BANK FINANCIAL MANAGEMENT IMPORTANT CASE STUDIES/NUMERICALS: 1

BFM IMPORTANT CASE STUDIES / NUMERICALS (applicable for both ABM and BFM)

1. A bond has been issued with a face value of Rs. 1000 at 8% Coupon for 3 years. The required rate of return is 7%. What is the value of the bond?
Explanation :
Here,
FV = 1000
Coupon Rate (CR) = 0.08
t = 3 yr
R (YTM) = 0.07
Coupon = FV × CR = 80
Bond Price = (1/(1+R)^t)((coupon*((1+R)^t-1)/R)+Face Value)
So, Value of bond = 1026.25
(Since Coupon rate > YTM, so Bond’s Value > FV)

2. A bond has been issued with a face value of Rs. 20000 at 12% Coupon for 3 years. The required rate of return is 10%. What is the value of the bond?
Explanation :
Here,
FV = 20000
Coupon Rate (CR) = 0.12
t = 3 yr
R (YTM) = 0.10
Coupon = FV × CR = 2400
Bond Price = (1/(1+R)^t)((coupon*((1+R)^t-1)/R)+Face Value)
So, Value of bond = 20995
(Since Coupon rate > YTM, so FV < Bond’s Value)

3. A bond has been issued with a face value of Rs. 1000 at 10% Coupon for 3 years. The required rate of return is 8%. What is the value of the bond if the Coupon amount is payable on half-yearly basis?
Explanation :
Here,
FV = 1000
CR = 10% half-yearly = 5% p.a.
Coupon = FV × CR = 50
R = 8% yearly = 4% p.a.
t = 3 years
Bond Price = (1/(1+R)^t)((coupon*((1+R)^t-1)/R)+Face Value)
= 1052
(Since Coupon rate > YTM, so FV < Bond’s Value)

4. A 10%, 6-years bond, with face value of Rs. 1000 has been purchased by Mr. x for Rs. 900. What is his yield till maturity?
Explanation :
Here,
FV = 1000
CR = 10%
R (YTM) =?
T = 6 years
Coupon = FV × CR = 100
Bond’s price = 900
Since FV > Bond’s Value, Coupon rate < YTM (based on above three observations)
So, we have to use trial and error method. We have to start with a value > 10 and find the price until we get a value < 900.
Bond Price = (1/(1+R)^t)((coupon*((1+R)^t-1)/R)+Face Value)
So,
If YTM = 11%, price =957.69 (> 900, so keep guessing)
If YTM = 12%, price = 917.78 (> 900, so keep guessing)
If YTM = 13%, price = 880.06 (< 900, so stop)
So, YTM must lie between 12 and 13.
So, using interpolation technique,
YTM
= 12 + (917.78 – 900) ÷ (917.78 – 880.06)
= 12 + 17.78 ÷ 37.72
= 12.47%
(Verification: Putting R = 12.47% in bond’s price formula leads to value of 899.80 which is closest to 900, so YTM = 12.47% is the right answer).

5. Ram purchased two bonds bond-1 & bond-2 with face value of Rs. 1000 each and Coupon of 8% and maturity of 4 years & 6 years respectively. If YTM is increased by 1%, the % change in prices of bond-1 & bond-2 would be ......
Explanation :
Bond Price = (1/(1+R)^t)((coupon*((1+R)^t-1)/R)+Face Value)
Bond 1:
If YTM is 9%, then bond’s price
= [80 × (1.09^4 – 1) ÷ 0.09 + 1000] ÷ 1.09^4
= 967.64
Bond 2:
If YTM is 9%, then bond’s price
= [80 × (1.09^6 – 1) ÷ 0.09 + 1000] ÷ 1.09^6
= 955.14
So, % change in price of bond 1
= (1000 – 967.04) ÷ 1000
= 0.03296
= 3.29%
& % change in price of bond 2
= (1000 – 955.14) ÷ 1000
= 0.04486
= 4.48%

6. Monica purchased a bond with face value of Rs. 1000 and Coupon of 8% and maturity of 4 years. If YTM is increased by 1%, the change in price of bond would be......
Explanation :
If YTM is 9%, then bond’s price
= [80 × (1.09^4 – 1) ÷ 0.09 + 1000] ÷ 1.09^4
= 967.604
So, change in price of the bond
= 1000 - 967.64
= 32.96 decrease
(Since Coupon rate < YTM, so Bond’s Value < FV)

7. Ashwini purchased a bond with face value of Rs. 1000 and Coupon of 8% and maturity of 6 years. If YTM is increased by 1%, the change in price of bond would be......
Explanation :
If YTM is 9%, then bond’s price
= [80 × (1.09^6 – 1) ÷ 0.09 + 1000] ÷ 1.09^6
= 955.14
So, change in price of the bond
= 1000 - 955.14
= Rs. 44.86 decrease
(Since Coupon rate < YTM, so Bond’s Value < FV)

​8. Priya purchased a bond with face value of Rs. 1000 and Coupon of 8% and maturity of 4 years. If YTM is reduced by 2%, the change in price of bond would be......
Explanation :
If YTM = 6%, bond’s price
= [80 × (1.06^4 – 1) ÷ 0.06 + 1000] ÷ 1.06^4
= 1069.30,
So, change in price of the bond
= 1069.30 - 1000
= Rs. 69.30

BACK
BACK TO JAIIB AND CAIIB HOME PAGE