due after 2 hours and half FINANCE

Today is Jack’s 30th birthday. Five years ago, Jack opened a brokerage account when his grandmother gave him $25,000 for his 25th birthday. Jack added $2,000 to this account on his 26th birthday, $3,000 on his 27th birthday, $4,000 on his 28th birthday, and $5,000 on his 29th birthday. Jack’s goal is to have $400,000 in the account by his 40th birthday. Starting today, he plans to contribute a fixed amount to the account each year on his birthday. He will make 11 contributions, the first one will occur today, and the final contribution will occur on his 40th birthday. Complicating things somewhat is the fact that Jack plans to withdraw $20,000 from the account on his 40th birthday to finance the down payment on a home. How large does each of these 11 contributions have to be for Jack to reach his goal? Assume the account has earned (and will continue to earn) an effective return of 12% a year.

Today is Jack’s 30

th

birthday. Five years ago, Jack opened a brokerage account when his grandmother gave him $25,000 for his 25

th

birthday. Jack added $2,000 to

this account on his 26

th

birthday, $3,000 on his 27

th

birthday, $4,000 on his 28

th

birthday, and $5,000 on his 29

th

birthday. Jack’s goal is to have $400,000 in the

account by his 40

th

birthday. Starting today, he plans to contribute a fixed amount to the account each year on his birthday. He will make 11 contributions, the first

one will occur today, and the final contribution will occur on his 40

th

birthday. Complicating things somewhat is the fact that Jack plans to withdraw $20,000 from the

account on his 40

th

birthday to finance the down payment on a home. How large does each of these 11 contributions have to be for Jack to reach his goal? Assume the

account has earned (and will continue to earn) an effective return of 12% a year.

A financial analyst has been following Fast Start Inc., a new high-growth company. She estimates that the current risk-free rate is 6.25%, the market risk premium is 5%, and that Fast Start's beta is 1.75. The current earnings per share (EPS0) is $2.50. The company has a 40% payout ratio. The analyst estimates that the company's dividend will grow at a rate of 25% this year, 20% next year, and 15% the following year. After three years the dividend is expected to grow at a constant rate of 7% a year. The company is expected to maintain its current payout ratio. The analyst believes that the stock is fairly priced. What is the current price of the stock?

A financial analyst has been following Fast Start Inc., a new high -growth company. She estimates that the current risk -free rate is 6.25%, the market risk premium is 5 %, and that Fast

Start's beta is 1.75. The current earnings per share (EPS

0

) is $2.50. The company has a 40% payout ratio. The analyst estimates that the company's dividend will grow at a rate of 25 %

this year, 20% next year, and 15% the following year. After three years the dividend is expected to grow at a constant rate of 7 % a year. The company is expected to maintain its current

payout ratio. The analyst believes that the stock is fairly priced. What is the current price of the stock?

You own 100 bonds issued by Euler, Ltd. These bonds have 8 years remaining to maturity, an annual coupon payment of $80, and a par value of $1,000. Unfortunately, Euler is on the brink of bankruptcy. The creditors, including yourself, have agreed to a postponement of the next 4 interest payments (otherwise, the next interest payment would have been due in 1 year). The remaining interest payments, for Years 5 through 8, will be made as scheduled. The postponed payments will accrue interest at an annual rate of 6%, and they will then be paid as a lump sum at maturity 8 years hence. The required rate of return on these bonds, considering their substantial risk, is now 28%. What is the present value of each bond?

You own 100 bonds issued by Euler, Ltd. These bonds have 8 years remaining to maturity, an annual coupon payment of $80, and a par v alue of $1,000.

Unfortunately, Euler is on the brink of bankruptcy. The creditors, including yourself, have a greed to a postponement of the next 4 interest payments (otherwise, the

next interest payment would have been due in 1 year). The remaining interest payments, for Years 5 through 8, will be made a s scheduled. The postponed

payments will accrue interest a t an annual rate of 6%, and they will then be paid as a lump sum at maturity 8 years hence. The required rate of return on these

bonds, considering their substantial risk, is now 28 %. What is the present value of each bond?

