Question

Three years ago you bought 200 shares of stock trading at $40 per share. One year after you bought the stock, it paid a dividend of $2 per share, which you then immediately reinvested in additional (fractional) shares of stock (at a price of $45 per share, which was the price immediately after the dividend was paid). There were no other dividends or cash flows, and today the stock sells for $52 per share. What is the annualized time-weighted return (i.e, geometric average annual return or CAGR)? Express your answer in decimal form, rounded and accurate to 5 decimal places (e.g., 0.12345).

Answer 1

The TWR = (1 + ) + ( 1 + ) + ..(1 + ) - 1

We will divide the transactions into 2 period

1st : Buying share to getting dividends.

2nd : Reinvesting the dividends to selling the shares.

1st : In the beginning I invested $40 in 200 shares each = 200*40 = $8000

At the end I receive dividend of $2 each on 200 shares = $400 (This is the absolute return on my investment of $8000)

Rate of return during first period = = 0.05 = 5%

2 nd : now the share price has increased upto $45. So now my investment is worth 200*45 = $9000

Also I reinvested $400 (dividend amt) Of which I could buy 8.889 shares (400 / 45 = 8.8889) .

This investment amounts to 8.889 * 45 = $400 Therefore total investment in the beginning = $9400

The total shares are now 208.889

At the end of the period we sell the share at $52. Therefore we receive 52 * 208.889 = $10862.22

The absolute return = 10862.22 - 9400 = $1462.22

Rate of return for the next period = = 0.1556 = 15.56%

Time weighted rate of return = (1 + 0.05) * (1 + 0.1556) - 1

Time weighted rate of return = 0.21338

=

Period	Beginning Fund value	Ending fund value	Absolute return (End - beginning)	Rate of return (Absolute / Beginning)
1st	$8000	$8400	$400	5% = 0.05
2nd	$9400	$10862.22	$1462.22	15.56% = 0.1556