Interest Rate

Interest Rate

Question one:

Given that the interest rate is 4% compound interest and that we deposit 1,000 each year for ten years, the following table summarizes the results:

year

principle amount

additional deposit

interest rate

interest earned

year end amount

1

1000

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Interest Rate

0

4%

40

1040

2

1040

1000

4%

81.6

2121.6

3

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Interest Rate

2121.6

1000

4%

124.864

3246.464

4

3246.464

1000

4%

169.85856

4416.32256

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Interest Rate

5

4416.32256

1000

4%

216.6529024

5632.975462

6

5632.975462

1000

4%

265.3190185

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Interest Rate

6898.294481

7

6898.294481

1000

4%

315.9317792

8214.22626

8

8214.22626

1000

4%

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Interest Rate

368.5690504

9582.795311

9

9582.795311

1000

4%

423.3118124

11006.10712

10

11006.10712

1000

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Interest Rate

4%

480.2442849

12486.35141

At the end of the ten years we will have 12,486.35141.

Question two:

Given that we invest 500 and that we make a 500 investment each year for 40 years, we determine the value in the account after 40 years: the following table sumarises the interest rates earned and total amounts for the first two and last two years:

principle

interest rate

interest earned

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Interest Rate

total principal

additional deposit

1

500

0.12

60

560

500

2

1060

0.12

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Interest Rate

127.2

1187.2

500

39

342005.0984

0.12

41040.6118

383045.7102

500

40

383545.7102

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Interest Rate

0.12

46025.48522

429571.1954

Therefore when one retires after 40 years the total amount will be 429571.1954

Question 3:

Given that the rate of interest is 9% compounded on a monthly basis, and that the amount borrowed is 70,000 and finally this is to be paid over a 15 year period per month. We first determine the amount to be paid each month A which is determined as follows:

A ={(IXP)(1+I)n}/ { (1+I)n – 1}

Where n is the number of months which is determined by multiplying 15 times 12, this gives us

180. I is the interest rate per year divided by 12 and P is the rpicncipal amount. After calculation the amount paid per month amount to 709.9866, we therefore sumarise the two month amortization period as follows:

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Interest Rate

month

principal

interest

P plus I

accumulated principal payment

accumulated interest payment

balance

0

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Interest Rate

70,000

1

184.9866089

525

709.9866089

184.9866089

525

69,290

2

190.3115085

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Interest Rate

519.6751004

709.9866089

375.2981174

1044.6751

68,580

Question 4:

Secured short term credit is a form of borrowing whereby an individual has to pledge an asset to secure the loan and if the amount is not paid bvack then the asset can be sold in order to recover the debt owned. For the unsecured short term credit the borrower does not pledge any property in order to acquire a loan.

Question 5:

A.

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Interest Rate

Current ration:

The current ratio is calculated by dividing the current assets by the current liabilities, in our case the current assets = 40,000 while current liabilities = 23,000

Current ratio = 40,000 / 23,000 = 1.739130435

Current ratio = 1.739

Return on total assets:

Return on assets = net income / total assets

Net income = 10,291

Total assets = 60,000

Return on asset = 10291 / 60,000 = 0.171516667

Return on assets = 0.1715

Net working capital:

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Interest Rate

Working capital = current assets – current liabilities

Current assets = 40,000

Current liabilities = 23,000

Working capital = 40,000 – 23,000 = 17,000

Working capital is 17,000

b.

if the comp[any decides to pay off its notes payable and issue a $12,000 in long term debts then the current liabilities will reduce by 12,000 while the long term liabilities will increase by 12,000. Net income was $5,500.

Current ratio

= Current assets / current liabilities

= 40,000/11,000 = 3.636363636

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Interest Rate

The current ratio is 3.6363 which is higher than the industry average which is 2.40

Net working capital

Working capital = current assets – current liabilities

Current assets = 40,000

Current liabilities = 11,000

Working capital = 40,000 – 11000 = 29,000

Therefore the working capital has increased.

Return on total assets:

Return on assets = net income / total assets

Net income = 5,500

Total assets = 60,000

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Interest Rate

Return on assets = 5,500/60,000 = 0.091666667

Return on assets has decreased.

c.

The company has improved on its liquidity through an increase in the working capital, however the profitability of the company has declined and this is evident from the decline in the return on total assets.

Question 6:

Given that the selling price of one rod is $132, variable cost is $80, average fixed cost is $90,000 we can determine the break even point, the break even point is the point where the cost is equal to the revenue, we state the cost and revenue function as follows:

Cost = 90,000 + 80 X where X is the number of rods produced

Revenue = 132 X where X is the number of rods sold

The break even point is the point where

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Interest Rate

Cost = revenue

Therefore the break even point is

90,000 + 80 X = 132 X

90,000 = 52X

X = 1730.769231

The break even point is where the number of rods produced equal 1730.769231

b.

Break even point in dollar sales

We derive it by multiplying the break even number of rods by the selling price

1730.769231 X 132 = 55384.61538

Therefore break even point in terms of sales = 55384.62

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Interest Rate

c.

profit or loss associated with producing 2000 rods and 10,000 rods

2,000 rods

Revenue = 2000 X 132 = 264,000

Cost = 90,000 + 80 (2000) = 250,000

Profit = revenue – cost

=264,000 – 250,000 = 14,000

Profit is equal to 14,000

10,000 rods

Revenue = 10,000 X 132 =1,320,000

Cost = 90,000 + 80 (10,000) = 890,000

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Interest Rate

Profit = 1,320,000 – 890,000 = 430,000

Profit = 430,000

d.

Degree of operation leverage

Degree of operating leverage = change in operating income / change in sales

For the two levels of production the following are the changes

units

operating income

sales

2000

250,000

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Interest Rate

264,000

10000

890,000

1,320,000

change

640,000

1,056,000

leverage

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Interest Rate

0.606060606

Therefore then operation leverage for the two production points is 0.6060

Question 7:

Current ratio

= Current assets / current liabilities

The following table summarizes the current ratio for the two years:

current assets

current liabilities

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Interest Rate

current ratio

1995

40

26

1.538461538

1996

46

28

1.642857143

For 1995 the current ratio was 1.538 while for the year 1996 the current ratio was 1.643

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Interest Rate

Acid test ratio:

The acid test is also known as the quick ratio,

Quick ratio = (current assets – inventory) / (current liabilities – overdrafts)

Current assets =46

Inventory =26

Current liabilities =28

Overdrafts or payables = 10

= (46–26)/(28–10)

= 20/18

= 1.11

Therefore the quick ratio value = 1.111

Long term debt to total capitalization

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Interest Rate

Long term debt to total capitalization = total long term debts / total equity

Long term debts=18

Total equity =40

= 18/40 = 0.45

Therefore the Long term debt to total capitalization is 0.45

Debt ratio

= total liabilities / total assets

The following table summarizes the debt ratio for the two years:

total liabilities

total assets

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Interest Rate

debt ratio

1995

72

100

0.72

1996

74

106

0.698113208

The debt ratio for 1995 was 0.72 while the debt ratio for 1996 was 0.698

Return on assets

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Interest Rate

= net income / total assets

The following table summarizes the ratio for year 1996

Net income = 26 million

Total assets = 100

Return on assets = 26/100 = 0.26

The return on assets = 0.26 for 1996

Return on common equity:

Return on equity = net income / shareholder equity

Return on common equity = net income / common equity

Net income = 26

Common equity = 40

Return on common equity = 26/40 = 0.65

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Interest Rate

Therefore return on sommon equity = 0.65

References:

John Tracy (2004) financial reports, John Wiley and Sons, New York

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