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Question:

Assume that you would like to purchase 100 shares of preferred stock that pays an annual dividend of $6 per share. However, you have limited resources now, so you cannot afford the purchase price. In fact, the best that you can do now is to invest your money in a bank account earning a simple interest rate of 6% but where interest is compounded daily (assume a 365-day year). Because the preferred stock is riskier, it has a required annual rate of return of 12%. (Assume that this rate will remain constant over the next 5 years.) For you to be able to purchase this stock at the end of 5 years, how much must you deposit in your bank account today, at t = 0?
a.2985
b.4291.23
c.3138.52
d.3704.18
e.4831.25

Answer:
I say d. 3704.18. Here's why I think that:
- The information says that the required rate of return is 12%. I believe that means the price of the stock is $50, since 12% of $50 is the $6 that's being paid. ($6/.12=$50)
- Preferred stock is in many ways more like a bond than a stock. The price of the stock doesn't go up and down much, so it will probably still be $50 in 5 years. (The primary benefit of a preferred stock is the dividends it pays.) I think that's what they're saying with the "assume this rate will remain constant" statement.
- To buy 100 shares of a $50 stock, you will need $5000 (not including commissions, which I guess they're ignoring).
- The formula for compounded interest is (1 plus the rate for one period) to the "number of periods" power or (1+r)^p.
- In this case, the period is one day since that's how often the interest is compounded.
- 6% annual simple interest is .06/365 per day, so that will be r
- 5 years at 365 days per year is 1825 days, so that will be p
- (1+(.06/365))^1825 = 1.3498255 so that's how much $1 invested today will be worth in 5 years (not including taxes which I guess they're ignoring also)
- So to know how many dollars you need to invest today, you need to divide the amount you need in 5 years by the amount each dollar you invest today will be worth then, in other words $5000/1.3498255 = $3704.18.

If you have to work this hard for the answer, you need a better financial planner.

You don't say the price of the shares now, but with a dividend of $6 I'm guessing between $100 and $200 so if you can't afford them now you certainly won't in 5 years even if you could find a bank paying 6% on $4831.25.
I have to assume I have completely misunderstood your question???
Very funny hrh_grac. But true.

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