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CAIIB - ABM- CASE STUDIES / NUMERICAL QUESTIONS

A zero-Coupon bond has a future value of Rs. 1000 and matures in 2 years and can be currently purchased for Rs. 925. Calculate its current yield.

a. 2.78
b. 2.98
c. 3.78
d. 3.98

Ans - d

Explanation :

Here
1000 = 925 × (1 + r)^2

So,
r = 1.0398 – 1
= 0.0398
= 3.98%
.............................................

Gaurav invested in 12.5%, 5-year bond of face value of Rs. 100. The expected market rate is 15%. What is the duration of the bond?

a. 3.98 years
b. 3.89 years
c. 2.98 years
d. 2.89 years

Ans - a

Explanation :

Bond’s Duration = ΣPV×T ÷ ΣP

Bond Price = (1/(1+R)^t)((coupon*((1+R)^t-1)/R)+Face Value)

ΣP = {12.5 × (1.155 -1) ÷ 0.15 + 100} ÷ 1.155
= 91.6196

Here a = 0.86956 and a^t = 0.497176
So, ΣPV × T = 12.5 × 6.66636 × {0.502824 ÷ 0.13044 – 2.4588} + 248.588
= 116.33046 + 248.588 = 364.92

So, Duration of the Bond
= 364.92 / 91.6196
= 3.98 years
.............................................

You recently earned a 13% return on an investment during the preceding year. If the inflation rate during that period is 8% what was your real return during that period?

a. 5%
b. 4.63 %
c. 4.42%
d. None

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

You find that the yield on a 6 year bond is 12% while that of 4 year bond is 9%. What should be the yield on a 2 year bond beginning 4 from now?

a. 18.25%
b. 16.56%
c. 12.65%
d. None

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

Kumar invested in 10%, 3-year bond of face value of Rs. 1000. The expected market rate is 12%. What is the duration of the bond?

a. 2.37 years
b. 2.73 years
c. 3.27 years
d. 3.72 years

Ans – b

Explanation :

Bond’s Duration = ΣPV×t ÷ ΣP
Bond Price = (1/(1+R)^t)((coupon*((1+R)^t-1)/R)+Face Value)

ΣP = {100 × (1.123 -1) ÷ 0.12 + 1000} ÷ 1.123
= 951.6

Here 1 ÷ 1.12 = 0.89286, so a^t = 0.711787
ΣPV × t = 100 × 8.33336 × [0.288213 ÷ 0.10714286 – 3 × 0.711787] + 3000 × 0.711787
= 833.336 × (2.689988 – 2.135361) + 2135.361
= 462.19 + 2135.36 = 2597.55

So, Duration of the Bond
= 2597.55 ÷ 951.6
= 2.73 years
.............................................

You have the choice between investing in a corporate bond with a yield of 8% or a municipal bond. If your marginal tax rate is 28% , what should be the yield on the municipal bond in order to be competitive?

a. 8.00%
b. 5.76 %
c. 11.11 %
d. 13. 69%

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

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

a. Rs 1200.00
b. Rs 1000.56
c. Rs 1198.57
d. Rs 762.56

Ans - c

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