A money manager is holding the following portfolio:

Stock Amount Invested Beta

1 $300,000 0.6

2 300,000 1.0

3 500,000 1.4

4 500,000 1.8

The risk-free rate is 6% and the portfolio’s required rate of return is 12.5%. The manager would like to sell all of her holdings of Stock 1 and use the proceeds to purchase more shares of Stock 4. What would be the portfolio’s required rate of return following this change?

A money manager is holding the following portfolio:

Stock Amount Invested Beta

1 $300,000 0.6

2 300,000 1.0

3 500,000 1.4

4 500,000 1.8

The risk-free rate is 6% and the portfolio’s required rate of return is 1 2.5%. The manager would like to sell all of her holdings of Stock 1 and use the proceeds to purchase more shares

of Stock 4. What would be the portfolio’s required rate of return following this change?

Watkins Inc. has never paid a dividend, and when it might begin paying dividends is unknown. Its current free cash flow (FCF) is $100,000 which is expected to grow at a constant 7% rate. The weighted average cost of capital (WACC=K) is 11%. Watkins currently holds $325,000 of non-operating marketable securities. Its long-term debt is $1,000,000, but it has never issued preferred stock.

a. Calculate Watkin’s value operations

b. Calculate the company’s total value

c. Calculate the value of common equity

Watkins Inc. has never paid a dividend, and when it might begin paying dividends is unknown. Its current free cash flow (FCF) is $100,000 which is expected to grow at a constant 7% rate.

The weighted average cost of capital (WACC=K) is 11%. Watkins currently holds $325,000 of non -operating marketable securities. Its long -term debt is $1,000,000, but it has never issued

preferred stock.

a. Calculate Watkin’s value operations

b. Calculate the company’s total value

c. Calculate the value of common equity

Six Sigma Software Co. is trying to estimate its optimal capital structure. Right now, Six Sigma has a capital structure that consists of 20% debt and 80% equity. (Its D/E ratio is 0.25.) %. Currently the company’s cost of equity is 12% and its tax rate is 40%. The risk The risk-free rate is 6% and the market risk premium is 5%.

What would be Six Sigma’s estimated cost of equity if it were to change its capital structure to 50% debt and 50% equity?

Six Sigma Software Co. is trying to estimate its optimal capital structure. Right now, Six Sigma has a capital structure that con sists of 20% debt and 80% equity. (Its D/E ratio is

0.25.) %. Currently the company’s cost of equity is 12% and its tax rate is 40 %. The risk The risk-free rate is 6% and the market risk premium is 5%.

What would be Six Sigma’s estimated cost of equity if it were to change its capital structure to 50% debt and 50% equity?

Firms U and L are in the same risk class and that both have EBIT = $1,000,000. Firm U uses no debt financing and its cost of equity is KsU=15%. Firm L has $2 million of debt outstanding at a cost of Kd = 5%. There are no taxes and MM assumptions hold.

1. Find V, S, Ks, and WACC for firms U and L.

2. Using the data given above, but now assuming that firms L and U are both subject to a 40% corporate tax rate, repeat the analysis under the MM with-tax model.

3. Now suppose investors are subject to the following tax rates: TD=20% and TS=10%. What is the gain from leverage according to the Miller’s Model?

4. How does this gain compare to the gain in the MM model with corporate taxes?

Firms U and L are in the same risk class and that both have EBIT = $1,000,000. Firm U uses no debt financing and its cost of equity is K

sU

=15%. Firm L has $2 million of debt

outstanding at a cost of K

d

= 5%. There are no taxes and MM assumptions hold.

1. Find V, S, K

s

, and WACC for firms U and L.

2. Using the data given above, but now assuming that firms L and U are both subject to a 40% corporate tax rate, repeat the anal ysis under the MM with-tax model.

3. Now suppose investors are subject to the following tax rates: T

D

=20% and T

S

=10%. What is the gain from leverage according to the Miller’s Model?

4. How does this gain compare to the gain in the MM model with corporate taxes?

You have just inherited $300,000 and have decided to purchase at least one established franchise in the fast food industry or possibly two if profitable. Your investment horizon is 3 years. You have narrowed down your choices to two choices:

(1) Franchise L: Lisa’s Soups, Salads, and Stuff and

(2) Franchise S: Sam’s Fried Chicken. The net cash flows shown below include the price you would receive for selling the franchise in 3 years and the forecast of how each franchise will do over the 3-year period.

