Ch 4- Interest

annualized rate

= a periodic rate x a number of periods

Consols (Perpetual Bonds)

= bonds that never matures and continuously make coupon payments to perpetuity no return of the face value. (very rare; not really used anymore)

difference between APR and APY

APY is the rate of return; APR is the interest rate stated that you start with

If you made a 15% from bond investment, and your federal income tax rate is 20%, what is your after-tax ROR?(get to keep 80%)

AT-ROR = 15% x (1 - 0.2) = 15% x 0.8 = 12%

current yield formula

CY = C / PB = Annual Coupon payment /Price Paid for bond (coupon/ price)

ROR total bonds equation

Coupon+ price received-price paid/ price paid ROR= CY + CGL

Time Value of Money Equation TVM

FV = PV (1 + r )t

What is the price of a consol that pays $100 annually when the current market interest rate is 10%?

PV = C/r = $100/0.1 = $1,000

price of a consol

PV of a consol = C / r (annual coupon payments/ interest rate)

par bond

Price of Bond (PB) = FV. This occurs when CR = APR. (pay same price as face value)

premium bond

Price of Bond (PB) > FV. This occurs when CR > APR. (pay more than face value because your interest rate that you will be paid from buying that bond will be greater than the current market rate you would be earning)

abbreviated total ROR equation (stock investment return)

ROR= DY+CGL = %

ROR equation stock investment return

ROR= dividend+ price received-price paid/ price paid

true or false: Bond price (= PV of bond) and market interest rate (r) are inversely related.

TRUE ((bond price increases; interest rate decreases and vice versa)

what does compounding do to the ending balance?

The compounding allows an interest to be earned on an interest. Therefore, more frequent compounding yields a larger ending balance.

If you are to receive $100 one year (t=1) from now, when current APR = 12% (=r) with annual compounding, how much that $100 (=FV) will be worth to you NOW?

Therefore, PV = $100/(1+0.12)1 = $89.29 For 2 years from now: PV=100/(1+0.12)2=$79.72 For 3 years from now: PV=100/(1+0.12)3=$71.18

What is the price of a 12% coupon bond with a maturity of two years and a face value of $100,000 when the current market interest rate (= APR) is 10%? (Assume annual coupon payment!) what is its present value?

Thus, annual coupon payment = CR x FV (coupon rate x face value) = 0.12 x $100,000 = $12,000 3 payments: 1st (12,000) and 2nd (12,000) coupon payments and the final face value (100,000) PV = $12,000/(1+0.10) + ($12,000+$100,000)/(1+0.10)2 = $103,471.07 = Price of the 12% coupon $100,000 bond.

Time Value of Money

Time determines the value of money. For example, if you wait the consumption of $1 for a year, you must be compensated for the wait The compensation comes in the form of an interest earned.

When does APR=APY?

When there is no compounding

zero coupon bond pricing: What is the price of a zero-coupon bond with a maturity of two years and a face value of $100,000 when the current market interest rate is 10%?

Zero-coupon bonds do not make coupon payments; only pays the final, maturity, or face value at maturity. PV = $0/(1+0.10) + ($0+$100,000)/(1+0.10)2  = $100,000/(1+0.10)2 = $82,644.63

bond duration

bond price volatility (not about maturity)

zero-coupon bonds

bonds that make NO (=zero) coupon payments but will return the face value at bond maturity.

interest rate

the price of using (=lending and borrowing) money.

True or False: APY will be greater when there is more compounding

true

True or false: APY is always greater than or equal to APR

true

ROR (Yield) formula

what you received-what you paid/ what your paid x 100 (income-expense/ expense x 100)

discount bond

when Price of Bond (PB) < FV. This occurs when CR < APR. (pay less than face value because you are paid less than the current interest rate of the market)

Suppose that you bought an IBM share at $100 which you sold it back a year later at $110. During the year, IBM paid a total dividend of $5. What is your ROR from this IBM stock investment?

(5+110)-100/ 100 = .15

expected inflation

(tricky; measured monthly)

who issues debt?

(who is borrowing (issuing the debt))

capital gain/loss (CGL)

*negative= loss price received-price paid/ price paid

If r = 3% and EI = 2%, what is R? If R = 2% and r = 5%, what is EI?

