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CAIIB - ABM- CASE STUDIES / NUMERICAL QUESTIONS

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......

a. 23.69
b. 32.69
c. 23.96
d. 32.96

Ans - d

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)
.............................................

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......

a. 63.90
b. 69.30
c. 36.90
d. 39.60

Ans - b

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
.............................................

You bought a 5 year Zero Coupon bond with a Rs 1000 face value for Rs 735.67. What is the YTM of this bond?

a. 10.36%
b. 6.33%.
c. 4.69%
d. 8.18%

Ans - b
........................................................

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?

a. 12.47
b. 14.27
c. 11.74
d. 11.27

Ans - a

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%
.............................................

A bond with a par-value of Rs. 100 is purchased for 95.92 and it paid a Coupon rate of 5%. Calculate its current yield.

a. 5.12
b. 5.21
c. 5.34
d. 5.43

Ans - b

Explanation :

Coupon = Face value × Coupon Rate
And annual interest paid = Market Price × Current Yield
5 = 95.92 × CY
CY = 0.0521 = 5.21%

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