Bond Analysis

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Chapter 10: Bond Return and Valuation

Q. 6.Find out the yield to maturity on a 8 per cent 5 year bond selling at Rs 105?

Solution:
Yield to Maturity= [pic]
= [pic]
= [pic] × 100 = [pic] × 100
YTM= 6.82.

Q. 7.(a)Determine the present value of the bond with a face value of Rs 1,000, coupon rate of Rs 90, a maturity period of 10 years for the expected yield to maturity of 10 per cent.

(b)In N is equal to 7 years in the above example, determine the present value of the bond. Discuss the effect of the maturity period on the value of the bond.

Solution:

Face Value= Rs 1,000
Coupon Rate= Rs 90
Maturity Period= 10 years
YTM= 10 %
Present value= C(PVI FA k,n) + F (PVIF k,n)
= 90 (6.145) + 1000 (0.386)
= 553.05 + 386
= Rs 939.05
If N = 7 years
Present Value= 90 (4.868) + 1,000 (0.513)
= 438.12 + 513
P0= Rs 951.12
With the increase in maturity period, the discount rate has increased, the discount is more (1000 – 939.05 = Rs 60.95) in 10 year bond than 7 year bond (1000 – 951.12 = Rs 49.88)

Q. 8.Ann’s bond portfolio manager advises her to buy a 7 years, Rs 5,000 face value bond that gives 8 per cent annual coupon payments. The appropriate discount rate is 9 per cent. The bond is currently selling at Rs 4,700. Should Ann adhere to the manager’s advice?

Solution:
N= 7 years, C = 8 %, Discount rate = 9 %
Market price= Rs 4700, Face value = Rs 5,000.
P0= C(PVIFA k,n) + Face value (PVIF k,n)
= 400 (5.033) + 5,000 (0.547)
= 2,013.2 + 2,735
= Rs 4,748.2
Rs 4,700< 4,748
Ann can buy the bond.

Q. 9.Bonds A and B have similar characters except the maturity period. Both the bonds carry 9 per cent coupon rate with the face value of Rs 10,000. The yield to maturity is 9 per cent. If the yield to maturity is to rise to 11 per cent what will be the respective price change in bond A with 7 years to maturity and B with 10 years to maturity?

Solution:

| |A |B | | N |7 |10 | | C |9 per cent |9 per cent | | YTM |9 per cent |9 per cent | | Face Value |10,000 |10,000 |

Bond A

If YTM = 9 % P0 = 900 (5.033) + 10,000 (0.547) = 4527.7 + 5470
= Rs 9999.7 (or) 10,000
If YTM = 11 %
P0 = 900 (4.713) + 10,000 (0.482)
= 4241.7 + 4820 = Rs 9061.7
The P0 declined by Rs 938.3

Bond B

If YTM 9 %
P0= 900 (6.418) + 10,000 (0.422)
= 5776.2 + 4220
= Rs 9996.2
If YTM 11 %
P0= 900 (5.889) + 10,000 (0.352)
= 5300 + 3520
P0= Rs 8820
The P0 declined by Rs 1176.2

Q. 10.Consider a bond selling at a par value of Rs 1,000 with 7 years to maturity and 8 per cent coupon payment. Calculate the bonds duration.

(b) If the yield to maturity increases to 9 per cent, what would be the price change?

Solution: (a) [pic]

N= 7 years, C = 8 per cent P0 = Rs 1,000

|Years |Ct |PVIF (8 per cent) |Pi Total of PV |Pi /P0 × Yrs | |1 | 80 |0.926 | 74.08 |0.074 | |2 | 80 |0.857 | 68.56 |0.137 | |3 | 80 |0.794 | 63.52 |0.191 | |4 | 80 |0.735 | 58.8 |0.235...
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