MGT 326 Ch 5: Interest Rates (bdh) (The Cost of Money) 1 The Cost of Money: Learning Objectives: Explain why lenders charge interest Define the components

MGT 326 Ch 5: Interest Rates (bdh) (The Cost of Money)

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The Cost of Money:

Learning Objectives:

Explain why lenders charge interestDefine the components of interest rates (r = r*+IP+DRP+LP+MRP)Know what a term structure of interest rates isDefine an interest rate Yield Curve

how to read it what influences the shape of the yield curve what the shape tells us about future interest rates

Make borrowing decisions using yield curve informationUnderstand the Opportunity Cost of Capital

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The Cost of Money: Is the interest rate you pay a lenderIs what borrowers pay to use (rent) money

Inflation: Definition: The decrease of the purchasing power of currency over timeCause: various factors; chief among them:

demand for goods & services grows faster than the supply of goods & services; as time goes by, goods & services become more valuable thus more expensive; this reduces the purchasing power of currencyAn increase in the amount of money in circulation in an economy; as quantity of currency increases, value of currency decreases with respect to the value of goods & services; it takes more money to purchase goods & services, thus the purchasing power of currency is reduced

What is an Interest Rate?When someone decides to lend money, they want compensation for:

the loss of the opportunity to use that money while it’s loaned out (opportunity cost)the loss of value over time due to inflationthe chance that they won’t get the money back

The interest rate (r) one pays for the privilege of using someone else’s money is the sum of these different compensations Thus r = r* + IP + RP

r* = “real (risk free) rate” which is the opportunity costIP = the Inflation Premium which compensates for inflationRP = Risk Premium which compensates for possible default (this premium can be broken down into sub-premiums)

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The Cost of Money: (continued)

Interest rates are usually expressed and quantified as a percentage of the principle (the amount borrowed).

Example: A $1,000 face value bond has a coupon rate of 6.0000% per year. Interest is paid annually. How much interest is earned each year?

Interest PMT = Principle(Interest Rate) = $1,000(0.06) = $60

Symbols: r or k or i

Two basic types of interest:Simple Interest:

paid all at once either upon initiating or closing (at the end of) the loanno compounding

Compound Interest: paid in little chunks throughout the life of the loan, usually at the end of the periodinterest earned is reinvested; thus interest earns interest (as discussed in Ch 4)

The “cost of money” (an interest rate) is also referred to as:The “cost of borrowed capital”The “cost of debt”The “cost of leverage”


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Major factors that affect the cost of money: Opportunity Costs

Internal investment vs. externalDesire to consume (spend) money now versus investing it.

RiskExpected Inflation (has the greatest influence on cost of money)Federal Reserve PolicyBusiness Activity / State of the EconomyFederal DeficitsForeign Trade Balance


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The Components of an Interest Rate: This is how the major factors that influence the cost of money are quantified and factored into interest rates

Nominal Interest Rate r = r* + IP + DRP + LP + MRP

r = Nominal Rate in a particular market1; also called the “Quoted Rate”

r* = Real Interest Rate (Real Risk-Free Rate )Compensates the lender for his opportunity costs, regardless of inflation or any other risks

→Production Opportunities→Time Preference for Consumption

No one really knows what the real risk-free rate isA commonly accepted value for the real risk-free rate can be found by subtracting current inflation rate from the current 30-day Treasury-bill rate. (See Nominal Risk-free Rate p. 6)r* is not constant; it changes over time

IP = Inflation PremiumCompensates the lender for loss in value over time due to inflation. This is computed as the average expected inflation rate over the life of the loan (more on this later)The IP that is often applied is derived from government economic forecasts. No one really knows what the current inflation rate is but the one the U.S. Government reports is the commonly accepted valueNo one ever really knows what the inflation rate will be in the future (but we have some indication of what it might be; more on this later)

Note 1: we will talk about different loan markets later

Risk Premium


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DRP = Default Risk PremiumCompensates the lender for possible default. This is kind of like an “insurance payment”30-day Treasury bills (T-bills; $1,000 face value very short term bonds) have a DRP of 0% Why? Answer: T-bills are considered “riskless”.

