**Principals of Investments**

**Problem Set 3**

- King Waterbeds has an annual cash dividend policy that raises the dividend each year by 4%. Last year’s dividend was $0.40 per share. What is the price of this stock if an investor wants a 5% return?
- Staton-Smith Software is a new up-start company and will not pay dividends for the first five years of operation. It will then institute an annual cash dividend policy of $2.50 with a constant growth rate of 5% with the first dividend at the end of year six. What is the price of this stock if an investor wants a 10% return?
- Suppose that the consensus forecast of security analysts of your favorite company is that earnings next year will be E1 = $5.00 per share. Suppose that the company tends to plowback 50% of its earnings and pay the rest as dividends. If the Chief Financial Officer (CFO) estimates that the company’s growth rate will be 8% from now onwards, answer the following questions.

**Principals of Investments**

3.1 If your estimate of the company’s required rate of return on its stock is 10%, what is the equilibrium price of the stock?

3.2 Suppose you observe that the stock is selling for $50.00 per share, and that this is the best estimate of its equilibrium price. What would you conclude about either (i) your estimate of the stock’s required rate of return; or (ii) the CFO’s estimate of the company’s future growth rate?

3.3 Suppose your own 10% estimate of the stock’s required rate of return is shared by the rest of the market. What does the market price of $50.00 per share imply about the market’s estimate of the company’s growth rate?

- Consider a bond paying a coupon rate of 8% per year annually when the market interest rate is 6% per year. The bond has six years until maturity and its par value is $1000. What are the bond’s price today (P0), its price 1 year from now after the next coupon is paid (P1), and its holding period return (r) over the 1-year period? Assume market interest rate stays the same after 1 year.
- Answer question 4 if the market interest rate drops to 5% after 1 year?
- You have just bought a 5 year 10% annual coupon bond with a par value of $1000 at a price of $963.04

6.1 What is the YTM of the bond?

6.2 Immediately after you bought the bond, the market interest rate changed to 8% per year. If the interest rate does not change from this level for the next 5 years, what is the realized compound yield from the bond if you hold it until maturity?

**Principals of Investments**

- The prices of zero coupon bonds (all with face value of $1,000) maturing in years 1, 2, 3 are given below. Time to Maturity 1 2 3

Price 961.54 890.00 816.30

What is the YTM on a risk-free 5% annual coupon bond (face value of $1,000) that matures in three years?

- Calculate the term structure of interest rates (y1, y2, y3, y4) and implied forward rates (1f1, 2f1, 3f1) based on the following discount bond prices.

Maturity | 1 | 2 | 3 | 4 |

Price | 961.53 | 907.03 | 839.62 | 762.90 |

- A 5-year bond with YTM of 12% and par value of $1000 pays an 8% annual coupon.

9.1 What is the bond’s price?

9.2 What is the bond’s duration?

9.3 Use the duration to calculate the effect of 0.2% increase in the market interest rate on the bond’s price.

9.4 Recalculate the bond’s price on the basis of a 12.2% YTM.

- Construct profit diagrams or profit tables on expiration to show what position in IBM puts, calls and/or underlying stock best expresses the investor’s objectives described below. Assume IBM currently sells for $150 so that profit tables for stock prices between $100 and $200 (in $10 increments) are appropriate. Also assume that “at the money” puts and calls cost $15 each.

**Principals of Investments**

An investor wants upside potential if IBM increases but wants (net) losses no greater than $15 if prices decline.

An investor wants to capture profits if IBM declines in price but wants a guaranteed limited loss if prices increase.

An investor wants to profit if IBM’s upcoming earnings announcement is either unexpectedly good or disappointingly bad.

An investor already owns IBM (at a price of $150) and wants to protect against price declines but wants to retain upside if prices rise. Only one transaction is permitted here.

- Suppose a European call option has an exercise price of $100 and the underlying stock has a price of

$100. The stock will pay no dividends over the next year. The option expires in 1 year and the continuously compounded interest rate is 6%.

**Principals of Investments**

Is the call option in-the-money, at-the-money or out-of-money?

What will the option be worth on expiration if the stock price in 1 year is $110? What if the stock price is $90?Will the value of the option be larger or smaller if the volatility of the underlying asset is higher than otherwise?

Will the value be larger or smaller if the option has 3 months rather than 6 months to expiration?

Suppose there is a European put option on the same underlying stock that that has an exercise price of $100 and expires in 1 year. What’s the price of the put option if the price of the call option is $6.5? APA.