Lecture 4. Banking products and their pricing Outline 2 4.1. - - PowerPoint PPT Presentation

Part B. Banking products and services

Lecture 4. Banking products and their pricing

Outline

4.1. Deposits pricing

 Simple interest rate  Compounded interest rate  Periodic  Continuous

4.2. Loans pricing

 Interest  Cost of Borrowing  Effective Annual Rate

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4.1. Deposits pricing

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Fixed and Floating interest rate

 Fixed interest does not fluctuate during the fixed

rate period of the contact.

 Floating interest (variable or adjustable rate)

typically change based on a reference rate (a benchmark of any financial factor)

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Fixed and Floating interest rate

When the reference rate is historically low, fixed

rates are normally higher than variable rates because interest rates are more likely to rise during the fixed rate period. Conversely, when interest rates are historically high, lenders normally offer a discount to borrowers to fix their interest rate over time, as rates are more likely to fall during the fixed rate period.

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Simple and Compounded interest rate

 Simple interest is calculated once in a given period

• f time and for the amount that was deposited

called the principal.

 Compound interest allows the saver to earn

interest not only on the amount that was deposited (principal) but also on the earned interest.

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Simple interest

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Compound interest

F = $100 (1 + 0.02)4 = $108.24

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Compound interest

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Compound interest

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Compound interest

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Compound interest

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Period compounded interest with different compounding frequencies

 The compounding frequency refers to how often interest is credited.  Annual compounding means that interest is paid at the end of the year.  Quarterly compounding means that interest is paid at the end of every

three months.

 Monthly compounding means interest is paid at the end of every month.  !!! How quickly an amount of money grows under compound

interest depends on both the stated interest rate and the frequency

• f compounding.

Compound interest

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Which option is better? (1) Invest $1000 for one year at 4% APR compounded annually. (2) Invest $1000 for one year at 4% APR compounded semiannually. APR = Annual Percentage Rate (%)

Compound interest

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Which option is better? (1) compounded annually F = $1000 (1 + 0.04)1 = $1040 (2) compounded semiannually F = $100 (1 + 0.02)2 = $1040.40

Compound interest

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Period compound interest, compounded m times per year

 Suppose $P is invested for t years at an annual interest rate of r per year

compounded m times per year

 i = r/m; i is the interest rate per period  n = m·t; n in the number of periods

 The future value of the deposit (F) will be:

F = P (1 + i)n F = P (1 + r/m)m·t

Compound interest

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Continuous compound interest

 A measure of interest earned over an infinitesimally small

length of time. Basically, it is a measure of how fast the value of the investment is growing now, at this precise moment in time.

 Increasing the frequency of the compounding does increase the

effective annual rate, but as the frequency increase infinitesimally, the amount of the increase becomes infinitesimally small (approaching a limiting interest rate)

 Example: daily compounding

Compound interest

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Continuous compound interest

In 1626 Peter Minuit purchased Manhattan Island from the Native Americans for about $24 worth of trinkets. If the tribe had taken cash instead and invested it to earn 6% per year compounded monthly, how much would the Indians have had in 2016? What if compounded continuously?

Compound interest

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Continuous compound interest

compounded monthly

F = $24·(1 + (0.06/12)) 12·(2016-1626)

compounded continuously

F = $24·e 0.06·(2016-1626)

F = P ·e it

Compound interest

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Continuous compound interest

Interest rates and average interest rate spread percentage points

• n outstanding leu-denominated loans to and deposits from

non-financial corporations and households, as well as lending rate

• n new business

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3.2. Banking services Deposit and lending services

The average bank interest rates on outstanding loans and deposits

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3.2. Banking services Deposit and lending services

The average bank interest rates on new loans and deposits

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3.2. Banking services Deposit and lending services

Interest rate margins on outstanding loans and deposits

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3.2. Banking services Deposit and lending services

Interest rate margins on new loans and deposits

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4.2. Loans pricing

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Loans pricing Interest

 Fixed interest rate

 10%

 Floating (variable) interest rate

 LIBOR + 9%

! LIBOR is the average interbank interest rate at which a selection of banks

• n the London money market are prepared to lend to one
• another. LIBOR comes in 7 maturities (from overnight to 12 months) and in 5

different currencies.

