Question

Show all work please

Calculate the price and duration for the following bond when the going rate of interest is 4%. The bond offers 3.5% coupon rate, matures in 3 years and has a par value of $1,000. Show full calculations and fill the table below. YR PV of $ 1 Bond Cash Flows PV (Cash Flows) Year * Present Value of Cash Flow 1 2 3 3 Total Price = Duration

What would be the new price if the market rate of interest rises to 5%? Show by using the duration only and show all calculations. If you do not use and do not apply the duration concept, you will not get credit for this.

Explain the concept of duration. Why is duration thought of as a measure of risk? If duration is a measure of risk, what would you do if interest rates are expected to rise (assume you want to be fully invested in bonds). Would you buy bonds with shorter or longer durations?

Answer 1

Formula sheet

A	B	C	D	E	F	G	H	I	J
2
3		Face value	1000
4		Coupon rate	0.035
5		Market interest rate	0.04
6		Maturity	3	years
7		Annual Coupon	=D3*D4	=D3*D4
8
9		Bond Price will be the present value of bond cash flows at market rate.
10
11		Macaulay Duration is the weightage average of the time to present value of cash flows.
12		Formula for Macaulay duration is as follows:
13
14
15
16
17
18
19		Where, Ct is cash flow at time t, PV(Ct) is the present value of cash flow at time t and T is the total time horizon.
20
21		Year	PV of $1	Bond Cash Flows	PV(Cash Flows)	Year*Present Value of Cash Flows
22		1	=1/((1+$D$5)^C22)	=$D$7	=D22*E22	=C22*F22
23		2	=1/((1+$D$5)^C23)	=$D$7	=D23*E23	=C23*F23
24		3	=1/((1+$D$5)^C24)	=$D$7	=D24*E24	=C24*F24
25		3	=1/((1+$D$5)^C25)	=D3	=D25*E25	=C25*F25
26		Total			=SUM(F22:F25)	=SUM(G22:G25)
27
28		Price	=F26
29		Duration	=G26/F26	Year
30
31		Calculation of price of bond on the basis of duration rule:
32		Using duration rule, change in bond price can be calculated as:
33		Change in Bond price/Price of the bond = - (Duration / (1+ Yield)) * Change in yield
34
35		Presnet Yield	=D5
36		New Yield	0.05
37		Change in Yield	=D36-D35
38		Current Price of Bond	=D28
39		Duration	=D29
40
41		Change in Bond price/Price of the bond	= - (Duration / (1+ Yield)) * Change in Yield
42			=-(D29/(1+D35))*D37	=-(D29/(1+D35))*D37
43
44		Change in Bond Price	=D42*D38	=D42*D38
45
46		New Bond Price	=Current Price of Bond + Change in Bond Price
47			=D38+D44	=D38+D44
48
49		Hence as per duration rule,
50		New Bond Price	=D47
51