Problem 77 Interest rate sensitivity An investor purchased t

Problem 7-7 Interest rate sensitivity An investor purchased the following 5 bonds. Each bond had a par value of $1,000 and an 8% yield to maturity on the purchase day. Immediately after the investor purchased them, interest rates fell and each then had a new YTM of 6%, what is the percentage change in price for each bond after the decline in interest rates? Fill in the following table. Round your answers to the nearest cent or to two decimal places. Price @ 8% Price 6% Percentage Change 10-year, 10% annual coupon 10-year zero s-year zero 30-year zero $100 perpetuity

Solution

Particulars

Price @8%

Price @6%

Percentage Change

10-year, 10% annual coupon

$1,134.20

$1,294.40

14.12%

10-year zero

$463.19

$558.39

20.55%

5-year zero

$680.58

$747.26

9.80%

30-year zero

$99.38

$174.11

75.20%

$100 Perpetuity

$1,250.00

$1,666.67

33.33%

Using financial calculator BA II Plus - Input details:

Particulars

Yield

PMT

FV

N

CPT > PV

10-year, 10% annual coupon

8

-$100.00

-$1,000.00

10

$1,134.20

10-year zero

8

$0.00

-$1,000.00

10

$463.19

5-year zero

8

$0.00

-$1,000.00

5

$680.58

30-year zero

8

$0.00

-$1,000.00

30

$99.38

$100 Perpetuity

8

-$100.00

$0.00

1000

$1,250.00

Using financial calculator BA II Plus - Input details:

Particulars

Yield

PMT

FV

N

CPT > PV

10-year, 10% annual coupon

6

-$100.00

-$1,000.00

10

$1,294.40

10-year zero

6

$0.00

-$1,000.00

10

$558.39

5-year zero

6

$0.00

-$1,000.00

5

$747.26

30-year zero

6

$0.00

-$1,000.00

30

$174.11

$100 Perpetuity

6

-$100.00

$0.00

1000

$1,666.67

Notes:

For perpetuity we can use an assumed N = 1000; you can assume any number between 500-1000 years result will be same

Prercentage change in % = (Price @6%-Price@8%)/Price @8%

Particulars	Price @8%	Price @6%	Percentage Change
10-year, 10% annual coupon	$1,134.20	$1,294.40	14.12%
10-year zero	$463.19	$558.39	20.55%
5-year zero	$680.58	$747.26	9.80%
30-year zero	$99.38	$174.11	75.20%
$100 Perpetuity	$1,250.00	$1,666.67	33.33%