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Loans pricing - LIBOR

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Loans pricing - LIBOR

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Breakdown of new loans by type of interest rate

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Loans pricing

Commissions and fees

All type of loans

 Loan review fee  Management fee  Early repayment  Evaluation of the guarantees (apartment, house, land, etc.)  Drafting agreements of security in personal and real property for

authentication with the Notary Office/registration with the Land Register

• r the Electronic Archive

Lines of credit have in addition

 Commitment Fees 31

Loans pricing

Commitment Fees

 the fee charged by the lender for agreeing to hold credit

available

 it is applied on the unused portions of credit

Example: $1 million revolving credit at 10% stated interest rate for 1 year; borrowing for the year was $600,000; a required 5% compensating balance on borrowed funds; and a 0.5% commitment fee on $400,000 of unused credit.

What is the cost of borrowing?

Loans pricing

Revolving credit (Line of credit - LOC) Revolving credit is a line of credit where the customer pays a commitment fee and is then allowed to use the funds when they are needed up to a specific limit. It is usually used for operating purposes and can fluctuate each month depending on the customer's current cash flow needs. Revolving lines of credit can be taken out by corporations or individuals.

Loans pricing

Revolving credit (Line of credit - LOC) Typical characteristics:

 The borrower may use or withdraw funds up to a pre-approved credit

limit.

 The amount of available credit decreases and increases as funds are

borrowed and then repaid.

 The credit may be used repeatedly.  The borrower makes payments based only on the amount he or she has

actually used or withdrawn, plus interest.

 The borrower may repay over time (subject to any minimum payment

requirement), or in full at any time.

Loans pricing

Compensating balance on borrowed funds A compensating balance is a minimum balance that must be maintained in a bank account, and the compensating balance is used to offset the cost incurred by a bank to set up a business loan. The compensating balance is not available for company use, and may need to be disclosed in the borrower’s notes to the financial statements. The bank is free to loan the compensating balance to other borrowers and profit from differences between the interest rates.

Loans pricing

Compensating balance on borrowed funds Example:

• Assume a clothing store needs a $100,000 line of credit (LOC) to

manage its operating cash flow each month.

• The store plans on using the LOC to make inventory purchases at

the beginning of the month, and then pay down the balance as the store generates sales.

• The bank agrees to charge a lower interest rate on the LOC if the

clothing store deposits a $30,000 compensating balance.

• The bank loans the clothing store’s compensating balance to other

borrowers, and profits on the difference between the interest earned and the lower rate of interest paid to the clothing store.

Loans pricing

Commitment Fees

 the fee charged by the lender for agreeing to hold credit

available

 it is applied on the unused portions of credit

Example: $1 million revolving credit at 10% stated interest rate for 1 year; borrowing for the year was $600,000; a required 5% compensating balance on borrowed funds; and a 0.5% commitment fee on $400,000 of unused credit.

What is the cost of borrowing?

$60,000 in interest + $2,000 in commitment fees

$570,000 in usable funds

Loans pricing

Interest: ($600,000) x (10%) = $ 60,000 Commitment Fee: ($400,000) x (0.5%) = $ 2,000 Compensating Balance: ($600,000) x (5%) = $ 30,000 Usable Funds: $600,000 - $30,000 = $570,000 Cost of borrowing:

= 10.88%

Loans pricing

Effective Annual Rate of Interest

!!! In many countries and jurisdictions banks are required to disclose the "cost" of borrowing in some standardized way as a form of consumer

• protection. The EAR has been intended to make it easier to compare lenders

and loan options. In the EU, the focus of EAR standardization is heavily on transparency and consumer rights: «a comprehensible set of information to be given to consumers in good time before the contract is concluded and also as part of the credit agreement [...] every creditor has to use this form when marketing a consumer credit in any Member State» so marketing different figures is not allowed.

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Loans pricing

Effective Annual Rate of Interest

 describes the interest rate for a whole year (annualized on

a loan, mortgage loan, credit card, etc.)

 it is a finance charge expressed as an annual rate  it includes the fee + compound interest rate (calculated across a

year)

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Assume the same loan described before except that the loan is for 270 days and the 10% rate is on an annual basis. What is the EAR?

Loans pricing

Effective Annual Rate of Interest (generally) =

Total interest paid + Total fees paid 365 days . Usable funds # of days loan is outstanding

X

Assume the same loan described before except that the loan is for 270 days and the 10% rate is on an annual basis. What is the EAR? $44,384 in interest $2,000 in commitment fees $570,000 in usable funds $44,384 + $2,000 365 $570,000 270

Loans pricing

Effective Annual Rate of Interest (generally) =

Total interest paid + Total fees paid 365 days . Usable funds # of days loan is outstanding = 8.137% x 1.3519 = 11.00%

X

X