LP = Liquidity Premium:Accounts for the ability of a borrower to repay a loan with the firm’s assets. If these assets are not very liquid (i.e. real estate, buildings, equipment, etc.), LP will be higherAlthough it’s very difficult to calculate LP, it tends to differ 2 to 5 percent between the most liquid and least liquid financial assets

MRP = Maturity Risk Premium “Maturity” is the length of the loanCompensates for Interest Rate Risk. The longer the term (time till maturity), the greater the interest rate risk, thus a higher MRP. (We will talk more about interest rate risk later in the semester)Compensates for Reinvestment (Rate) Risk. When a loan matures, the interest rate might be lower than when the loan was issued Therefore the lender can’t reinvest the repaid principle at the same rate at which he originally loaned it.

Nominal Risk-Free Rate (rRF):Since no one really knows what r* is, the financial world uses a commonly accepted formula: r* ≈ rRF - Current Inflation RateThe above equation can be re-written as rRF ≈ r* + IP This is the “Nominal” or “Quoted” Risk-Free Rate (rRF)The yield (interest rate) on a 30-day T-bill is usually used for rRF

See also Ch 5 pp. 144


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Quoted Interest Rate r = rRF + DRP + LP + MRP

This equation is the one most commonly used to compute interest rates since it’s easy to find rRF (the yield on a 30-day T-bill); just read the Wall Street Journal

Example: Jungle Jim’s Outfitters, a local outdoor equipment retail store, wants a 1-year, $50k loan from your bank. You have already determined that this firm warrants an DRP of 5%, an LP of 1% and an MRP of 0.5%. Today’s WSJ reports 30-day T-bills are currently yielding 2.3%. What is an appropriate interest rate for this loan?

r = rRF + DRP + LP + MRP = 2.3% + 5% + 1% + 0.5% = 8.8%

Note: We assumed that the Inflation Premium (IP) will be the current inflation rate as implied by the rate on a 30-day T-bill. This usually is acceptable only for relatively short-term loans (less than 1 year maturity).

r* + IP


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How do you compute r for loans longer than 1 year maturity?

Use r = r* + IP + DRP + LP + MRPFind current inflation (what the gov’t reports as current inflation)Find the yield on a 30-day T-bill Compute r* (r* = rRF - Current Inflation Rate)Find expected inflation for upcoming yearsCompute the average value for expected inflation; this is IP

IP = ( I1 + I2 + I3 ……..In) / n where n is the number of years of maturity and In is the expected inflation for a particular year

Example: Jihad Jim’s Travel Adventures, a new travel agency, wants a 3-year, $500k loan from your bank. You have already determined that this firm warrants an DRP of 10%, an LP of 3% and an MRP of 1.5%. Today is 2 January. Inflation for the rest of this year is expected to remain at 2 %. Next year’s inflation is expected to be 2.5% and the following year’s inflation is expected to be 3%. Today’s WSJ reports 30-day T-bills are currently yielding 2.3%. What is an appropriate interest rate for this loan?

1) Find r*: r* = rRF - Current Inflation Rate r* = 2.3% - 2% = 0.3%

2) Find IP: IPn = ( I1 + I2 + I3 ……..In) / n IP3 = (2% + 2.5% + 3%)/3 = 2.5%3) Find r: r = r* + IP + DRP + LP + MRP

r = 0.3% + 2.5% + 10% +3% + 1.5% = 17.3%


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What factors tend to lower interest rates?Answer:Everyone in the lending business wants to lend you (or your company) money because they want the cash flow from your interest paymentsIt’s very competitive. Lenders are always trying to offer more attractive rates than their competitors in order to get you to borrow from themThis is the root cause for many banking fiascoes; banks often enter into risky lending in pursuit of cash flow

Why should you care about this interest rate stuff?Answer:If you are a lender, it will enable you to determine an appropriate, competitive rateIf you are a borrower, it will help you shop for moneyRelated economic indicators may help you determine likely future interest rates (by examining affects on interest rate factors and components)

thus helping you in deciding whether to lend/borrow now or wait or whether to bargain for higher/lower ratesthis is a form of risk management; reducing uncertainty concerning future interest rates

It will help you minimize your firm’s financing costJust about all the other topics we will cover during this course involve interest rates or other factors that are similar in function to interest rates (i.e. bond valuation, stock valuation, required rates of return for individual stocks and the stock market as a whole, risk adjusted required rate of return, etc.)


