Par Value
Par Value is the
Face Value of Bond. If face value of bond is not given then face value can be
assumed either Rs. 100 or Rs. 1000 or Rs. 10000 depending upon question.
Coupon Rate
Coupon Rate is the
fix Rate of Interest which a bondholder receives as Interest Payment. Coupon
Rate remains same until the bond matures.
Yield Rate
Current Yield/Yield
Rate is Rate at which a bondholder receives as Interest Income on the Current
Value of Bond.
Current Yield =
Interest/Market Price of Bond
Yield to
Maturity (YTM)
Yield to Maturity
(YTM) is Rate of Earning if bond is held until Maturity.
YTM = [(Interest +
(Redemption Value (RV) - Net Proceeds (NP))/Maturity Period of
Bond]/[(RV+NP)/2]
YTM = IRR can be
used
Value of Bond
Value of Bond = ∑
PV of Interest Receivable + PV of Redemption Value
Value of Perpetual
Bond = Interest/Yield Rate
Value of Bond if
Company offers any Discount then
Value of Bond =
Value of Bond As usual – Discount on Bond
Value of Discount
on Bond
For 1st
Year = [1- 1/ (1 + Discount Rate)] x Face Value
For 2nd
Year = [1 – 1/ (1 + Discount Rate)2] x Face Value
And so on
If Redemption value
of bond is not given then, face value of will be assumed as redemption value.
Yield to Call
(YTC)
Return an Investor
gets if bond is called after lock in period.
YTC = [(Interest +
(Call Price – Market Price (MP))/Lock in Period of Bond]/[(Call Price +MP)/2]
Yield to Put
(YTP)
Return an Investor
gets if bond is retained after lock in period.
YTP = [(Interest +
(Put Price – Market Price (MP))/Lock in Period of Bond]/[(Put Price +MP)/2]
Relation between
Current Yield and Value of Bond – Bond Value Theorems
If Current Yield
(Yield Rate) = Coupon Rate
Then Bond is
selling at Par.
If Current Yield
(Yield Rate) > Coupon Rate
Then Bond is
selling at Discount.
If Current Yield
(Yield Rate) < Coupon Rate
Then Bond is
selling at Premium.
Forward Rate
Current Price =
Interest1/(1 + r1) + Interest2/[(1 + r1)
x(1 + r2)] + .. +{Interestn + Redemption Value}/[(1
+ r1) x…(1+ rn)]
Commercial Paper
Effective Interest
Rate = [(Redemption Value – Issue Price) x 100]/Issue Price
Stock Value of Bond
= (No of Share per bond) x (Market Price per share)
Downside Risk
If the Actual
Market Price of Assets (Bond) is greater than fundamental price then the Assets
(bond) may correct i.e. there is probability of price going down.
Upside Premium
If the Actual
Market Price is less than fundamental price then there is possibility of the
price going up.
Downside Risk =
[Market Price of Convertible Bond – Straight Value (Fundamental Value of Bond)]
/Theoretical (Straight) Value of Bond
Conversion Premium
= [(Market Price of Convertible Bond – Stock Value of Bond) x 100]/stock Value
of Bond
Conversion
Parity Price of Stock
Price of share is to
be issued in lieu of convertible debenture (bond) such that there is no
arbitrage opportunity to investor.
Conversion Parity
Price = (Market Price of Convertible Bond)/No of Shares per Bond
Interest Rate
Risk
Re – Investment
Risk
It is the risk of
interest rate falling because if the interest rate falls, then investor would
able to re – invest the coupon amount at lower rate [Compounding Effect].
Price Risk
It is the risk of
rising of Interest Rate because if the interest rate rises, then value of bond
will fall [Discounting Effect].
So both the effects
act in the opposite direction. They tends to cancel out each other and the
period at which both cancels out each other is known as Macaqulay’s Duration.
So duration I that
immunizing period at which re- investment effect cancel out the effect and
realized yield is equal to promised by yield irrespective of interest rate
changing.
Duration
Duration is nothing
but the average time taken by an investor to collect his investment. If an
investor receives a part of his investment over the time on specific intervals
before the investment will offer him duration which would be lessor than the
maturity of the bond.
Duration = ∑Wx/W
Where,
Wx = Weight x
Discounted Annual Cash flows
W = value of Bond
Duration = [Current
Yield x PVAF(YTM, n) x (1 + YTM)]/YTM + [{1 – (Current Yield)/YTM) }
x n]
If Bond Trades at
par
Current Yield = YTM
= Coupon Rate
Then
Duration = PVAF(YTM,
n) x (1 + YTM)
Duration of ZCB is
the life of ZCB
Immunization
Theorem
Duration of
Liability = Duration of Assets
Duration of
Portfolio = DA x WA + DB x WB
Price Volatility
of Bond
Price Volatility of
a bond is the sensitivity of bond price to the interest rate i.e. if interest
rate changing by 1% then what would be % change in Bond Price.
Modified Duration =
Duration/ (1+YTM)
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