Question

On the advice of your uncle, you purchased 10 shares of a well-established U.S.-based corporate stock for $20.5 per share. After 1 quarter, you received $0.25 per share dividends each quarter for 2 years. At that point, the stock price had gone down in a short-term recession, so you purchased 10 more shares at $14 per share. The stock continued to pay 25¢ a share on all 20 shares. After 3 years (12 quarters), you decided to sell the stock since it had increased in market value to $22 per share. Make the following assumptions: (a) no commissions for the purchase or sale of the stock, (b) no government taxes on the dividends, and (c) quarterly compounding of the rate of return. What is the effective interest rate per year?

The effective interest rate per year is __________________%.

Answer 1

^{A clarifying assumption I'm making is that the period of 3 years after which all shares are sold includes the first 2 years. Hence dividend is on 10 shares for 8 quanrters, adn on 20 shares for 4 quarters. Now we can treat each quarter as a period and calculate IRR for these cash flows in step 1. Pls see table below for the cash flows and IRR. In step 2, we just need to annualize the rate of interest per period by using (1+r)^4 - 1, since there are 4 quarters in a year.}

Step 1

Period	Investment	Dividend	Net Cash Flow
0	-205		-205
1		2.5	2.5
2		2.5	2.5
3		2.5	2.5
4		2.5	2.5
5		2.5	2.5
6		2.5	2.5
7		2.5	2.5
8	-140	2.5	-137.5
9		5	5
10		5	5
11		5	5
12	440	5	445
IRR			3.91%

Step 2

Annual rate of return = (1+3.9%)^4 - 1 = 16.54%