Seminar in Financial Services

INSTRUCTIONS:

1.                  Show all calculations where necessary; the final answer carries very little weight in determining your score for a problem.

2.                  Congratulations and best wishes to those who are graduating.

 1.         (25 points)

Firm XYZ is trying to determine the optimal amount of cash to obtain when required.  The opportunity cost of holding cash is 2.75% annually, and the firm has determined that a minimum cash balance (or safety stock) of $1000 is optimal.  Each time the firm obtains new cash supplies, there is a transaction cost of $25.

a.                   If the firm is operating in an environment where cash needs are relatively stable at a daily amount of $500, what is the optimal order quantity for XYZ? (7 points)

b.                  What will be the total cost of holding cash for the year? Make sure you include the cost of holding the safety stock.  (4 points)

c.                   Suppose that the firm is operating in an environment where daily cash needs are variable with a standard deviation of .  Find the target cash balance, and the upper and lower cash balance limits for XYZ.  (10 points)

d.                  What is the critical difference between the model used in (a) and the model used in (c)?  (4 points)

2.         (25 points)

Firm ABC has debt with a face value of $40m (which could be considered to be the exercise price on call and put options on the firm).  The standard deviation of assets is.  The risk-free rate is currently 4.5% and a time to expiration of 30 years is sufficiently long to use for option valuation.  The market value of the firm is $80m.

a.                   Find the market value of debt and equity using the Black-Scholes Option Pricing Model.  (10 points)

b.                  If the firm decides to increase the volatility of its assets to , what will happen to the market values of debt and equity?  Find the new values.    (10 points)

c.                   Briefly explain the conflict between shareholders and bondholders for a firm.  (5 points)

3.         (25 points) 

You are given the following data for treasury securities;

0.5 yrs                                     0%                               4%                               98.039

1.0 yrs                                     4%                               5%                               99.036

Note:  Coupon rates and yields are stated in annual terms.  The 1.0 yr security pays interest semi-annually, and the analysis must be done in semi-annual periods.  YTM denotes yield to maturity.

a.                                           Find the zero coupon rates of return  and (10 points)

b.                                          Use the zero-coupon rates to calculate the forward rates  and .  (10 points)

c.                   Graph the yield curve and state the market’s expectations about future interest rates.  (5 points)