Franchise L’s cash flows will start off slowly but will increase rather quickly as people become more health conscious, while Franchise S’s cash flows will start off high but will trail off as other chicken competitors enter the marketplace and as people become more health conscious and avoid fried foods.

Franchise L serves breakfast and lunch, while franchise S serves only dinner, so it is possible to invest in both franchises. You see these franchises as perfect complements to on another: you could attract both the lunch and dinner crowds and the health conscious and not so health conscious crowds with the franchises directly competing against one another.

Below are the projects’ net cash flows (in thousands of dollars):

Expected Net Cash Flows

Year Franchise L Franchise S

0 ($100) ($100)

1 10 70

2 60 50

3 80 20

Depreciation, salvage values, net working capital requirements, and tax effects are all included in these cash flows. You have made subjective risk assessment of each franchise, and concluded that both franchise have risk characteristics that require a return 10%. You must now determine whether one or both of the projects should be accepted.

1. The NPV of franchise L is ____________

2. The NPV of franchise S is ____________

3. The IRR of franchise L is _____________

4. The IRR of franchise S is _____________

5. The MIRR of L is ________

6. The MIRR is S is ________

7. Draw NPV profiles for both franchises. Show at what discount rate do the profiles cross?

You have just inherited $300,000 and have decided to purchase at least one established franchise in the fast food industry or possibly two if profitable. Your investment horizon is 3 years. You

have narrowed down your choices to two choices:

(1) Franchise L: Lisa’s Soups, Salads, and Stuff and

(2) Franchise S: Sam’s Fried Chicken. The net cash flows shown below include the price you would receive for selling the fra nchise in 3 years and the forecast of how each franchise will do over

the 3-year period.

Franchise L’s cash flows will start off slowly but will increase rather quickly as people become more health conscious, while Franchise S’s cash flows will start off high but will trail off as other

chicken competitors enter the marketplace and as people b ecome more health conscious and avoid fried foods.

Franchise L serves breakfast and lunch, while franchise S serves only dinner, so it is possible to invest in both franchises. You see these franchises as perfect complements to on another: you

could attract both the lunch and dinner crowds and the health conscious and not so health conscious crowds with the franchises directl y competing against one another.

Below are the projects’ net cash flows (in thousands of dollars):

Expected Net Cash Flows

Year Franchise L Franchise S

0 ($100) ($100)

1 10 70

2 60 50

3 80 20

Depreciation, salvage values, net working capital requirements, and tax effects are all included in these cash flows. You ha ve made subjective risk assessment of each franchise, and concluded

that both franchise have risk characteristics that require a return 10%. You must now determine whether one or both of the p rojects should be accepted.

1. The NPV of franchise L is ____________

2. The NPV of franchise S is ____________

3. The IRR of franchise L is _____________

4. The IRR of franchise S is _____________

5. The MIRR of L is ________

6. The MIRR is S is ________

7. Draw NPV profiles for both franchises. Show at what discount rate do the profiles cro ss?

During the past few years, Harry Davis Industries (HDI) has been constrained by high cost of capital to make many capital investments. Recently, though, capital costs have been declining and the company has decided to look seriously at a major expansion program that had been proposed by the marketing department. Assume that you are an assistant to the CFO. Your first task is estimate HDI’s cost of capital. The CFO has provided you with the following data, which is considered to your task:

1. The current price of HDI’s 12% coupon , seminal annual, non-callable bonds with 15 years to maturity is $1153.72. HDI does not use short-term interest bearing debt on a permanent basis. New bonds would be privately placed with no flotation costs.

2. The current price of HDI’s 10%, $100 par value, quarterly dividend, perpetual preferred stock is $113.10. HDI would incur flotation cost of $2.00 per share.

3. HDI’s common stock is currently selling for $50 per share. Its last dividend (d0) was $4.19, and dividends are expected to grow at a constant rate of 5% in the foreseeable future. HDI’s beta is 1.2; the yield on T-Bonds is 7%; and the market risk premium is estimated to be 6%. For the bond-yield-plus-risk-premium approach, the firm uses a 4% point risk premium.

