Question

• Now, it is end of 2018, Ron has been investing with Bloom mutual fund for 4 years now. This morning, Ron was reviewing his investment statements and show the following information (Please ignore any fund expenses info. in solving this question) Year Beginning balance Ending balance Dividends per share No. Shares Share price No. Shares Share price 2015 20,000 15 20,000 16 0.50 2016 20,625 16 20,625 13.75 0.60 2017 21,525 13.75 21,525 17 0.632 2018 22,325 17 22,325 18 0.80 (please notice that the dividends received at the end of each year have been used to purchase new shares at the beginning of the following year)

What is the dollar weighted average return of Ron during the period 2015-2018?

A. 7.58%

B. 8.76%

C. 10.38%

D. 11.53%

Assuming that the dollar weighted return is Ron’s nominal rate of return, what is Ron’s real rate of return if the annual rate of inflation during the investment period is 3%?

A. 5.59%

B. 11.76%

C. 10.76%

D. 1.92%

Answer 1

Year	Opening balance			Closing balance			dividend		Return
	share	Rate$	Amount$	Share	Rate $	Amount$	Rate$	Amount$	(B+C-A)/A
			(A)			(B)		(C)
2015	20,000	15	300000	20000	16	320000	0.50	10,000	10%
2016	20625*	16	3,30000	20625	13.75	283593.75	0.60	12375	-10.35%
2017	21525**	13.75	295968.75	21525	17.00	365925	0.632	13603.8	28%
2018	22325***	17	379525	22325	18	401850	0.80	17860	10.59%

*20625= 20,000+10,000/16

** 20625+12375/13.75

*** 22375=21525+13603.8/17

Weighted average return=(10x1 -10.35x2 +28x3   +10.59x4)/ 1+2+3+4   =11.53%

And hence the correct answer is option is “D”

(B) Calculation of real rate of return :

Real rate of return ={(1+nominal return)/(1+inflation rate)} - 1           

Where nominal return= 11.53%and inflation rate =3% for 4 years or 0.75% P.A.

Substituting this value in the above formula we get –

Real rate of return= {(1+11.53%/0.75%)} - 1    = 10.7%

Therefore real rate of return =10.7% and the answer is option “C”