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