4. HDI’s target capital structure:30% long-term, 10% pref. stock, and 60% common equity.

5. The firm’s tax rate is 40%

To structure the task somewhat, CFO has asked you to answer the following questions:

1. The after-tax cost of HDI’s debt, Kd is ___________

2. The firm’s cost of preferred stock, Kp, is __________

3. Using CAPM the firm’s cost of equity, Ke is _______

4. The estimated cost of equity using Discounted Cash Flow (DCF) model is ______

5. The cost of equity, Ke, based on the bond-yield-plus-risk-premium method is ____

6. The overall cost of equity, Ke is __________

7. The weighted average cost of capital (WACC) is _________

8. HDI estimates that if it issues new common stock, the flotation cost will be 15%. HDI incorporates the flotation costs into the DCF approach. The estimated cost of newly issued

common stock, taking into account the flotation cost is _________

9. Suppose HDI has historically earned 15% on equity (ROE) and retained 35% of earnings, and investors expect this situation to continue in the future. How could you use this

information to estimate the future dividend growth rate, and what growth rate would you get? Is this consistent with the 5% growth rate given?

HDI is interested in establishing a new division, which will focus primarily on developing new internet-based projects. In trying to determine the cost of capital for this new division,

you discover that stand-alone firms involved in similar projects have on average the following characteristics:

- Capital structure of 10% debt and 90% equity.

- Cost of debt of 12% and beta of 1.7.

10. Given this information, your estimate of the division’s cost capital is _______

During the past few years, Harry Davis Industries (HDI) has been constrained by high cost of capital to make many capital inv estments. Recently, though, capital costs have been declining

and the company has decided to look seriously at a major expansion pr ogram that had been proposed by the marketing department. Assume that you are an assistant to the CFO. Your first

task is estimate HDI’s cost of capital. The CFO has provided you with the following data, which is considered to your task:

1. The current price of HDI’s 12% coupon , seminal annual, non-callable bonds with 15 years to maturity is $1153.72. HDI does not use short -term interest bearing debt on a permanent

basis. New bonds would be privately placed with no flotation costs.

2. The current price of HDI’s 10%, $100 par value, quarterly dividend, perpetual preferred stock is $113.10. HDI would incur flotation cost of $2.00 per share.

3. HDI’s common stock is currently selling for $50 per share. Its last dividend (d

0

) was $4.19, and dividends are expected to grow at a constant rate of 5% in the foreseeable future.

HDI’s beta is 1.2; the yield on T-Bonds is 7%; and the market risk premium is estimated to be 6%. For the bond -yield-plus-risk-premium approach, the firm uses a 4% point risk

premium.

4. HDI’s target capital structure:30% long-term, 10% pref. stock, and 60% common equity.

5. The firm’s tax rate is 40%

To structure the task somewhat, CFO has asked you to answer the following questions:

1. The after-tax cost of HDI’s debt, K

d

is ___________

2. The firm’s cost of preferred stock, K

p

, is __________

3. Using CAPM the firm’s cost of equity, K

e

is _______

4. The estimated cost of equity using Discounted Cash Flow (DCF) model is ______

5. The cost of equity, K

e,

based on the bond-yield-plus-risk-premium method is ____

6. The overall cost of equity, K

e

is __________

7. The weighted average cost of capital (WACC) is _________

8. HDI estimates that if it issues new common stock, the flotation cost will be 15%. HDI incorporates the flota tion costs into the DCF approach. The estimated cost of newly issued

common stock, taking into account the flotation cost is _________

9. Suppose HDI has historically earned 15% on equity (ROE) and retained 35% of earnings, and investors expect this situa tion to continue in the future. How could you use this

information to estimate the future dividend growth rate, and what growth rate would you get? Is this consistent with the 5% g rowth rate given?

HDI is interested in establishing a new division, which wil l focus primarily on developing new internet-based projects. In trying to determine the cost of capital for this new division,

you discover that stand-alone firms involved in similar projects have on average the following characteristics:

- Capital structure of 10% debt and 90% equity.

- Cost of debt of 12% and beta of 1.7.

