Explanation:
To find the dollar-weighted rate of return (Internal Rate of Return, IRR), we set the present value of cash outflows equal to the present value of cash inflows.
Time 0: Buy 1 share for $40. Cash flow = -$40.
Time 1: Receive $4 dividend, buy 1 share for $42. Net cash flow = $4 - $42 = -$38.
Time 2: Receive $4 dividend per share (2 shares = $8) and sell 2 shares at $43 (2 * 43 = $86). Net cash flow = $8 + $86 = $94.
The equation is: -40 - 38/(1+r) + 94/(1+r)^2 = 0
Let x = 1/(1+r): 94x^2 - 38x - 40 = 0 Using the quadratic formula, x = [38 ± sqrt((-38)^2 - 4 * 94 * (-40))] / (2 * 94) x = [38 ± sqrt(1444 + 15040)] / 188 x = [38 ± 128.39] / 188 Taking the positive root: x ≈ 166.39 / 188 ≈ 0.88505 Since x = 1/(1+r), 1+r = 1 / 0.88505 ≈ 1.1298 r ≈ 12.98%, which rounds to 13%.
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Q.18 Consider a stock paying dividend of $4 annually that currently sells for $40. You buy one share now and add another share at the end of the year when the share has a price of $42. Assume that you hold both shares until the end of year 2, at which point you sell each share for $43. Calculate the dollar-weighted rate of return on your investment.
A
13%
B
10%
C
19.5%
D
15%