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Nataly [62]
3 years ago
5

Resolve (7x+19)/(x+1)(x+5) into partial fraction​

Business
1 answer:
Volgvan3 years ago
5 0

Answer:

\dfrac{7x+19}{(x+1)(x+5)}=\dfrac{3}{x+1}+\dfrac{4}{x+5}

Explanation:

The given expression is  

\dfrac{7x+19}{(x+1)(x+5)}

We need to resolve this into partial fraction.

The form of the partial fraction decomposition is

\dfrac{7x+19}{(x+1)(x+5)}=\dfrac{A}{x+1}+\dfrac{B}{x+5}        ...(1)

\dfrac{7x+19}{(x+1)(x+5)}=\dfrac{A(x+5)+B(x+1)}{(x+1)(x+5)}

7x+19=Ax+5A+Bx+B

7x+19=(A+B)x+(5A+B)

On comparing both sides, we get

A+B=7      ...(2)

5A+B=19    ...(3)

Subtract (2) from (3), we get

4A=12

A=3

Put A=3 in (1).

3+B=7

B=4

Put A=3 and B=4 in (1).

\dfrac{7x+19}{(x+1)(x+5)}=\dfrac{3}{x+1}+\dfrac{4}{x+5}

Therefore, \dfrac{7x+19}{(x+1)(x+5)}=\dfrac{3}{x+1}+\dfrac{4}{x+5} .

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As a financial manager for WillPower, Inc, you have the following information: a) The company follows a residual dividend policy
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b. Dividend is $3,200,000

c. Dividend Payout ratio is 40.00%

Explanation:

Note: This question is incomplete, and the complete one is as follows:

As a financial manager for WillPower, Inc, you have the following information: a) The company follows a residual dividend policy; b) The total capital budget for next year is likely to be $8,000,000; c) The forecasted level of earnings next year is $8,000,000; d) The target or optimal capital structure is a debt ratio of 40%;

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a. What will be the amount funded with equity for the project ? (Keep the answer to a whole number. Example of answer format: $1,000,000)

b. Compute the amount of the dividend . (Keep the answer to a whole number. Example of answer format: $1,000,000)

c. Compute the dividend pay-out ratio . (Keep the answer to two decimals. Example of the answer format: 55.55%)

The following are therefore the explanation of the answers to the question:

a. What will be the amount funded with equity for the project ? (Keep the answer to a whole number. Example of answer format: $1,000,000)

Given that the target or optimal capital structure is a debt ratio of 40%, this implies that there will be 40% debt finance and 60% (100% - 40%) equity finance. Therefore, we have:

Amount funded with equity = Total capital budget for next year * Percentage of equity finance = 8,000,000 * 60% = $4,800,000

b. Compute the amount of the dividend. (Keep the answer to a whole number. Example of answer format: $1,000,000)

Since the company follows a residual dividend policy, it implies that the earnings available are employed to finance capital expenditure budget first before dividends are paid to the shareholders.

Since amount funded with equity is $4,800,000 as obtained in part a, it implies that this must be deducted first from the forecasted level of earnings next year to obtain the residual that will be paid as dividend as follows:

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Therefore, WillPower, Inc is expected to pay 40% of its earnings as dividend to its shareholders.

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