Answer - Bond Valuation Practice - Tài liệu tham khảo | Đại học Hoa Sen

Answer - Bond Valuation Practice - Tài liệu tham khảo | Đại học Hoa Sen thông tin bổ ích giúp sinh viên tham khảo, ôn luyện và phục vụ nhu cầu học tập của mình cụ thể là có định hướng, ôn tập, nắm vững kiến thức môn học và làm bài tốt trong những bài kiểm tra, bài tiểu luận, bài tập kết thúc học phần, từ đó học tập tốt và có kết quả cao cũng như có thể vận dụng tốt những kiến thức mình đã học.

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Môn: Corporate Finance (CF2033)

Trường: Đại học Hoa Sen

Thông tin:

6 trang 4 tuần trước

Tác giả:

Profile Kim Oanh
1. What is the present value (i.e., price) today of a bond that will pay its owner
$1,000,000 five years from today if the discount rate is 4% per annum?
Ans: This is called a zero-coupon or pure discount bond
821, 27.11P V
Bond
=
F V
(1+ ) (1+4%)r
5
=
5
$1,000,000
= $ 9
2. Assume that a bond makes 30 equal annual payments of $1,000 starting one year
from today. If the discount rate is 3.5% per annum, what is the current price of the
bond? Face value of bond is $10,000
Ans: Recognize that this cash flow stream is an annuity and that the price of an
asset is the present value of its future cash flows.
urrent price of bond P V C = =
r
C
*
1
[
−
1
(1+ )r
n
]
+
F V
(1+ ) 3.5%r
n
=
$1,000
*
1
[
−
1
(1+3.5%)
30 ]
+
$10,000
(1+3.5%)
30
18, 92.05 3, 62.78 21, 54.83= $ 3 + $ 5 = $ 9
3. Coupon Bond: Assume that a bond makes 10 equal annual payments of $1,000
starting one year from today. The bond will make an additional payment of
$100,000 at the end of the last year, year 10. If the discount rate is 3.5% per
annum, what is the current price of the bond?
Ans:
urrent price of bond P V C = =
r
C
*
1
[
−
1
(1+ )r
n
]
+
F V
(1+ ) 3.5%r
n
=
$1,000
*
1
[
−
1
(1+3.5%)
10 ]
+
100,000
(1+3.5%)
10
8, 16.61 70, 91.88 79, 08.49= $ 3 + $ 8 = $ 2
4. The price of a US government issued five year zero coupon bond, with a face
value of $1000, is $744.09. What is the yield to maturity of the bond if the interest
is compounded yearly?
Answer:
rice of bond zero oupon VP − c = P =
F V
(1+ )r
n
V 744.09P = $
V 1, 00F = $ 0
n = 5
=> ield to maturity .09%Y = 6
5. What is the market value of a 20-year bond with face value of $1000, which
makes quarterly coupon payments at a coupon rate of 10%, if the required rate of
return is 8% per year, compounded quarterly?
Ans:
0 0 years periodsn = 2
*
4 = 8
=> 0%/year .5%/quarterc = 1 =
4
10%
= 2 V .5% 1, 00 25C = c
*
F = 2
*
$ 0 = $
%/ %/year quarterr = 8 = 2
V 1, 00F = $ 0
arket value of bond V m = P =
r
C
*
1
[
−
1
(1+ )r
n
]
+
F V
(1+ ) 2%r
n
=
$25
*
1
[
−
1
(1+2%)
80 ]
+
$1,000
(1+2%)
80
993.61 205.11 1, 98.72= $ + $ = $ 1
6. You have just purchased a newly issued $1,000 five-year Vanguard Company
bond at par. This five-year bond pays $60 in semi-annual coupon payments. You
are also considering the purchase of another Vanguard Company bond that pays
$30 in semi- annual coupons and has six years remaining before maturity. This
bond also has a face value of $1000. Both bonds make coupon payments
semiannually.
What is the yield-to-maturity on the five-year bond?
Answer:
Bond 1: (five-year bond)
V 1, 00F = $ 0
arket value V 1, 00m = P = $ 0
0 years periodsn = 5
*
2 = 1
oupon payment 60C = $
Because , yield to maturity = coupon rate =arket value F VM =
2%
F ace V alue
Coupon payment of a year
=
$1000
$60 2
*
= 1
7. Refer back to Question 6. What is the effective annual yield on the five-year bond?
Answer:
ARE = (1 ) 2.36%+
r
m
m
− 1 = (1 )+
2
12%
2
− 1 = 1
8. Refer back to Question 6. Assume that the five-year bond and the six-year bond
have the same yield. What should you be willing to pay for the six-year bond?
Answer:
Bond 2 : the same company issuer as Bond 1, at the same time
V 1, 00F = $ 0
2 years periodsn = 6
*
2 = 1
semi-annualoupon payment 30C = $
ield to maturity of bond 2 r %y = =
2
12%
= 6
arket value of bond 2 V M = P =
r
C
*
1
[
−
1
(1+ )r
n
]
+
F V
(1+ )r
n
=
30
6%
*
1
[
−
1
(1+6%)
12 ]
+
$1,000
(1+6%)
12
251.52 $496.97 748.49= $ + = $
9. Suppose that you purchased a 15-year bond that pays semi-annual coupon of $20
and is currently selling at par. What would your realized annual return be if you
sold the bond five years later when the yield is 5.5%? Assume the face value of the
bond is $1,000.
Ans:
V 1, 00F = $ 0
rice you buy the bond arket value V V 1, 00P = m = P F= = $ 0
5 0 years periodsn = 1
*
2 = 3
oupon payment 20C = $
he price you sell the bond five years later when the yield is 5.5%T =
V 283.44 $581.25 P =
r
C
*
1
[
−
1
(1+ )r
n
]
+
F V
(1+ )r
n
=
$20
2.75%
*
1
[
−
1
(1+2.75%)
20 ]
+
$1,000
(1+2.75%)
20
= $ +
$864.69=
ealized rate of return .5%/5yearsR =
1000
$20 10+864.69−1000
*
= 6
nnual Realized rate of return .27% A =
√
5
(1 .5%)+ 6 − 1 = 1
| 1/6
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Preview text:

