# Issue Price and Secondary Market Prices of CDs

CDs are issued as interest bearing instruments. For example suppose that South Bank, a natural borrower of six-month Australian dollars is contacted by a money broker, who says that a lender is willing to lend six month Australian dollars at 61/16 % or alternatively will buy paper at 6%.

### Primary Issue

South Bank agrees to issue a CD, and a deal is agreed for 20 milion Australian dollars (4 x AUD 5 Million). The lender/investor pays South Bank AUD 20 million (5 million for each CD).

Suppose there are 183 days in the six-month period. Each individual CD will promise to pay the presenter (bearer) at maturity the face value of the CD, AUD 5 million, plus interest of AUD 150,410.96 (day base= 365 days).

Note

Interest at 6% is calculated for each CD or AUD 5 million, as

AUD 5 million x (6/100) x (183/365)

### Secondary Market Pricing

Let’s now suppose that buyer of the paper is Omega Bank, and that three months after the purchase, Omega Bank wants to sell two of the CDs.

Through a broker, a buyer has been identified who would be willing to buy the paper to yield 5% over the remaining term to maturity of 91 days.

Each CD has a defined value at maturity of AUD 5,150,410.96. A method has to be established for pricing such instruments (i.e., with a fixed terminal value) in the secondary market.

#### Method 1

An appropriate formula to use is the formula used for discount securities:

V = F/(1+(D/B*Y/100))

Where:

V is the secondary market price of the CD

F is the amount payable to the CD holder at maturity, i.e., principal plus accrued interest

D is the number of days to maturity

Y is the investment yield for the CD holder

B is the day base

In our example the CD buyer requires a yield of 5%.Each CD will therefore be sold at a price of:

AUD 5,150,410.96/ [1 + (91/365 x 5/100 )]

\= AUD 5086997.70

#### Method 2

Another formula given in the formula sheet for your examination is a formula for calculating the proceeds of secondary market CDs.

Proceeds = FV   x  [(Coupon x Original life) + (B x 100)] / [(YTM x Days remaining) + (B x 100)]

Where:

FV  = face value of the CD

Coupon = interest rate payable on the original deposit (7.5% =7.5 etc)

YTM = Yield to Maturity, i.e., the interest rate yield required by the buyer in the secondary market (8.5%= 8.5 etc)

B= day base

In this example:

Proceeds = AUD 5 million x [(6 x 183)  + (365 x 100)] / [(5 x 91) + (365 x 100)]

\=AUD 5 Million x (37,598/36955)

\= AUD 5086997.70

The sale price of a CD can be higher or lower than its original purchase price, depending on how interest rates have changed between the purchase and resale date.

As a general rule however the resale price should usually be higher than the original purchase price. Given stable interest rates the value of a CD should rise gradually up to maturity. However if there is an increase in interest rates the value of a CD can fall.

In summary you should note that for primary CDs (new issue) the methodology for calculating interest is the same as for straightforward interbank deposits. The pricing methodology for secondary CDs is either the ‘discount to yield’ formula or the formula for calculating the proceeds of a secondary market CD.

### Practice Problem

Attempt your own solution to this problem before checking the answer below.

A USD is issued at 5% in USD 1000000, 4/3/96 -29/11/96.On 2,June 1996, you buy the CD at 71/4%.

#### Required

a)     What is the purchase price you have to pay?

b)     If you were the seller of the CD what was your yield for the period in which you held the CD?

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