Chapter 3: Time Value of Money Flashcards
Simple vs. Compounded interest
Simple: interest due along with amount borrowed (principle) at the end of loan period. (Amount owed, F=P[1+i*n])
Compounded: interest due at the end of each period, amount based on amount owed at the beginning of period.
Effective interest rate
Rate which if compounded once per standard period yields same F as nominal compounded m times per period.
EIR=(F-P)/P=[1+(r/m)]^m-1
r=nominal int rate
m=number of compounding period per year
Nominal interest rate
Interest rate per standard period of time. AKA: nominal annual rate unless otherwise specified
Continuous compounding
Compounding occurs infinitely. EIR=e^r-1
Replace all (1+i)^n in factors with e^(r*n)
Infinite time period
(F/P)=(F/A)=inf
(P/F)=(A/F)=0
(P/A)=1/I
(A/P)=i
Time has no value (i=0)
(F/P)=1
(F/A)=n
(A/F)=1/n
Interest changes over time
(F/P, i, n): (1+i1)(1+i2)..(1+in)
End of period changes
- Increasing/decreasing by constant amount per time
- Increasing/decreasing by constant rate per time
BOND CERTIFICATE
states terms of bond
MATURITY DATE
final repayment date
N
TERM
time remaining until repayment date
COUPON RATE
nominal interest rate applied to bond’s face value
> PMT
FACE VALUE
monetary value indicated on bond and received at maturity, when bond is redeemed
- FV
COUPON PAYMENT
CPN=(CRxFV)/(# coupon payment per year)
COUPON BOND
- pay face value at maturity
- pay coupon interest payments
YIELD TO MATURITY
- interest rate earned on the amount invested, specified as nominal interest rate
- discount rate that sets PV of promised bond payment equal to current market price of bond
DISCOUNT
- bond sells at discount if the price is less than face value
- investor earns return from receiving coupon and from receiving face value that exceeds price paid for bond
CR < YTM
PAR
- bond sells at par if the price is equal to face value
CR = YTM
PREMIUM
- bond is selling at premium is price is greater than face value
- will earn return from coupon but return is diminished from face value less than price paid for bond
CR > YTM
Sharpe Theory #1
bond pulses economy
YTM increases: present value decreases
YTM decreases: present value increases
Sharpe Theory #2
premium decays until PV->Par until end of contour at REDEMPTION DATE
discount increases until PV->Par
Sharpe Theory #3
YTM increases: risk of default increases
Bond: government, corporate, junk
Sharpe Theory #4
YTM increases: Present value decreases
x>y
Sharpe Theory #5
INTEREST RATE GYRATION: at larger periods of time, there is higher sensitivity to YTM changes (higher % change)
Sharpe Theory #6
higher coupon rate=lower sensitivity to INTEREST RATE GYRATION (lower % change)