1% ; 3%

basis point

A basis point = 0.01%. Thus, 1% = 100 basis points. *MEMORIZE When r increases from 2.05% to 2.07%, r is increased by 2 basis points. From 3 % to 1.92% decreased by 108 basis points. (1.08%)

after tax ror equation

After-Tax ROR = Before-Tax ROR * (1 - Tax Rate)

True or false: The longer the bond maturity, the lesser its price volatility (bond duration).

FALSE; longer maturity= greater volatility

How much will you receive if you make a loan of $100 to Billy Joe for one year at an annual percentage rate (APR) of 12%?

FV = $100 (1 + 0.12)1 = $112.00

How much will you receive if you make a $100 loan to Billy Joe for one year at an annual percentage rate (APR) of 12%? You ask for semi-annual compounding of interest during the loan period,

FV = $100 (1 + 0.12/2)2 = $100 (1.06)2 = $112.36

APY

FV = $100 (1 + 0.12/2)2 = $100 (1.06)2 = $112.36 While the loan amount of $100 and the APR of 12% remain the same, the ending balance is different due to the compounding effect This makes the rate of return, known as the Annual Percentage Yield (APY) different. Rate of return is 12.36, not 12% due to compounding enabling interest to be earned on interest

If you deposit (=lending to the bank) $100 (=PV) at APR of 12% (=r) with an annual compounding for 1 year (=t), you will get: for 2 years? for 3 years?

FV = PV (1 + r )t = $100 (1+0.12)1 = $112.00 For 2 years FV = 100 (1+0.12)2 = $125.44 For 3 years FV = 100 (1+0.12)3 = $140.49

PV equation

FV/ (1+r) ^t

coupon rate

Interest rate during life of loan that borrower will pay you (in contract; doesn't matter what market rate is)

fisher equation

Nominal Interest Rate = Real Interest Rate + Expected Inflation Rate r = R + EI

If the current APR = 5%, would you buy a consol at $100 that makes an annual payment of $6?

Note the consol yield = r = $6/$100 = 6%. Because you are getting 6% from the consol that is greater than the current APR of 5%, you should buy this. (earning more than current interest rate)

Bank A offers an APR of 12% and Bank B offers an APY of 12% if you open a 1-year certificate of deposit. Which bank would you deposit your money with if both banks calculate interest monthly?

Solution: monthly compounding to compare you must look at either both APRs or both APYS Choose Bank A since you know there is compounding, which would mean that the APY will be greater than 12 (Bank B's APY is 12)

If you are in a 25% federal tax bracket (rate) and wish to purchase one of the following two bonds. Which one would you buy? Choice A: A federal-tax-exempt bond with a yield of 7.4% (municipal bonds are tax exempt) Choice B: A corporate bond with a yield of 10%

You would buy the corporate bond with the yield of 10% which yields an after-tax ROR of 7.5% [=(1-0.25)x10% = 0.75x10%] is larger than the 7.4% yield from a federal-tax-exempt bond. -must change to after-tax ROR

coupon bonds

bonds that make coupon payments until the bond maturity At bond maturity, the last coupon payment AND the face value will be paid to the lender.

3 types of long term debts

coupon bonds, zero-coupon bonds ,consols (perpetual bonds)

what's different about bond investment return calculation

coupon payment takes place of dividends

coupon yield (CY)

coupon/ price paid

dividend yield (DY)

dividend/ price paid

face value

face value = terminal value = maturity value = final value. (at end of loan, borrower will give you the face value as stated in contract)

compounding interest

interest more than once within a given period such as a year

simple interest

is calculating interest only once within a given period such as a year.

periodic rate

is either a semi-annual rate, a quarterly rate, a monthly rate, a weekly rate, or a daily rate.

does the lender or borrower want to compound more?

lender: wants to compound as many times as possible (earn more money); borrower doesn't want to compound (pay more money back

nominal interest rate

one we see and hear all the time in the media; prevailing now in the market

real interest rate

real growth in our economy (not visible, not easy to see; abstract concept)

APR (annual percentage rate)

simple interest rate; All interest rates without any reference to a specific time period is assumed be

All zero-coupon bonds are discount bonds except...

when the market interest rate is negative. (happened in Europe but very rare)