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Interest Rates / Investment Rates of Return (ROR)

The interest rate that a borrower pays is exactly equal to the lender’s ROR; the lender is investing in the borrower

When you invest in stock, you should expect a ROR that compensates for the same things associated with lending money;

Required ROR of stock = rs = r* + IP + RP; (Note: the specific risks associated with stock may be different than those associated with lending money, but it’s the same idea

When you invest in anything, you should expect compensation for the same things; thus ranything = r* + IP + RP; thus your Required ROR is r* + IP + RP

Even if the investment is risk-free (such as a short-term U.S. Treasury bill) the minimum ROR you should expect is compensation for opportunity cost and inflation

thus rminimum = r* + IPthis is rRF

thus rminimum = rRF

this is why rRF is the benchmark for all other rates


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The Opportunity Cost of Capital

The best available expected return offered in the market on an investment of comparable risk and length (term)The return the investor forgoes on an alternative investment of equivalent risk and term when the investor takes on the alternative investment

Point: One always uses his/her Opportunity Cost of Capital as the discount/compound rate when solving TVM problems if a rate is not givenThe Opportunity Cost of Capital is your benchmark for comparing and choosing among options

Capital: Wealth in the form of money or property (real property or securities) that can be used to produce more wealth


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The Term Structure of Interest Rates

Term Structure: the relationship between interest rates (yields) and different loan lengths (maturities).

U.S. Treasury Bond Interest Rate Term Structure Term to Interest RateMaturity Mar. 1980 Mar. 1999 Jan. 2006 6 months 15.0% 4.6% 4.16% 1 year 14.0% 4.9% 4.23% 5 years 13.5% 5.2% 4.34%10 years 12.8% 5.5% 4.38%20 years 12.5% 5.9% 4.46%

Why do bonds of longer maturity have higher interest rates?

A graph of the term structure is called a yield curve. It graphically portrays the relationship between interest rates and maturities


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Yield Curve for March 1980 (Inflation: 12%) (downward sloping or inverted)

Short Term Intermediate Term Long Term Maturity

Yield Curve Comparison (U.S. Treasury Bonds)

The yield curve is a “snapshot” in time; it tells you what the relationship between maturities and interest rates are at a specific dateThe yield curve does not tell you what interest rates will be in the future (more on this later)Yield curves for different bond markets (i.e. U.S. Treasuries, investment grade, junk, etc.) usually have similar shapesYield curves change over time due changes in the factors that govern interest rate components (IP, DRP, LP & MRP). Historically, yield curves have mostly been upward sloping (i.e. interest on shorter term bonds were lower than longer term bonds)

Yield Curve for July 2003 (upward sloping)

Yield Curve for July 2000 (flat)


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The shape of the yield curve gives some indication about what bond markets think inflation (and thus, interest rates) might do in the future

Expected inflation has the greatest influence on yield curve shapeyield curves slope downward (Mar 1980) when debt markets expect inflation to decreaseyield curves slope upward (Mar 1999) when bond markets expect inflation to riseyield curves are concave (Feb 2002) when the direction of inflation change is about to change

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Yield Curve for March 1980 (Inflation: 12%) (downward sloping / inverted )

Yield Curve for March 1999 (upward sloping)

Yield Curve for February 2000 (concave)

Yield Curve for July 2003 (upward sloping)

Yield Curve for July 2000 (flat)

Yield Curve for August 2000 (downward sloping)


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The shape of the yield curve influences decisions on issuing debt Upward sloping: go with l-t debt instead of s-t debt; upward sloping means the market expects interest rates to rise in the futureDownward sloping: go with s-t debt instead of l-t debt; refinance later when interest rates are lowerCaution: the yield curve changes over time

Expectations Theory:

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High-risk Firms

Low-risk Firms

Moderate-risk Firms

U.S Treasuries

Other Yield CurvesThe relative riskiness of borrowers also influences the shape of the yield curve

Spread


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U.S. Treasuries Yield Curve as of 12 Sep 03

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U.S. Treasuries Yield Curve as of 16 Jan 04

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U.S. Treasuries Yield Curve as of 20 Jan 2005

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Documents

MGT 326 Ch 5: Interest Rates (bdh) (The Cost of Money) 1 The Cost of Money: Learning Objectives: Explain why lenders charge interest Define the components