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
Knowing P0, the bond equivalent yield is computed using
Pf  P0  365 


P0  n 
10000  9700  365 



9700
 180 
 6.2715%
ybe 
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.
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c. What interest rate (or yield) is earned by the lender?
On a bond equivalent yield basis, the yield
Prepo  P0  365 


P0
 n 
10, 000, 000  9,987,950  365 



9,987,950
 30 
 1.4679%
ybe 
9.
Suppose Fed Funds rate is quoted at 1.65%. What is this on a bond-equivalent yield
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. Consider the following data faced by the U.S. Treasury at the sale of its 182-day Tbill on xx/xx/xx. Specify the following items.
182-Day Bill
Issue date xx/xx/xx
Competitive
$3.0 billion 4.975%
Total Offering
$18 billion
$4.0 billion 4.980%
$5.0 billion 4.985%
Noncompetitive Tenders
$1.4 billion
$4.0 billion 4.990%
Competitive Tenders?
$36.0 billion
$7.0 billion 4.995%
$6.0 billion 5.000%
Highest Accepted Rate?
4.995%
$5.0 billion 5.005%
Bid-to-Cover Ratio?
37.4/18 = 2.0778
$2.0 billion 5.010%
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Tenders at High Rate Allocated?
.6/7.0 = 8.5714%
Price Per $100 for this issue?
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%
b.
On slide 9 of Module 3.7, consider the 26-week (i.e., 182-day) T-bill whose Issue Date
was 11-08-2012. Reconcile its Discount Rate % with its Price Per $100, and its Price
Per $100 with its Discount Rate %.
 P n yd 
P0  Pf   f

 360 
 100(182).0015 
 100  

360


 99.924167
yd 
Pf  P0  360 


Pf  n 
100  99.924167  360 


100
 182 
 .0015 or 0.15%

c.
In the case of the 52-week T-bill of 10-18-2012, verify, with a Price Per $100 of
99.818000, that the 0.183 figure in the Investment Rate % column is correct.
Pf  P0  365 


P0  n 
100  99.818000  365 



99.818000  364 
 .001828 or 0.183% (rounded)
ybe 
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d.
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 


400  182 
 3.4615%
yd 
Rounding using .005%, bank should bid 3.465%. Otherwise, if it bid 3.460% it would pay
more than the maximum of $393 million.
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 
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