How much could you take out each year and still keep

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Lesson 1: Financial Economics

1.1 Households make four kinds of economic decisions (textbook, pp.4–5). Consider two households, one with childrenaged 6 and 8, and the other with “children”aged26 and 28, that areotherwise identical. Usingthe four economic decision categories, discuss how these households’ financial decisions would be similar and how they would be different.

1.2 Three friends have just graduated with Bachelor of Management degrees fromAthabasca University. One wants to start a restaurant but is worried about the potential liability involved with serving food to other people. The second wants to work as a subcontractor in a building trade and expects to have her potential liability covered by the contractor’s insurance plan and through the Workers’ Compensation Board.

The third wants to team up with a couple of other graduates to create a financial services firm to provide insurance, financial planning services,and bookkeeping assistance. She wants to make sure that the partners have a strong incentive to work together to make good decisions and to grow the business for the benefit of all the service providers.

What form of business organization (textbook, pp. 8–9) would you suggest for each friend, and why?
 
Lesson 2: Financial Markets and Institutions

2.1 Adam Smith is often called the father of economics. His famous book, The Wealth of Nations, talks about an “invisible hand” thatautomatically allocates goods to the persons bestable to put them to good use. The invisible hand operatesthrough the price mechanism for goods and services, so that individuals who trade on the market, while seeking only their own good, actually allocatesociety’s resources efficiently.

Applied to modern capital markets, his ideas would imply that these markets would efficiently allocate investment capital to the firms thatwould use them most efficiently in producing goods and services for society—but only if they were left to operate without state intervention.

What benefits would be created if modern governments reduced financial regulations substantially in accordance with Smith’s thinking? From an ethical perspective, what societal costs might be created?

2.2 Consider a business firm, organized as a proprietorship, which has $100,000 invested in assets, a bank loan of $80,000, and $20,000 personal capital invested by the proprietor. Briefly describeand quantify the risk each party faces if the firm becomes insolvent.

2.3 The classic application of market failures ascribed to adverse selection and moral hazard were found in the health insurance markets.
Adverse selection caused market failure in health insurance because insurers were unaware of the health risks their customers faced. They overcame this market failure by taking detailed medical histories and asking about risky practices such as smoking or extreme sports.

Moral hazard caused market failure because insurers weren’t able to monitor customer behaviour(e.g., weight gain, drug use, taking up extreme sports) after customers signed a contract at a fixed price. This risk of market failure was commonly mitigated through co-payment terms where the customer had to pay part, but not all, of the costs of treatment.

How would these two kinds of market failure apply to owners and managers of business firms in absence of any measures to alleviate the risks?

What measures have been taken, or could be taken, to reduce adverse selection and moral hazard between owners and managers of business firms? Hint: consider who has an information advantage in this setting.
 
Lesson 3: Managing Financial Health and Performance

3.1 Use the information in the table below to calculate the following ratios.Discuss the results to compare the financial positions of the two firms:

Complete the empty frames in the following table and show your work below (identify calculations by letter).For example,Spaling’s interest expense can be inferred from EBIT and Times interest earned, since TIE = EBIT / Interest expense.

Calculation for A:

EBIT = 300,000, TIE = 30, so 30 = 300,000 / Interest expense, and Interest expense = 300,000 / 30 = 10,000

 

Spaling

Preston

EBIT (Earnings before interest and taxes)

300,000

190,000

Interest expense

A

15,000

Net income

200,000

J

Dividend payout ratio

35%

K

Retention ratio

B

60%

Dividends declared during the year

C

40,000

Sales

3,000,000

L

Average assets during the year

D

1,500,000

Average debt during the year

700,000

M

Average shareholders' equity during the year

1,800,000

N

Asset turnover ratio

E

1.3333

Debt ratio

F

0.3333=1/3

Return on sales

G

0.095

Return on assets

0.08

O

Return on equity

H

0.10

Market price per share, beginning of year

20

P

Market price per share, end of year

15

20

Total shareholder return

I

0.1556

Number of shares outstanding

150,000

50,000

Times interest earned

30

Q

3.2 You put $1000 in a savings account at 10% annually compounded interest.

a. How much could you take out each year and still keep the original $1000 in the account?Complete the table below to support your conclusion.

Year

Beginning balance

Interest earned (10%)

Withdrawal

Ending balance

1

$1000

 

 

$1000

2

1000

 

 

1000

3

1000

 

 

1000

4

1000

 

 

1000

b. If you left half of the interest earnings in the account, at what rate would the balance grow from year to year?Complete the table to show your calculations.

Year

Beginning balance

Interest earned (10%)

Withdrawal

(50% of interest)

Ending balance

1

1000

 

 

 

2

 

 

 

 

3

 

 

 

 

4

 

 

 

 

 

 

 

 

 

 

 

 

Annual growth rate =

%

c. If you took out 80% of the interest earnings in the account, at what rate would the balance grow each year?Complete the table to show calculations.

Year

Beginning balance

Interest earned (10%)

Withdrawal (80% of interest)

Ending balance

1

1000

 

 

 

2

 

 

 

 

3

 

 

 

 

4

 

 

 

 

 

 

 

 

 

 

 

 

Annual growth rate =

%

3.3 Imagine a corporation with $1,000,000 of assets and a debt ratio of 40%. ROE (return on equity) is expected to be 20% for the foreseeable future. Assuming the firm maintainsthe same amount of debt indefinitely (as opposed to keeping the same debt ratio), respond to the following questions.

a. If the firm doesn’t pay out any dividends or re-purchase any shares,what do you expect the firm’s earnings to be for the next three years?

