How to calculate Bond Sensitivity Macaulay’s Duration Modified Duration or Volatility and Intrinsic Value?

How to calculate Bond Sensitivity, Macaulay’s Duration, Modified Duration or Volatility and Intrinsic Value?

What is Intrinsic Value of Bond?
Present value of bond calculated using expected interest rate of return is called Intrinsic value of Bond.

Formula for calculating Bond's Intrinsic Value:
Intrinsic value
= ∑(Future Cash Flow x PVF)
=∑PV

*PVF = Present value factor and PV= Present Value.

Example 1:
No 1. A conventional Bond having following parameter- Face value ₹1000, Redeemable Value ₹1200, Remaining Life 5 Years and Coupon Rate 10%.
Find-
Intrinsic value when expected rate of Return is 12%.

Solution: Expected rate of Return (r)=0.12, PV factor = 1/(1+r)ⁿ.

Years(n)	Future Cash Flow	PV Factor	PV
1	100	0.8928	89.28
2	100	0.7971	79.71
3	100	0.7117	71.17
4	100	0.6355	63.55
5	100	0.5674	56.74
5	1200	0.5674	680.88
Intrinsic Value=			1041.33

What is Bond Sensitivity?
Interest rate sensitivity is a measure of how much the price of a bond will fluctuate due change in interest rate.

Expected rate of return and Fixed income security inversely correlated. Means- If your Expected rate of return rise, price of fixed income security (like Bond) fall and vice versa.
If you are dealing with Bond or other Fixed income securities, you must have to know the sensitivity.

Formula :
Sensitivity =∑nPV/(1+r).

Example 2:- Conventional Bond having following parameter- Face value ₹1000, Redeemable Value 1200, Remaining Life 5 Years and Coupon Rate 10%. Expected rate of Return 12%. Calculate Sensitivity of the Bond.

Solution: Expected rate of Return (r)=0.12, PV factor = 1/(1+r)ⁿ.

Years(n)	Future Cash Flow	PV Factor	PV	nPV
1	100	0.8928	89.28	89.28
2	100	0.7971	79.71	159.42
3	100	0.7117	71.17	213.51
4	100	0.6355	63.55	254.20
5	100	0.5674	56.74	283.70
5	1200	0.5674	680.88	3404.40
			1041.33	4404.56

Sensitivity =∑nPV/(1+r)=4404.56/1.12 = 3932.80

Example No.3.:
Use the previous question data and determine the intrinsic value of bond if the rate of return desired by the investor increases from 12% to 14% pa using Sensitivity.

Solution:. We know that, if desired rate of return or expected rate of return increase than intrinsic value decrease.
Intrinsic Value of Bond @12%=1041.33
Sensitivity @12% = 3932.56
Rate of Return increases=14%-12% =2%
Approx. decrease in Intrinsic Value = 3932.56 X 2% =78.66
Intrinsic Value @14% using sensitivity = 1041.33-78.66=962.73

You can viwe Lecture in Hindi on this Topic on My Youtube Channel. To view it Plesae Click the Link-Video Lecture in Hindi on Bond's Intrinsic vaule, Sensitivity, Macaulay’s Duration, Modified Duration or Volatility " or on Video Link Below

Duration of Bond

What is Duration of Bond?
Duration is the weighted average term to maturity of the cash flows from a bond.
This is also called Macaulay’s Duration of bond.
What is Modified Duration or Volatility of the Bond?
It is sensitivity in terms of per rupee of bond value.
Formula:
Macaulay’s Duration =∑nPV / ∑PV
Modified Duration (Volatility) =Sensitivity / Intrinsic Value
or
Modified Duration (Volatility) =Macaulay’s Duration /(1+i)

Example 4:-
Conventional Bond having following parameter- Face value ₹1000, Redeemable Value 1200, Remaining Life 5 Years and Coupon Rate 10%.Expected rate of Return 12%.
Calculate Macaulay's Duration of the Bond and Modified Duration (Volatility).

Years(n)	Future Cash Flow	PV Factor	PV	nPV
1	100	0.8928	89.28	89.28
2	100	0.7971	79.71	159.42
3	100	0.7117	71.17	213.51
4	100	0.6355	63.55	254.20
5	100	0.5674	56.74	283.70
5	1200	0.5674	680.88	3404.40
			1041.33	4404.56

Macaulay’s Duration =∑nPV / ∑PV=4404.56/1041.33=4.23 Years.
Modified Duration (Volatility) =Macaulay’s Duration /(1+i)=4.23 /1.12=3.78.

Practice Question

A non-conventional bond having following details-Face value ₹1200,Remaining Life 6 Years and Coupon Rate 9%.Return of Bond Value 50% with Rs. 100 Premium at the end of 3rd year and remain 50% with Rs. 100 Premium at the end of 6th year. Expected rate of Return 10%.
Calculate :
1. Intrinsic Value of the Bond
2. Sensitivity of the Bond.
4. Intrinsic Value using Sensitivity when Expected rate of return Decrease 10% to 8%.
5. Macaulay's Duration.
6. Modified Duration or Volatility .

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