Documents
Resources
Learning Center
Upload
Plans & pricing Sign in
Sign Out

Chapter 7 Recommended End-of-Chapter Problems and Solutions

VIEWS: 17 PAGES: 4

									Chapter 7 Recommended End-of-Chapter Problems and Solutions


      1.    If a 180-day T-bill has a face value of $10,000, calculate its price if purchased at a
            discount “Asked” rate of 6%? Also, what is the T-bill’s bond equivalent yield?

                                             P n y 
                                   P0  Pf   f d 
                                              360 
                                                  10000(180).06 
                                       10, 000                
                                                      360       
                                       $9, 700

                   Now knowing P0, the bond equivalent yield is computed using

                                          Pf  P0  365 
                                    ybe               
                                             P0  n 
                                          10000  9700  365 
                                                             
                                               9700       180 
                                         6.2715%




      8.    Suppose Fargood Corporation engages in a repurchase agreement with The
            National Bank of Nebraska. In the agreement, Fargood sells $9,987,950 worth of
            Treasury securities to the bank and agrees to repurchase the securities in 30 days
            for $10,000,000.

             a. Is this transaction a loan, and if so, who is the borrower and who is the lender?

                The transaction is a reverse-repurchase agreement for the bank because it agrees to
                purchase securities under agreement to resell. The bank is buying the Treasuries
                owned to provide Fargood liquidity. Technically, this is not a loan, but a purchase
                with agreement to resell, but the effect is the same as a loan to a customer.

            b. Is the loan collateralized? What is the collateral? Who holds the collateral
               during the term of the agreement?

                   The bank or an offsite depository would hold the securities (collateral) during the
               contract period. Although technically a purchase/sale, it is in effect a short-term
               collateralized loan.



            c. What interest rate (or yield) is earned by the lender?

                                               1
           On a bond equivalent yield basis, the yield

                                      Prepo  P0  365 
                               ybe                   
                                          P0      n 
                                    10, 000, 000  9,987,950  365 
                                                                 
                                             9,987,950        30 
                                   1.4679%


9.     Suppose 7-day fed funds trade at 1.65 percent annually. What is the yield on fed
       funds on a bond-equivalent basis?

       To compare yields in the fed funds market with those of other money market instruments,
       the fed funds rate must be converted into a bond equivalent yield.

                                               365 
                                   ybe  y ff      
                                               360 
                                                  365 
                                        1.65%        
                                                  360 
                                        1.6729%


a. On slide 9 of Module 3.7, consider the 26-week (in this case 182-day) T-bill whose Issue
   Date was 10-21-2010. Reconcile its Discount Rate % with its Price Per $100, and its
   Price Per $100 with its Discount Rate %.

                              Pf n yd 
                   P0  Pf           
                              360 
                               100(182).00170 
                       100                  
                                     360      
                       99.914056

                          Pf  P0  360 
                   yd                 
                            Pf  n 
                        100  99.914056  360 
                                            
                              100        182 
                       .00170 or 0.170%

b.   In the case of the 52-week T-bill of 10-21-2010, verify that with a Price Per $100 of


                                            2
     99.620833 that the figure in the Investment Rate % column 0.381.

                          Pf  P0  365 
                    ybe               
                             P0  n 
                         100  99.772500  365 
                                             
                            99.772500  364 
                        .002286 or 0.229% (truncated)



c.   Suppose a bank wishes to purchase $400 million face value of 182-day T-bills but is
     only willing to spend $393 million maximum. What should be its Discount Rate %
     bid?

                        400  393  360 
                    yd                
                           400  182 
                       3.4615%

     Rounding using .005%, bank should bid 3.465%. Otherwise, if it bid 3.460% it would pay
     more than to maximum of $393 million.

d.    Consider the following data faced by the U.S. Treasury at the sale of its 182-day T-bill
      on xx/xx/xx. Specify the following items.

             182-Day Bill                              Competitive
               Issue date xx/xx/xx                     $3.0 billion 4.975%

             Total Offering                            $4.0 billion 4.980%
               $18 billion
                                                       $5.0 billion 4.985%
             Noncompetitive Tenders
               $1.4 billion                            $4.0 billion 4.990%

             Competitive Tenders?                      $7.0 billion 4.995%
               $36.0 billion
                                                       $6.0 billion 5.000%
             Highest Accepted Rate?
                4.995%                                 $5.0 billion 5.005%

             Bid-to-Cover Ratio?                       $2.0 billion 5.010%
                37.4/18 = 2.0778

             Tenders at High Rate Allocated?
                 .6/7.0 = 8.5714%

             Price Per $100 for this issue?

                                          3
                  100 – (.04995*182*100/360) = 97.474750

              Investment Rate % for this issue?
                  ((1000 – 974.7475)/974.7475)*(365/182) = 5.1956%

              Lowest Rate?
                 4.975%



e. Suppose $18 million face value of 15-day commercial paper is being sold for
   $17,984,000. What bank discount rate pertains to this situation?

     18  17.984  360 
                        2.1333%
          18      15 

f.   Suppose that on 9/30/2010 the National Debt Held by the Public is $9.1 trillion.
     Roughly, how much of the this would be in the form of T-bills, T-notes, and T-bonds?

                T-bills: 9.1(.20) = $1.82 trillion
                T-notes: 9.1(.50) = $4.45 trillion
                T-bonds: 9.1(.10) = $0.91 trillion




                                            4

								
To top