XYZ stock price and dividend history are as follows: An investor buys three shar

Question

XYZ stock price and dividend history are as follows:

An investor buys three shares of XYZ at the beginning of 2013, buys another two shares at the beginning of 2014, sells one share at the beginning of 2015, and sells all four remaining shares at the beginning of 2016.

1.What are the arithmetic and geometric average time-weighted rates of return for the investor?

2 decimal place.

Arithmetic average rate of return: 5.94%

Geometric average rate of return: %

2. What is the dollar-weighted rate of return? (Hint: Carefully prepare a chart of cash flows for the fourdates corresponding to the turns of the year for January 1, 2013, to January 1, 2016. If your calculator cannot calculate internal rate of return, you will have to use trial and error.)

Dollar-weighted rate of return: %

XYZ stock price and dividend history are as follows:

Year Beginning-of-Year Price Dividend Paid at Year-End 2013 $100 $4 2014 120 4 2015 90 4 2016 100 4

An investor buys three shares of XYZ at the beginning of 2013, buys another two shares at the beginning of 2014, sells one share at the beginning of 2015, and sells all four remaining shares at the beginning of 2016.

1.What are the arithmetic and geometric average time-weighted rates of return for the investor?

2 decimal place.

Arithmetic average rate of return: 5.94%

Geometric average rate of return: %

2. What is the dollar-weighted rate of return? (Hint: Carefully prepare a chart of cash flows for the fourdates corresponding to the turns of the year for January 1, 2013, to January 1, 2016. If your calculator cannot calculate internal rate of return, you will have to use trial and error.)

Dollar-weighted rate of return: %

Explanation / Answer

(1) Computation of the arithmetic and geometric average time-weighted rates of return for the investor.We have,

Step1: Computation of the return.We have,

Step2: Computation of the arithmetic average rate of return.We have,

Arithmetic average rate of return = (24.00 - 21.67 + 15.56)/3 = 5.96%

Step3: Computation of the geometric average rate of return.We have,

Geometric mean = [(1+ra) (1+rb)(1+rc)]1/n - 1

Geometric mean = [ (1+0.24) (1- 0.2167)(1+0.1556)]1/3 - 1

Geometric mean =[(1.24)(0.7833)(1.1556)]1/3-1

Geometric mean = [1.129589]1/3 -1

Geometric mean = 1.0392 - 1 = 0.0392*100 = 3.92%

(2) Computation of the dollar-weighted rate of return.We have,

300 = -228/(1+r) + 110/(1+r)2 + 416/(1+r)3

If r = - 1%

Present value of return = -228/(0.99) + 90.90/(0.99)2 +416/(0.99)3

Present value of return = -230.30 + 92.75 + 428.73 = $ 291.18

If r = -2%

Present value of return = -228/(0.98) + 90.90/(0.98)2 +416/(0.98)3

Present value of return = - 232.65+94.65+442.00 = $304

Using the interpolation technique.We have,

r = -0.02 + (-0.02 - 0.01) (304 - 300)/(304 - 291.18)

r = - 0.02 + (-0.03) 4/12.82

r = -0.02 - 0.00936

r = - 0.0294*100 = - 2.94%

Dollar-weighted return = Internal rate of return

Hence, the dollar-weighted return is - 2.94%

Year Return=[(end price - beginning price)+ dividend]/Beginning price *100 Return(%) 2014 [(120-100) + 4]/100*100 24.00 2015 [(90 -120)+ 4]/120*100 - 21.67 2016 [(100 -90) +4]/90*100 15.56

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