a cost of $10m now, after which there’s a: • 70% chance that cash flows will be$1m per year forever, starting in 5 years (t=5). This is the A state of the world.
• 20% chance that cash flows will be $3m per year forever, starting in 5 years (t=5). This is the B state of the world. • 10% chance of a major break through in which case the cash flows will be$20m per year forever starting in 5 years (t=5), or the project can be expanded by investing another $10m (at t=5) which is expected to give cash flows of$60m per year forever, starting at year 9 (t=9). This is the C state of the world.

The firm's cost of capital is 10% pa.

What's the present value (at t=0) of the option to expand in year 5?

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

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 $9m and equity $(E_0)$ is$1m.

A new project presents itself which requires an investment of $2m and will provide a: •$6.6m cash flow with probability 0.5 in the good state of the world, and a
• -$4.4m (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? A levered firm has zero-coupon bonds which mature in one year and have a combined face value of$9.9m.

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:

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

A new project presents itself which requires an investment of $2m and will provide a certain cash flow of$3.3m 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? In a takeover deal where the offer is 100% cash, the merged firm's number of shares will be equal to the acquirer firm's original number of shares. or ? In a takeover deal where the offer is 100% scrip (shares), the merged firm's number of shares will be equal to the acquirer firm's original number of shares. or ? In a takeover deal where the offer is 100% scrip (shares), the merged firm's number of shares will be equal to the sum of the acquirer and target firms' original number of shares. or ? Acquirer firm plans to launch a takeover of Target firm. The deal is expected to create a present value of synergies totaling$105 million. A cash offer will be made that pays the fair price for the target's shares plus 75% of the total synergy value. The cash will be paid out of the firm's cash holdings, no new debt or equity will be raised.

 Firms Involved in the Takeover Acquirer Target Assets ($m) 6,000 700 Debt ($m) 4,800 400 Share price ($) 40 20 Number of shares (m) 30 15 Ignore transaction costs and fees. Assume that the firms' debt and equity are fairly priced, and that each firms' debts' risk, yield and values remain constant. The acquisition is planned to occur immediately, so ignore the time value of money. Calculate the merged firm's share price and total number of shares after the takeover has been completed. Acquirer firm plans to launch a takeover of Target firm. The deal is expected to create a present value of synergies totaling$105 million. A scrip offer will be made that pays the fair price for the target's shares plus 75% of the total synergy value.

 Firms Involved in the Takeover Acquirer Target Assets ($m) 6,000 700 Debt ($m) 4,800 400 Share price ($) 40 20 Number of shares (m) 30 15 Ignore transaction costs and fees. Assume that the firms' debt and equity are fairly priced, and that each firms' debts' risk, yield and values remain constant. The acquisition is planned to occur immediately, so ignore the time value of money. Calculate the merged firm's share price and total number of shares after the takeover has been completed. Acquirer firm plans to launch a takeover of Target firm. The firms operate in different industries and the CEO's rationale for the merger is to increase diversification and thereby decrease risk. The deal is not expected to create any synergies. An 80% scrip and 20% cash offer will be made that pays the fair price for the target's shares. The cash will be paid out of the firms' cash holdings, no new debt or equity will be raised.  Firms Involved in the Takeover Acquirer Target Assets ($m) 6,000 700 Debt ($m) 4,800 400 Share price ($) 40 20 Number of shares (m) 30 15

Ignore transaction costs and fees. Assume that the firms' debt and equity are fairly priced, and that each firms' debts' risk, yield and values remain constant. The acquisition is planned to occur immediately, so ignore the time value of money.

Calculate the merged firm's share price and total number of shares after the takeover has been completed.

Acquirer firm plans to launch a takeover of Target firm. The deal is expected to create a present value of synergies totaling $105 million. A 40% scrip and 60% cash offer will be made that pays the fair price for the target's shares plus 75% of the total synergy value. The cash will be paid out of the firm's cash holdings, no new debt or equity will be raised.  Firms Involved in the Takeover Acquirer Target Assets ($m) 6,000 700 Debt ($m) 4,800 400 Share price ($) 40 20 Number of shares (m) 30 15

Ignore transaction costs and fees. Assume that the firms' debt and equity are fairly priced, and that each firms' debts' risk, yield and values remain constant. The acquisition is planned to occur immediately, so ignore the time value of money.

Calculate the merged firm's share price and total number of shares after the takeover has been completed.

Acquirer firm plans to launch a takeover of Target firm. The deal is expected to create a present value of synergies totaling $2 million. A cash offer will be made that pays the fair price for the target's shares plus 70% of the total synergy value. The cash will be paid out of the firm's cash holdings, no new debt or equity will be raised.  Firms Involved in the Takeover Acquirer Target Assets ($m) 60 10 Debt ($m) 20 2 Share price ($) 10 8 Number of shares (m) 4 1

Ignore transaction costs and fees. Assume that the firms' debt and equity are fairly priced, and that each firms' debts' risk, yield and values remain constant. The acquisition is planned to occur immediately, so ignore the time value of money.

Calculate the merged firm's share price and total number of shares after the takeover has been completed.

Acquirer firm plans to launch a takeover of Target firm. The deal is expected to create a present value of synergies totaling $2 million. A scrip offer will be made that pays the fair price for the target's shares plus 70% of the total synergy value.  Firms Involved in the Takeover Acquirer Target Assets ($m) 60 10 Debt ($m) 20 2 Share price ($) 10 8 Number of shares (m) 4 1

Ignore transaction costs and fees. Assume that the firms' debt and equity are fairly priced, and that each firms' debts' risk, yield and values remain constant. The acquisition is planned to occur immediately, so ignore the time value of money.

Calculate the merged firm's share price and total number of shares after the takeover has been completed.

Acquirer firm plans to launch a takeover of Target firm. The deal is expected to create a present value of synergies totaling $0.5 million, but investment bank fees and integration costs with a present value of$1.5 million is expected. A 10% cash and 90% scrip offer will be made that pays the fair price for the target's shares only. Assume that the Target and Acquirer agree to the deal. The cash will be paid out of the firms' cash holdings, no new debt or equity will be raised.

 Firms Involved in the Takeover Acquirer Target Assets ($m) 60 10 Debt ($m) 20 2 Share price (\$) 10 8 Number of shares (m) 4 1

Assume that the firms' debt and equity are fairly priced, and that each firms' debts' risk, yield and values remain constant. The acquisition is planned to occur immediately, so ignore the time value of money.

Calculate the merged firm's share price and total number of shares after the takeover has been completed.