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kramer
3 years ago
5

Dirty Don's Bicycle Shop is current financed with 100% equity. The firm currently has 100,000 shares of common stock outstanding

, selling for $50 per share. Don is considering a capital restructuring project, where the firm would be financed with 45% debt and 55% equity. How many bonds would Don have to sell at par value? (Remember that par value of a bond is $1,000).
Business
1 answer:
Stella [2.4K]3 years ago
6 0

Answer:

Number of bonds to raise = 2250

Explanation:

given data

current financed = 100% equity

common stock outstanding = 100,000 shares

selling = $50 per share

debt = 45%

equity =55%

par value of a bond = $1,000

to find out

How many bonds would Don have to sell at par value

solution

we get here first the value of equity that is express as

value of equity = Number of shares × Price per share .................1

put here value

value of equity = 100,000 × $50

value of equity = $5,000,000

and

financed with bonds = 45 % of value of equity

financed with bonds = 45 % × $5,000,000

financed with bonds = $2,250,000

so

Number of bonds to raise is express as

Number of bonds to raise = \frac{2,250,000}{1000}

Number of bonds to raise = 2250

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Here are returns and standard deviations for four investments. Return (%) Standard Deviation (%) Treasury bills 4.5 0 Stock P 8.
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Answer:

a. Standard deviation of the portfolio = 7.00%

b(i) Standard deviation of the portfolio = 30.00%

b(ii) Standard deviation of the portfolio = 4.00%

b(iii) Standard deviation of the portfolio = 21.40%

Explanation:

Note: This question is not complete. The complete question is therefore provided before answering the question as follows:

Here are returns and standard deviations for four investments.

                                  Return (%)           Standard Deviation (%)

Treasury bills                4.5                                    0

Stock P                          8.0                                   14

Stock Q                        17.0                                  34

Stock R                       21.5                                    26

Calculate the standard deviations of the following portfolios.

a. 50% in Treasury bills, 50% in stock P. (Enter your answer as a percent rounded to 2 decimal places.)

b. 50% each in Q and R, assuming the shares have:

i. perfect positive correlation

ii. perfect negative correlation

iii. no correlation

(Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.)

The explanation to the answer is now provided as follows:

a. Calculate the standard deviations of 50% in Treasury bills, 50% in stock P. (Enter your answer as a percent rounded to 2 decimal places.)

Since there is no correlation between Treasury bills and stocks, it therefore implies that the correlation coefficient between the Treasury bills and stock P is zero.

The standard deviation between the Treasury bills and stock P can be calculated by first estimating the variance of their returns using the following formula:

Portfolio return variance = (WT^2 * SDT^2) + (WP^2 * SDP^2) + (2 * WT * SDT * WP * SDP * CFtp) ......................... (1)

Where;

WT = Weight of Stock Treasury bills = 50%

WP = Weight of Stock P = 50%

SDT = Standard deviation of Treasury bills = 0

SDP = Standard deviation of stock P = 14%

CFtp = The correlation coefficient between Treasury bills and stock P = 0.45

Substituting all the values into equation (1), we have:

Portfolio return variance = (50%^2 * 0^2) + (50%^2 * 14%^2) + (2 * 50% * 0 * 50% * 14% * 0) = 0.49%

Standard deviation of the portfolio = (Portfolio return variance)^(1/2) = (0.49%)^(1/2) = (0.49)^0.5 = 7.00%

b. 50% each in Q and R

To calculated the standard deviation 50% each in Q and R, we first estimate the variance using the following formula:

Portfolio return variance = (WQ^2 * SDQ^2) + (WR^2 * SDR^2) + (2 * WQ * SDQ * WR * SDR * CFqr) ......................... (2)

Where;

WQ = Weight of Stock Q = 50%

WR = Weight of Stock R = 50%

SDQ = Standard deviation of stock Q = 34%

SDR = Standard deviation of stock R = 26%

b(i). assuming the shares have perfect positive correlation

This implies that:

CFqr = The correlation coefficient between stocks Q and = 1

Substituting all the values into equation (2), we have:

Portfolio return variance = (50%^2 * 34%^2) + (50%^2 * 26%^2) + (2 * 50% * 34% * 50% * 26% * 1) = 9.00%

Standard deviation of the portfolio = (Portfolio return variance)^(1/2) = (9.00%)^(1/2) = (9.00%)^0.5 = 30.00%

b(ii). assuming the shares have perfect negative correlation

This implies that:

CFqr = The correlation coefficient between stocks Q and = -1

Substituting all the values into equation (2), we have:

Portfolio return variance = (50%^2 * 34%^2) + (50%^2 * 26%^2) + (2 * 50% * 34% * 50% * 26% * (-1)) = 0.16%

Standard deviation of the portfolio = (Portfolio return variance)^(1/2) = (0.16%)^(1/2) = (0.16%)^0.5 = 4.00%

b(iii). assuming the shares have no correlation

This implies that:

CFqr = The correlation coefficient between stocks Q and = 0

Substituting all the values into equation (2), we have:

Portfolio return variance = (50%^2 * 34%^2) + (50%^2 * 26%^2) + (2 * 50% * 34% * 50% * 26% * 0) = 4.58%

Standard deviation of the portfolio = (Portfolio return variance)^(1/2) = (4.58%)^(1/2) = (4.58%)^0.5 = 21.40%

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Answer:

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