10. Given this information, your estimate of the division’s cost capital is _______

Miller Technologies recently reported the following balance sheet in its annual report (all numbers are in millions of dollars):

Cash $ 100 Accounts payable $ 300

Accounts receivable 300 Notes payable 500

Inventory 500 Total current liabilities $ 800

Total current assets $ 900 Long-term debt 1,500

Total debt $2,300

Common stock 500

Retained earnings 400

Net fixed assets 2,300 Total common equity $ 900

Total assets $3,200 Total liabilities & equity $3,200

Miller also reported sales revenues of $4.5 billion and a 20% ROE for this same year.

A. What is Miller’s ROA?

B. Miller Technologies is considering issuing $300 million in notes payable to purchase new fixed assets (for this problem, ignore depreciation). If this plan were carried out,

what would Miller’s current ratio be immediately following the transaction?

Miller Technologies recently reported the following balance sheet in its annual report (all numbers are in millions of dollar s):

Cash $ 100 Accounts payable $ 300

Accounts receivable 300 Notes payable 500

Inventory 500 Total current liabilities $ 800

Total current assets $ 900 Long-term debt 1,500

Total debt $2,300

Common stock 500

Retained earnings 400

Net fixed assets 2,300 Total common equity $ 900

Total assets $3,200 Total liabilities & equity $3,200

Miller also reported sales revenues of $4.5 billion and a 20% ROE for this same year.

A. What is Miller’s ROA?

B. Miller Technologies is considering issuing $300 million in notes payable to purchase new fixed assets (for th is problem, ignore depreciation). If this plan were carried out,

what would Miller’s current ratio be immediately following the transaction?

ABC Corp is a full-service truck leasing, maintenance, and rental firm with operations in North America and Europe. The following are selected numbers from the financial statements for 2014 and 2015(in millions).

	2014	2015
Revenues	$5,192.0	$5,400.0
(Less) Operating Expenses	($3,678.5)	($3848.0)
(Less) Depreciation	($573.5)	($580.0)
= EBIT	$940.0	$972.0
(Less) Interest Expenses	($170.0)	($172.0)
(Less) Taxes	($652.1)	($670.0)
= Net Income	$117.9	$130.0
Working Capital	$92.0	<$370.0>
Total Debt	$2,000 mil	$2,200 mil

The firm had capital expenditures of $800 million in 2014 and $850 million in 2015. The working capital in 2014 was $34.8 million, and the total debt outstanding in 2014 was $1.75 billion. There were 77 million shares outstanding, trading at $29 per share.

A. Estimate the cash flows to equity in 2014 and 2015.

B. Estimate the cash flows to the firm in 2014 and 2015.

C. Assuming that revenues and all expenses (including depreciation and capital expenditures) increase 6%, and that working capital remains unchanged in 2016 estimate the projected cash flows to equity and the firm in 2016. (The firm is assumed to be at its optimal financial leverage.)

D. How would your answer in (c) change if the firm planned to increase its debt ratio in 2016 by financing 75% of its capital expenditures (net of depreciation) with new debt issues?

ABC Corp is a full-service truck leasing, maintenance, and rental firm with operations in North America and Europe. The following are selected numbers

from the financial statements for 2014 and 2015(in millions).

2014 2015

Revenues $5,192.0 $5,400.0

(Less) Operating Expenses ($3,678.5) ($3848.0)

(Less) Depreciation ($573.5) ($580.0)

= EBIT $940.0 $972.0

(Less) Interest Expenses ($170.0) ($172.0)

(Less) Taxes ($652.1) ($670.0)

= Net Income $117.9 $130.0

Working Capital $92.0 <$370.0>

Total Debt $2,000 mil $2,200 mil

The firm had capital expenditures of $800 million in 2014 and $850 million in 2015. The working capital in 2014 was $34.8 million, and the total debt

outstanding in 2014 was $1.75 billion. There were 77 million shares outstanding, trading at $29 per share.

A. Estimate the cash flows to equity in 2014 and 2015.

B. Estimate the cash flows to the firm in 2014 and 2015.

C. Assuming that revenues and all expenses (including depreciation and capital expenditures) increase 6%, and that working capital remains unchanged

in 2016 estimate the projected cash flows to equity and the firm in 2016. (The firm is assumed to be at its optimal financial leverage.)

D. How would your answer in (c) change if the firm planned to increase its debt ratio in 2016 by financing 75% of its capital expenditures (net of

depreciation) with new debt issues?