Question

Ron Carr

7.Ron Car is an income investor who has a relatively low risk tolerance. He is considering the purchase of a $1,000 face value bond with the following characteristics:

•Coupon: 4 percent

•Coupon payments per year: one

•Maturity: five years

•Current market interest rate: 8 percent

•Yield to maturity: 8 percent

a.What is the bond’s current price?

b.What is the bond’s modified duration?

c.Based on your answer to the previous question, what will happen to the value of the bond if interest rates increase by 1 percent?

Answer 1

a

K = N

Bond Price =∑ [( Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N

k=1

K =5

Bond Price =∑ [(4*1000/100)/(1 + 8/100)^k]     +   1000/(1 + 8/100)^5

k=1

Bond Price = 840.29

b

Period	Cash Flow	Discounting factor	PV Cash Flow	Duration Calc
0	($840.29)	=(1+YTM/number of coupon payments in the year)^period	=cashflow/discounting factor	=PV cashflow*period
1	40.00	1.08	37.04	37.04
2	40.00	1.17	34.29	68.59
3	40.00	1.26	31.75	95.26
4	40.00	1.36	29.40	117.60
5	1,040.00	1.47	707.81	3,539.03
			Total	3,857.52

Macaulay duration =(∑ Duration calc)/(bond price*number of coupon per year)

=3857.52/(840.29*1)

=4.590703

Modified duration = Macaulay duration/(1+YTM)

=4.59/(1+0.08)

=4.25065

c

Using only modified duration

Mod.duration prediction = -Mod. Duration*Yield_Change*Bond_Price

=-4.25*0.01*840.29

=-35.72

%age change in bond price=Mod.duration prediction/bond price

=-35.72/840.29

=-4.25%

New bond price = bond price+Modified duration prediction

=840.29-35.72

=804.57