__BANK FINANCIAL MANAGEMENT IMPORTANT CASE STUDIES/NUMERICALS: 1__

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

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

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

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