Complete the table to show your calculations.

Year

Beginning balance, equity

Net income

Return on equity = net income /opening equity

Dividends and/or repurchases

Ending balance, equity

1

 

 

%

0

 

2

 

 

%

0

 

3

 

 

%

0

 

b. If the firm doesn’t pay any dividends or re-purchase any shares, at what rate would the firm grow from year to year?

Complete the table.

Year

Beginning balance, equity

Net income

Return on equity = net income /opening equity

Dividends and/or repurchases

Ending balance, equity

Growth rate

1

 

 

%

0

 

%

2

 

 

%

0

 

%

3

 

 

%

0

 

%

c. If the firm pays 50% of its earnings as dividends, at what rate would the firm grow from year to year?

Complete the table.

Year

Beginning balance, equity

Net income

Return on equity = net income /opening equity

Dividends

Ending balance, equity

Growth rate

1

 

 

%

 

 

%

2

 

 

%

 

 

%

3

 

 

%

 

 

%

d. If the firm uses 80% of its earnings to re-purchase shares from its shareholders, at what rate would the firm grow from year to year?

Complete the table.

Year

Beginning balance, equity

Net income

Return on equity = net income /opening equity

Repurchases

Ending balance, equity

Growth rate

1

 

 

%

 

 

%

2

 

 

%

 

 

%

3

 

 

%

 

 

%

e. If the firm pays 50% of its earnings as dividends and uses an additional 20% of its earnings to repurchase shares from its shareholders, at what rate would the firm grow from year to year?

Complete the table.

Year

Beginning balance, equity

Net income

Return on equity = net income /opening equity

Dividends

Repur-chases

Ending balance, equity

Growth rate

1

 

 

%

 

 

 

%

2

 

 

%

 

 

 

%

3

 

 

%

 

 

 

%

f. If you have done the calculations correctly in the tables above, you should have the same growth rate every year. How long could the company grow at this constant rate if all the given factors remained the same?

Lesson 4: Allocating Resources Over Time

4.1 Assume that the correct discount rate for the following cash flows is 8%. Today is January 1, year 1. Calculate the present value of each of the following cash flows.

a. $50 at the end of 3 years, i.e., December 31, year 3

b. $50 at the end of 100 years, i.e., December 31, year 100

c. $50 received at the end of each year for 20 years, i.e., December 31 each year from year 1 to year 20

d. $50 received at the beginning of each year for 20 years, i.e., January 1 each year from year 1 to year 20

4.2 Today is January 1, year 1. Assuming an 8% discount rate, what is the future value of each of the following cash flows?

a. Future value in 3 years of $50 received now, i.e., the value on December 31, year 3

b. Future value in 100 years of $50 received now, i.e., the value on December 31, year 100

c. Future value at the end of 20 years of $50 received each year at the end of the year, i.e., the value at December 31, year 20, with one payment received each December 31 from year 1 to year 20

d. Future value at the end of 20 years of $50 received each year at the beginning of the year, i.e., the value at December 31, year 20, with one payment received each January 1 from year 1 to year 20.

4.3 Today is January 1, year 1. Given a discount rate of 8%, calculate the following values.

a. Present value of a perpetuity (also called a perpetual annuity) of $50 received each year at the end of each year, i.e., each December 31 from now to the end of time

b. Chop the perpetuity from part a into threeparts, and calculate the present value today of each part:

i. Part 1, an annuity of $50 received at the end of each year for 5 years, i.e., each December 31 from year 1 to year 5

ii. Part 2, an annuity of $50 received at the end of each year for 10 years, i.e., each December 31 from year 6 to year 15

iii. Part 3, a perpetuity of $50 received at the end of each year from year 16 to the end of time, i.e., each December 31 from year 16 and forever thereafter.

c. Add the parts of b together, and ensure that the total is the same as the value calculated in part a.

Hint: you might find a timeline helpful in answering this question.

You need two things for a timeline:times and cash flows.

Here, you have annual cash flows thatcontinue indefinitelyin part a. Youthen split them up into three partsin part b. So, in the top line record Time 0 1 2 3 4 5 6 ... 15 16 ... forever. Use tabs to separate the numbers at even intervals. Then, in the line beneath, add cash flows, and enter the $50 payments under the appropriate time. Part a would have $50 payments under each time, to continue indefinitely.
Then, for parts b,i, ii, and iii,  set up another timeline and enter the three parts, perhaps in three separate timelines, and you should be able to see that each payment in your part a timeline has exactly one corresponding payment in one of your three timelines for part b.

4.4 
a. Today is January 1, year 1. Vivian is 20 years old today. Vivian is going to put $1000 into her savings account on her 21st birthday and on every birthday after that for 20 payments (i.e.,until her 40th birthday). She will earn 5%, paid annually. After she makes her final deposit, how much money will be in the account after the bank depositsher interest into the account, i.e., on January 1, year 21, the day she turns 40, after she makes her 20th payment?

b. Calculate how much money she could take out each year for the next 20 years, from her 41st birthday till her 60th birthday, assuming she still earns 5%, takes out the same amount each year, and drains the account to exactly $0 after taking her 20th payment.

Reading- Financial Economics By Zvi Bodie, Robert C. Merton and David L. Cleeton.

Reference no: EM132374062

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