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CAIIB - ABM- CASE STUDIES / NUMERICAL QUESTIONS

Salim purchased 8%, 3 years bond of Rs. 10 lac, with annual interest payment and face value payable on maturity. The YTM is assumed@ 6%. Calculate % change in the price of the bond when the decrease in YTM is 100 basis points from 6% to 5% and the duration is 2.79 years and modified duration is 2.63 years.

a. 2.36
b. 2.63
c. 3.26
d. 3.62

Ans - b

Explanation :

Percentage change in price of bond

= -MD × Change in Price
= -2.63 × (6% - 5%)
= 2.63%,

That means a fall in YTM by 1% increases the price of the bond by 2.63%.
.............................................

What is the price of a 20-year, zero-coupon bond with a 5.1% yield and Rs. 1000 face value?

a. Rs. 359
b. Rs. 369
c. Rs. 379
d. Rs. 389

Ans - b

Solution :

PV = 1000/(1+0.051)^20
= 369
........................................................

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?

a. 1062.25
b. 1625.25
c. 1026.25
d. 1052.25

Ans – c

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

A 5-year Govt. bond with a coupon rate of 8% has a face value of 1000. What is the annual interest payment?

a. 80
b. 40
c. 100
d. None of the above

Ans - a
.............................................

ABC Inc has a 12 year bond outstanding that makes 9.5% annual coupon payments. If the appropriate discount rate is for such a bond is 7% , what is the appropriate price of bond ?

a. 1254.87
b. 1198.57
c. 1158.57
d. 1232.56

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

A 5-year Govt. bond with a coupon rate of 8% has a face value of 1000. What is the annual interest payment?

A. 80
B. 40
C. 100
D. None of the above

Ans - a
.............................................

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 ......

a. 2.39 & 4.84
b. 3.29 & 4.84
c. 3.29 & 4.48
d. 2.39 & 4.48

Ans - c

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%

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