NOTES
Price=Coupon/(1+i)n+ FV/(1+i)n
• Coupon rate is NOT discount rate.
• Here I is interest/coupon rate
• C is coupon payment annually
• FV is the maturity amount
• Yield to Maturity(YTM) is the rate of return the bond generates
YTM of zero-coupon bond= [(fv/pv)1/n] -1
RATE OF RETURN
R= (C/Pt) + (Pt+1 - Pt)/Pt OR R= ic + g
• Pt is the price of bond at T
• Pt+1 is the price of bond at t+1
• (C/Pt) is the current yield (ic)
• (Pt+1 - Pt)/Pt is the capital gain/loss (g)
MACAULAY DURATION
To identify the duration after which the cashflow will be received
weight = Ct/ (1+i)t OR PV/PRICE
P
Duration = Summation of [Ct/ (1+i)t * t /P] OR w*t
MODIFIED DURATION
Measures the price sensitivity of a bond when there’s change in YTM
Modified duration= -1/p * change in price/ change in rate of return
Change in price (%) = Modified duration* change in interest rate
CONVEXITY
Measure how duration changes as the yield changes
CV= 1/P * (Change in price)2/(change in ytm)2
, Change in price (%) = [-modified duration *change in ytm] +[1/2 * convexity *
(change in ytm)2]
PRESENT VALUE OF MONEY
Present value= future cash flow/ (1+ r)t
Note: The higher the r , the lower the PV required to achieve the future cashflow
1. ANNUITY – Fixed amount, periodically and specified time period
PVA = CF* [ 1/r - 1/r(1+r)t]
2. PERPETUITY
PV = CF/R
3. DISCOUNT RATE
PV = CF * Discounted flow
Discounted flow= 1/(1+r)t
Discount factor
DF = 1/(1+r)
BUILD IN FORMULA (EXCEL)
PV= (RATE, NUMBER OF PERIOD, PAYMENT, FACE VALUE, TYPE)
NET PRESENT VALUE
In case of annuity i.e. periodic fixed amount cashflows
NPV= - INVESTMENT+ PVA OF INFLOWS
Worth of asset = CF [1/r – 1/r(1+r)t - time remaining
In case of different cashflows annually
NPV = - INVESTMENT + [CF1/(1+r)1 + CF2/ (1+r)2 + CFt/ (1+r)t]
Price=Coupon/(1+i)n+ FV/(1+i)n
• Coupon rate is NOT discount rate.
• Here I is interest/coupon rate
• C is coupon payment annually
• FV is the maturity amount
• Yield to Maturity(YTM) is the rate of return the bond generates
YTM of zero-coupon bond= [(fv/pv)1/n] -1
RATE OF RETURN
R= (C/Pt) + (Pt+1 - Pt)/Pt OR R= ic + g
• Pt is the price of bond at T
• Pt+1 is the price of bond at t+1
• (C/Pt) is the current yield (ic)
• (Pt+1 - Pt)/Pt is the capital gain/loss (g)
MACAULAY DURATION
To identify the duration after which the cashflow will be received
weight = Ct/ (1+i)t OR PV/PRICE
P
Duration = Summation of [Ct/ (1+i)t * t /P] OR w*t
MODIFIED DURATION
Measures the price sensitivity of a bond when there’s change in YTM
Modified duration= -1/p * change in price/ change in rate of return
Change in price (%) = Modified duration* change in interest rate
CONVEXITY
Measure how duration changes as the yield changes
CV= 1/P * (Change in price)2/(change in ytm)2
, Change in price (%) = [-modified duration *change in ytm] +[1/2 * convexity *
(change in ytm)2]
PRESENT VALUE OF MONEY
Present value= future cash flow/ (1+ r)t
Note: The higher the r , the lower the PV required to achieve the future cashflow
1. ANNUITY – Fixed amount, periodically and specified time period
PVA = CF* [ 1/r - 1/r(1+r)t]
2. PERPETUITY
PV = CF/R
3. DISCOUNT RATE
PV = CF * Discounted flow
Discounted flow= 1/(1+r)t
Discount factor
DF = 1/(1+r)
BUILD IN FORMULA (EXCEL)
PV= (RATE, NUMBER OF PERIOD, PAYMENT, FACE VALUE, TYPE)
NET PRESENT VALUE
In case of annuity i.e. periodic fixed amount cashflows
NPV= - INVESTMENT+ PVA OF INFLOWS
Worth of asset = CF [1/r – 1/r(1+r)t - time remaining
In case of different cashflows annually
NPV = - INVESTMENT + [CF1/(1+r)1 + CF2/ (1+r)2 + CFt/ (1+r)t]
