A bond with 5 years left to maturity, $1,000 par value and a YTM of 11%...

A bond with 5 years left to maturity, $1,000 par value and a YTM of 11% (APR, semi-annual compounding) pays an 8% coupon semi-annually. • What is the bond’s price? • What are the bond’s Macaulay and modified duration? Interpret them. • What is the the new bond price if the yield decreases by 25bp? • Recalculate the bond’s price on the basis of 10.75% YTM, and verify that the result is in agreement with your answer to the previous question.

Expert Solution

Bond Price	$886.94
Face Value	1,000
Coupon Rate	8.00%
Life in Years	5
Yield	11.00%
Frequency	2

Price: =PV(0.055,10,40,1000)
=$886.94

Period	Cash Flow	PV Cash Flow	Duration Calc
0	($886.94)
1	40.00	37.91	37.91
2	40.00	35.94	71.88
3	40.00	34.06	102.19
4	40.00	32.29	129.15
5	40.00	30.61	153.03
6	40.00	29.01	174.06
7	40.00	27.50	192.48
8	40.00	26.06	208.51
9	40.00	24.71	222.35
10	1,040.00	608.85	6,088.48

Total

7,380.04

Macaulay Duration	4.16
Modified Duration	3.94

The Macaulay duration is the weighted average term to maturity of the cash flows from a bond. For 4.16 it means weighted average maturity of bond = 4.16 years

Modified duration is change in bond price to 1 unit change in yield to maturity. Hence for 1 percentage change in YTm the bond shall change by 3.94%. the sign would be opposite i.e. for increase in yield the price shall go down and vice versa

If decrease by 0.25%, price shall be 886.94*(1+(0.0025*3.94))=895.67

Face Value	1,000
Coupon Rate	8.00%
Life in Years	5
Yield	10.75%
Frequency	2

Price = $895.73 which is very close to as caclulate dby modified duration method

jeff jeffy answered 2 years ago

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