Question

Consider a bond that has a coupon rate of 5%, five years to maturity, and is currently priced to yield 6%. Calculate the following:  Macaulay duration  Modified duration  Percentage change in price for a 1% increase in the yield to maturity

Answer 1

Final answers

Macaulay duration = 4.53

Modified duration = 4.28

Percentage change in price for a 1% increase in the yield to maturity = 4.28 % decrease or - 4.28 %

Explanation

Let ......... "T" .... represents the time ........ 1, 2 , 3 , 4,........5 years

CF = Cash flow

DF = Discounting factors taken at 6% yield to maturity

PV = Present values of cash flows = DF * CF

W = Weight ....... these values to computed by dividing each year PV with total of PV column.

T	CF	DF (6%)	PV	W	W * T
1	50	0.943396	47.17	0.049244	0.049244
2	50	0.889996	44.50	0.046457	0.092913
3	50	0.839619	41.98	0.043827	0.131481
4	50	0.792094	39.60	0.041346	0.165385
5	50	0.747258	37.36	0.039006	0.195029
5	1000	0.747258	747.26	0.780117	3.900583
		Total PV	957.88	Total (W*T)=	4.534635

Macaulay's Duration = Total of ( W * T) = 4.53 Years .

Modified Duration = Macaulay's Duration / ( 1 + ytm) = 4.53 / (1.06) = 4.28

Modified duration measures how sensitive is the bond price to interest rate changes.

Hence for 1 % change in Interest, bond price shall change by 4.28%

YTM increases by 1 % .......... it means bond price decreases by 4.28 % .