An investor has two bonds in his or herportfolio, Bond C and Bond Z. Each mature
ID: 2661404 • Letter: A
Question
An investor has two bonds in his or herportfolio, Bond C and Bond Z. Each matures in 4 years, has aface value of $1,000, and has a yield to maturity of 9.6percent. Bond C pays a 10 percent annual coupon, while Bond Zis a zero coupon bond. Assuming that the yield to maturity ofeach bond remains 9.6% over the next four years, calculate theprice of each of the bonds at the following years tomaturity:
Years to Maturity
Price of Bond C
Price of Bond Z
4
3
2
1
0
Years to Maturity
Price of Bond C
Price of Bond Z
4
3
2
1
0
Explanation / Answer
Bond “C” Bond“Z”
Number of years tomaturity 4years 4 years
Yield toMaturity 9.6% 9.6%
Annual Couponrate 10% 0%
Face Value of thebond $1,000 $1,000
Bond “C”
Calculating Bond Value, if the bond matures in 4years:
Bond Value = C * {1-1/(1+r)t} / r + F / (1+r)t
Bond Value = $100* [1-1/(1.096)4 / 0.096 +$1,000 / (1.096)4
Bond Value = $100 * 3.1974+ $693.05
Bond Value = $319.74 + $693.05
Bond Value = $1,012.79
Calculating Bond Value, if the bond matures in 3years:
Bond Value = C * {1-1/(1+r)t} / r + F / (1+r)t
Bond Value = $100* [1-1/(1.096)3 / 0.096 +$1,000 / (1.096)3
Bond Value = $100 * 2.5043 + $759.59
Bond Value = $250.43 + $759.59
Bond Value = $943.48
Calculating Bond Value, if the bond matures in2years:
Bond Value = C * {1-1/(1+r)t} / r + F / (1+r)t
Bond Value = $100* [1-1/(1.096)2 / 0.096 +$1,000 / (1.096)2
Bond Value = $100 * 1.7449 + $832.489
Bond Value = $174.49 + $832.489
Calculating Bond Value, if the bond matures in1years:
Bond Value = C * {1-1/(1+r)t} / r + F / (1+r)t
Bond Value = $100* [1-1/(1.096)1 / 0.096 +$1,000 / (1.096)1
Bond Value = $100 * 0.9125 + $912.40
Bond Value = $91.25 + $912.40
Bond Value = $1,003.65
Bond “Z”
Calculating Bond Value, if the bond matures in 4years:
Bond Value = C * {1-1/(1+r)t} / r + F / (1+r)t
Bond Value = $0* [1-1/(1.096)4 / 0.096 +$1,000 / (1.096)4
Bond Value = $0 * 3.1974+ $693.05
Bond Value = $0 + $693.05
Bond Value = $693.05
Calculating Bond Value, if the bond matures in 3years:
Bond Value = C * {1-1/(1+r)t} / r + F / (1+r)t
Bond Value = $0* [1-1/(1.096)3 / 0.096 + $1,000/ (1.096)3
Bond Value = $0 * 2.5043 + $759.59
Bond Value = $0 + $759.59
Bond Value = $759.59
Calculating Bond Value, if the bond matures in2years:
Bond Value = C * {1-1/(1+r)t} / r + F / (1+r)t
Bond Value = $0* [1-1/(1.096)2 / 0.096 + $1,000/ (1.096)2
Bond Value = $0 * 1.7449 + $832.489
Bond Value = $0 + $832.489
Bond Value = $832.49
Calculating Bond Value, if the bond matures in1years:
Bond Value = C * {1-1/(1+r)t} / r + F / (1+r)t
Bond Value = $0* [1-1/(1.096)1 / 0.096 + $1,000/ (1.096)1
Bond Value = $0 * 0.9125 + $912.40
Bond Value = $0 + $912.40
Bond Value = $912.40
Years to Maturity
Price of Bond "C"
Price of Bond "Z"
4
$1,012.79
$693.05
3
$943.48
$759.59
2
$1,006.98
$832.49
1
$1,003.65
$912.40
Years to Maturity
Price of Bond "C"
Price of Bond "Z"
4
$1,012.79
$693.05
3
$943.48
$759.59
2
$1,006.98
$832.49
1
$1,003.65
$912.40
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