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Chapter 17: Q5. (page 368)

Corporations often distribute profits to their shareholders in the form of dividends, which are quarterly payments sent to shareholders. Suppose that you have the chance to buy a share in a fashion company called Rogue Designs for \(35 and that the company will pay dividends of \)2 per year on that share. What is the annual percentage rate of return? Next, suppose that you and other investors could get a 12 percent per year rate of return on the stocks of other very similar fashion companies. If investors care only about rates of return, what should happen to the share price of Rogue Designs? (Hint: This is an arbitrage situation.)

Short Answer

Expert verified

The annual percentage rate of return is 12%.

If the investors care only about rates of return, the share price of Rogue Designs and the other very similar fashion companies will be the same.

Step by step solution

01

Step 1. Annual percentage rate of return

The annual percentage rate of return is the percentage gain or loss (relative to the buying price) over a given period of time, typically a year. The dividends of $2 per year are divided by the price of share $35 and multiplied by 100 to get the annual percentage return of 12%.

02

Step 2. Arbitrage

The other investor could also get a 12% per year rate of return on the stocks of other very similar fashion companies. The share price of Rogue Designs and the other fashion company will become equal. According to the concept of arbitrage, if the rate of returns on the shares of products simultaneously differs, the share price will change to equate the rate of returns.

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Most popular questions from this chapter

Suppose that a risk-free investment will make three future payments of \(100 in one year, \)100 in two years, and $100 in three years. If the Federal Reserve has set the risk-free interest rate at 8 percent, what is the proper current price of this investment? What is the price of this investment if the Federal Reserve raises the risk-free interest rate to 10 percent?

Suppose initially that two assets, A and B, will each make a single guaranteed payment of \(100 in 1 year. But asset A has a current price of \)80 while asset B has a current price of $90.

  1. What are the rates of return of assets A and B at their current prices? Given these rates of return, which asset should investors buy and which asset should they sell?

  2. Assume that arbitrage continues until A and B have the same expected rate of return. When arbitrage ends, will A and B have the same price?

Consider an asset that costs \(120 today. You are going to hold it for 1 year and then sell it. Suppose that there is a 25 percent chance that it will be worth \)100 in a year, a 25 percent chance that it will be worth \(115 in a year, and a 50 percent chance that it will be worth \)140 in a year. What is its average expected rate of return? Next, figure out what the investment鈥檚 average expected rate of return would be if its current price were $130 today. Does the increase in the current price increase or decrease the asset鈥檚 average expected rate of return? At what price would the asset have a zero average expected rate of return?

If the Fed increases interest rates, the SML will shift _______ and asset prices will _______.

  1. down; rise

  2. down; fall

  3. up; rise

  4. up; fall

What determines the vertical intercept of the Security Market Line (SML)? What determines its slope? And what will happen to an asset鈥檚 price if it initially plots onto a point above the SML?
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