10(a) Suppose a stock had an initial price of $86 per share, paid a dividend of
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Question
10(a)
Suppose a stock had an initial price of $86 per share, paid a dividend of $1.80 per share during the year, and had an ending share price of $94.
Compute the percentage total return. (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
10(b)
Using the returns shown above, calculate the average returns, the variances, and the standard deviations for X and Y (Do not round intermediate calculations and round your final percentage answer to 2 decimal places. (e.g., 32.16) and variances to 5 decimal places. (e.g., 32.16161))
10(c)
You purchased a zero coupon bond one year ago for $173.85. The market interest rate is now 9 percent. If the bond had 20 years to maturity when you originally purchased it, what was your total return for the past year? Assume semiannual compounding. (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
10(d)
You bought a share of 3 percent preferred stock for $97.48 last year. The market price for your stock is now $99.69
10(e)
You bought a stock three months ago for $43.28 per share. The stock paid no dividends. The current share price is $46.51
Suppose a stock had an initial price of $86 per share, paid a dividend of $1.80 per share during the year, and had an ending share price of $94.
Explanation / Answer
Suppose a stock had an initial price of $86 per share, paid a dividend of $1.80 per share during the year, and had an ending share price of $94.
Compute the percentage total return.
Income = 1.80+(94-86)/86 = 1.80+8/86 = 9.80/86 = 11.39%
Using the returns shown above, calculate the average returns, the variances, and the standard deviations for X and Y
Arithmetic average X: (13 + 27 - 20 + 8 + 10) / 5 = 38 / 5 =7.6%
Arithmetic average Y: (18 + 28 - 25 + 10 + 19) / 5 = 30 / 5 =6%
VarianceX = averaged square of difference from mean = [(13 - 7.6) ^ 2 + (27 - 7.6) ^ 2 + (-20 - 7.6) ^ 2 + (8 - 7.6) ^ 2 + (10 - 7.6) ^ 2] / 5 = 234.64
Variance Y = averaged square of difference from mean = [(13 - 7.6) ^ 2 + (27 - 7.6) ^ 2 + (-20 - 7.6) ^ 2 + (8 - 7.6) ^ 2 + (10 - 7.6) ^ 2] / 5 = 354.80
StDev = Sqrt(varinace)x = 234.64 = 15.32
StDev = Sqrt(varinace)Y =354.80= 18.84
You purchased a zero coupon bond one year ago for $173.85. The market interest rate is now 9 percent. If the bond had 20 years to maturity when you originally purchased it, what was your total return for the past year? Assume semiannual compounding
It will be Zero as bonmd is not paying any coupon.
You bought a share of 3 percent preferred stock for $97.48 last year. The market price for your stock is now $99.69?
It's the return on your total position PLUS the dividend received over the year divided by initial investment.
In this case: (99.69-97.48+3)/97.48. = 5.34%
Note: the 3 is the coupon payment on $100 face value of preferred stock (Check if there is a face/par value in the question, if not, usually the face value is $100. If there is, multiply the face value by 0.03 and that's the coupon instead of the 3 I have used
You bought a stock three months ago for $43.28 per share. The stock paid no dividends. The current share price is $46.51
The gain on this investment is $46.51 - 43.28= $3.23
The percentage gain is 3.23/43.28= 0.0746 = 7.46% for 3 months.
The APR is twice that, or 14.193
The EAR is: (1+i/n)^n - 1 = (1+0.0.746)^2 - 1 = (1.0746)(1.0746) -1 = 0.15483 = 15.48%
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