Question

Suppose the coupon rate on a bond is 10% paid annually, the yield to maturity is 12%, the face value of the bond is $1000, the maturity is 2 years, and the price of the bond is $966.20.

a. According to his information, you can say that this bond is sold on the market:

A) at par value

B) at a premium

C) at a discount

b. Using the information provided above, calculate the duration of the annual coupon bond:

c. If the yield to maturity increased to 12.1% and duration is 1.92 years, what would the new price of the bond be

Answer 1

A. if using financial calculator

as the price of the bond (966.2) is currently below the face value (1000) of the bond it can be said to be at a discount. so C is correct

a is incorrect because at par value face value = market price of the bond

b is incorrect because if it is at premium, market price of bond > face value

B. DURATION OF BOND = 1.84

period (d)	cash flow(a)	discount factor	PV of $1 cash flow(b)	PV of cash flow (c = a*b)	period*pv ofcashflow (e = c*d)
1	100	1.12	1/ 1.12 = 0.892	89.29	89.28
2	1100	(1.12)2 = 1.2544	1/1.2544 = 0.797	876.91	1753.82
total					1843.11

duration = sum of  (E) / current bond price

duration = 1843.11/966.2 = 1.91

C. new price of bond = 958.28

period (d)	cash flow(a)	discount factor	PV of $1 cash flow(b)	PV of cash flow	period*pv ofcashflow
				(c = a*b)	(e = c*d)
1	100	1.121	0.89206066	89.21	89.20606601
2	1100	(1.121)2 = 1.256641	0.795772221	875.35	1750.698887
total					1,839.90

duration = sum of  (E) / current bond price

current bond price = 1839.9/1.92 = 958.28