Question

You purchase a stock for $100 that pays an annual dividend of $5.50. At the beginning of the second year, you purchase an additional share for $130. At the end of the second year, you sell both shares for $140.

Determine the dollar-weighted return and the time-weighted compounded (i.e., geometric) return on this investment. Repeat the process but assume that the second share was purchased for $110 instead of $130.

Why do the rates of return differ?

Please show how to solve within excel and provide the formulas

Answer 1

Dollar weighted retrun is also known as Internal Rate of Return

Cash flow at:

T0 = -100

T1 = 5.5-130 = -124.5

T2 = 5.5*2+140*2 = 291

Now applying IRR formula in excel:

= IRR(Values, Guess)

IRR = 19.3%

TIme weighted return:

Return in year 1 = (5.5+130-100)/100 = 35.5%

Return in year 2 = (5.5+140-130)/130 = 11.92%

Return = (1.355*1.1192)^(1/2)-1 = 23.15%

IF SECOND SHARE WAS $110 INSTEAD OF $130: Dollar weighted return:

IRR = -100-104.5/(1+i)+291/(1+i)^2 IRR = 26.16%

Time weighted return: Return in year 1 = (5.5+110-100)/100 = 15.5%

Return in year 2 = (5.5+140-110)/110 = 32.27%

Return = (1.155*1.3227)^(1/2)-1 = 23.60%

Reason of difference: Time weighted return calculate the return based on return earned by the stock

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