1. A Rs.1000 par value bond, bearing a coupon rate of 12 percent will mature after 6 years. What is the value of the bond, if the discount rate is 16 percent?

Solution:6 120 1000

P = +t=1 (1.16)t (1.16)6

= Rs.120 x PVIFA(16%, 6 years) + Rs.1000 x PVIF (16%, 6 years)= Rs.120 x 3.685 + Rs.1000 x 0.410= Rs. 852.20

2.. A Rs.100 par value bond, bearing a coupon rate of 9 percent will mature after 4 years. What is the value of the bond, if the discount rate is 13 percent?

Solution:

4 9 100P = +

t=1 (1.13)t (1.13)4

= Rs.9 x PVIFA(13%, 4 years) + Rs.100 x PVIF (13%, 4 years)= Rs.9 x 2.974 + Rs.100 x 0.613= Rs. 88.07

3. The market value of a Rs.1,000 par value bond, carrying a coupon rate of 10 percent and maturing after 5 years, is Rs.850. What is the yield to maturity on this bond?

Solution:

The yield to maturity is the value of r that satisfies the following equality.

5 100 1,000Rs.850 = +

t=1 (1+r) t (1+r)5

Try r = 14%. The right hand side (RHS) of the above equation is:Rs.100 x PVIFA (14%, 5 years) + Rs.1,000 x PVIF (14%, 5 years)= Rs.100 x 3.433 + Rs.1,000 x 0.519= Rs.862.30

Try r = 15%. The right hand side (RHS) of the above equation is:Rs.100 x PVIFA (15%, 5 years) + Rs.1,000 x PVIF (15%, 5years)= Rs.100 x 3.352 + Rs.1,000 x 0.497= Rs.832.20

Thus the value of r at which the RHS becomes equal to Rs.850 lies between 14% and 15%.

Using linear interpolation in this range, we get

862.30 – 850.00Yield to maturity = 14% + 862.30 – 832.20 x 1%

= 14.41%

4. The market value of a Rs.100 par value bond, carrying a coupon rate of 8.5 percent and maturing after 8 years, is Rs.95. What is the yield to maturity on this bond?

Solution:

The yield to maturity is the value of r that satisfies the following equality.

8 8.5 100 95 = +

t=1 (1+r) t (1+r)8

Try r = 10%. The right hand side (RHS) of the above equation is:8.5 x PVIFA (10%, 8 years) + Rs.100 x PVIF (10%, 8 years)

= Rs.8.5 x 5.335 + Rs.100 x 0.467= Rs.92.05

Try r = 9%. The right hand side (RHS) of the above equation is:8.5 x PVIFA (9 %, 8 years) + Rs.100 x PVIF (9%, 8years)= 8.5 x 5.535 + Rs.100 x 0.502= 47.04 + 50.20 = 97.24

Thus the value of r at which the RHS becomes equal to Rs.95 lies between 9% and 10%.

Using linear interpolation in this range, we get

97.24 – 95.00Yield to maturity = 9 % + 97.24 – 92.05 x 1%

= 9.43 %

5. A Rs.1000 par value bond bears a coupon rate of 10 percent and matures after 5 years. Interest is payable semi-annually. Compute the value of the bond if the required rate of return is 18 percent.

Solution:

10 50 1000P = +

t=1 (1.09) t (1.09)10

= 50 x PVIFA (9%, 10 years) + 1000 x PVIF (9%, 10 years)= 50 x 6.418 + Rs.1000 x 0.422= Rs. 742.90

6. A Rs.100 par value bond bears a coupon rate of 8 percent and matures after 10 years. Interest is payable semi-annually. Compute the value of the bond if the required rate of return is 12 percent.

Solution:

20 4 100P = +

t=1 (1.06) t (1.06)20

= 4 x PVIFA (6%, 20 years) + Rs.100 x PVIF (6%, 20 years)= 6 x 11.470 + Rs.100 x 0.312= Rs.100.02

7. You are considering investing in one of the following bonds:

Coupon rate Maturity Price/Rs.100 par valueBond A 11% 8 yrs Rs.80Bond B 9% 9 yrs Rs.70

Your income tax rate is 34 percent and your capital gains tax is effectively 10 percent. Capital gains taxes are paid at the time of maturity on the difference between the purchase price and par value. What is your post-tax yield to maturity from these bonds?

Solution:

The post-tax interest and maturity value are calculated below: Bond A Bond B

* Post-tax interest (C ) 11(1 – 0.34) 9 (1 – 0.34)=Rs.7.26 =Rs.5.94

* Post-tax maturity value (M) 100 - 100 -[ (100-80)x 0.1] [ (100 – 70)x 0.1]=Rs.98 =Rs.97

The post-tax YTM, using the approximate YTM formula is calculated below

7.26 + (98-80)/8Bond A : Post-tax YTM = --------------------

0.6 x 80 + 0.4 x 98

= 10.91%

5.94 + (97 – 70)/9Bond B : Post-tax YTM = ----------------------

0.6x 70 + 0.4 x 97

= 11.06 %

8. You are considering investing in one of the following bonds:

Coupon rate Maturity Price/Rs.1000 par valueBond A 12% 7 yrs Rs. 930Bond B 8 % 5 yrs Rs. 860

Your income tax rate is 33 percent and your capital gains tax is effectively 10 percent. Capital gains taxes are paid at the time of maturity on the difference between the purchase price and par value. What is your post-tax yield to maturity from these bonds?

Solution:

The post-tax interest and maturity value are calculated below:

Bond A Bond B

* Post-tax interest (C) 120(1 – 0.33) 80 (1 – 0.33)=Rs.80.40 =Rs.53.6

* Post-tax maturity value (M) 1000 - 1000 -[(1000-930) x 0.1] [ (1000 – 860)x 0.1]=Rs. 993 =Rs.986

The post-tax YTM, using the approximate YTM formula is calculated below

80.40 + (993-930)/7Bond A : Post-tax YTM = --------------------

0.6 x 930 + 0.4 x 993

= 9.36 %

53.6 + (986 – 860)/5Bond B : Post-tax YTM = ----------------------

0.6x 860 + 0.4 x 986

= 8.66 %

9. A company's bonds have a par value of Rs.100, mature in 5 years, and carry a coupon rate of 10 percent payable semi-annually. If the appropriate discount rate is 14 percent, what price should the bond command in the market place?

Solution:10 5 100

P = +t=1 (1.07) t (1.07)10

= Rs.5 x PVIFA(7%, 10) + Rs.100 x PVIF (7%, 10)= Rs.5 x 7.024 + Rs.100 x 0.508= Rs. 85.92

10. A company's bonds have a par value of Rs.1000, mature in 8 years, and carry a coupon rate of 14 percent payable semi-annually. If the appropriate discount rate is 12 percent, what price should the bond command in the market place?

Solution:16 70 1000

P = +t=1 (1.06) t (1.06)16

= Rs.70 x PVIFA(6%, 16) + Rs.1000 x PVIF (6%, 16)= Rs.70 x 10.106 + Rs.1000 x 0.394 = Rs. 1101.42