Question

Insook, Inc., and Hankyu Corp. both have 7 percent coupon bonds outstanding, with semi-annual interest payments, and both are prices at par value. The Insook, Inc. bond has 2 years to maturity, whereas the Hankyu Corp. bond has 5 years to maturity.

a. If the interest rates suddenly rise by 2 percent, what is the price of Insook, and Hankyu’s bonds respectively?

b. What is the Macaulay duration of Insook, and Hankyu’s bonds respectively if the interest rates increase by 2%?

c.Which bond (Insook or Hankyu) is exposed to higher interest rate risk? Why?

d) What are factors affecting interest rate risk?

Which bond (Insook or Hankyu) is exposed to higher interest rate risk? Why?

Answer 1

Solution

Since both the bonds are trading at par value, YTM = interest rate = 7%

Now YTM is increased by 2% , and hence new YTM = 9%

Since interest is paid semi annual , YTM = 9%/2 = 4.5%

Statement showing Price and Macaulay duration of Insook, Inc

No of payments	Interest payments	Redemption value	Total cash flow	PVIF @ 4.5%	PV of cash flow	Weightage of PV of cash flow	Macaulay duration
1	35		35	0.9569	33.49	0.0347	0.03
2	35		35	0.9157	32.05	0.0332	0.07
3	35		35	0.8763	30.67	0.0318	0.10
4	35	1000	1035	0.8386	867.91	0.9002	3.60
					964.12		3.80

Price of bond is nothing but present value of future cash flow

Thus price of Insook, Inc = $964.12

Macaulay duration = 3.80/2 = 1.9 years

Statement showing Price and Macaulay duration of Hankyu Corp.

No of payments	Interest payments	Redemption value	Total cash flow	PVIF @ 4.5%	PV of cash flow	Weightage of PV of cash flow	Macaulay duration
A						B	C =A x B
1	35		35	0.9569	33.49	0.0364	0.04
2	35		35	0.9157	32.05	0.0348	0.07
3	35		35	0.8763	30.67	0.0333	0.10
4	35		35	0.8386	29.35	0.0319	0.13
5	35		35	0.8025	28.09	0.0305	0.15
6	35		35	0.7679	26.88	0.0292	0.18
7	35		35	0.7348	25.72	0.0279	0.20
8	35		35	0.7032	24.61	0.0267	0.21
9	35		35	0.6729	23.55	0.0256	0.23
10	35	1000	1035	0.6439	666.47	0.7237	7.24
					920.87		8.54

Price of bond is nothing but present value of future cash flow

Thus price of Hankyu Corp. = $920.87

Macaulay duration = 8.54/2 = 4.27 years

Thus

a) If interest rate rises by 2% then

Price of Insook, Inc = $964.12

Price of Hankyu Corp. = $920.87

b) If interest rate rises by 2% then

Macaulay duration Insook, Inc = 1.9 years

Macaulay duration Hankyu Corp = 4.27 years

c) Hankyu Corp's bond is exposed to higher interest rate risk because it has larger duration, greater the duration more price is sensitive to interest rate change

d) Factors affecting interest rate risk are duration of bond , coupon rate of bond, credit risk of the company issuing the bonds etc