8 years ago, you paid $961 for a $1,000 par bond that has a 7% coupon rate and m
ID: 2621309 • Letter: 8
Question
8 years ago, you paid $961 for a $1,000 par bond that has a 7% coupon rate and makes annual payments. You are selling it today, after receiving 8 coupon payments, for $1099. You reinvested coupons at the 4.3% annual rate. What is your total return? (Report your answer to two decimals, without the % symbol. E.g., if your answer is 5.1538%, enter it as 5.15.)
What is the duration (D) of a 2-year bond with a $54 annual coupon (paid annually), $1,000 par, and a yield of 1.8%? Record your answer to the nearest 0.001 years.
Explanation / Answer
8 years ago, you paid $961 for a $1,000 par bond that has a 7% coupon rate and makes annual payments. You are selling it today, after receiving 8 coupon payments, for $1099. You reinvested coupons at the 4.3% annual rate. What is your total return?
Initial Price of the bond P0 = $961
Par value of bond = $1000
Coupon rate 7% per annum = 7% * $1000 = $70 per annum
The coupons are reinvested at 4.3% per annum and bond is sold at $1099, therefore total value of investments today is
Year (t)
Cash Flow from coupon payments and maturity amount (CF)
CF are reinvested 4.3% [FV=CF*(1+4.3%)^(8-t)]
1
$70.0
$93.99
2
$70.0
$90.12
3
$70.0
$86.40
4
$70.0
$82.84
5
$70.0
$79.42
6
$70.0
$76.15
7
$70.0
$73.01
8
$70.0
$70.00
8
$1,099.0
$1,099.00
Sum
$1,750.93
Total Value of investment?
Total return =
82.1989%
Total return = (Total Value of investment - Initial Price of the bond)/ Initial Price of the bond *100
= ($1,750.93 - $961)/ $961 *100
= 82.1989%
Annual return = (1+82.1989%) ^ (1/8) -1
= 1.077875 -1
= 0.077875 or 7.7875%
What is the duration (D) of a 2-year bond with a $54 annual coupon (paid annually), $1,000 par, and a yield of 1.8%?
The duration (D) Calculation:
Year (t)
Cash Flow from coupon payments and maturity amount (CF)
Present value (PV) of CF discounted at 1.8% [PV=CF/(1+1.8%)^t]
PV *t
1
$54.0
$53.05
$53.05
2
$54.0
$52.11
$104.21
2
$1,000.0
$964.95
$1,929.90
Sum
$1,070.10
$2,087.16
Bond's Price?
Duration D = Sum of (PV*t)/Bond's Price =
$2,087.16/$1,070.10
1.950
Years
The duration (D) is 1.950 years
Year (t)
Cash Flow from coupon payments and maturity amount (CF)
CF are reinvested 4.3% [FV=CF*(1+4.3%)^(8-t)]
1
$70.0
$93.99
2
$70.0
$90.12
3
$70.0
$86.40
4
$70.0
$82.84
5
$70.0
$79.42
6
$70.0
$76.15
7
$70.0
$73.01
8
$70.0
$70.00
8
$1,099.0
$1,099.00
Sum
$1,750.93
Total Value of investment?
Total return =
82.1989%
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