1. What is the present value (i.e., price) today of a bond that will pay its owner
$1,000,000 five years from today if the discount rate is 4% per annum?
Ans: This is called a zero-coupon or pure discount bond $1,000,000 P V = FV = = $ 9 5 5 821, 27.11 Bond (1+r) (1+4%)
2. Assume that a bond makes 30 equal annual payments of $1,000 starting one year
from today. If the discount rate is 3.5% per annum, what is the current price of the
bond? Face value of bond is $10,000
Ans: Recognize that this cash flow stream is an annuity and that the price of an
asset is the present value of its future cash flows.
Current price of bond = P V = C * [1 − 1 ] + FV = $1,000 [ − 1 ] + $10,000 n n * 1 r (1+r) (1+r) 3.5% (1+3.5%)30 (1+3.5%)30 = $18, 9 3 2.05 + 3 $ , 6 5 2.78 = $21, 954.83
3. Coupon Bond: Assume that a bond makes 10 equal annual payments of $1,000
starting one year from today. The bond will make an additional payment of
$100,000 at the end of the last year, year 10. If the discount rate is 3.5% per
annum, what is the current price of the bond? Ans:
Current price of bond = P V = C * 1
[ − 1 ] + FV = $1,000 [ − 1 ] + 100,000 n n * 1 r (1+r) (1+r) 3.5% (1+3.5%)10 (1+3.5%)10 = $8, 316.61 + $70, 9 8 1.88 = $79, 208.49
4. The price of a US government issued five year zero coupon bond, with a face
value of $1000, is $744.09. What is the yield to maturity of the bond if the interest is compounded yearly? Answer: P rice of zero − o c upon bond = P V = F V (1+r)n P V = $744.09 F V = $1, 000 n = 5 => Y ield to maturity = . 6 09%
5. What is the market value of a 20-year bond with face value of $1000, which
makes quarterly coupon payments at a coupon rate of 10%, if the required rate of
return is 8% per year, compounded quarterly? Ans: n = 0 2 years * 4 = 80 periods c = 0
1 %/year = 10% = 2.5%/quarter => = 2 $ 0 = $ 4 C = c * F V .5% * 1, 00 25 r = % 8 /year = 2%/quarter F V = $1, 000 a
m rket value of bond = P V = C * [1 − 1 ] + FV = $25 ] + $1,000 n n * 1 [ − 1 r (1+r) (1+r) 2% (1+2%)80 (1+2%)80 = $993.61 + 2 $ 05.11 = $1, 198.72
6. You have just purchased a newly issued $1,000 five-year Vanguard Company
bond at par. This five-year bond pays $60 in semi-annual coupon payments. You
are also considering the purchase of another Vanguard Company bond that pays
$30 in semi- annual coupons and has six years remaining before maturity. This
bond also has a face value of $1000. Both bonds make coupon payments semiannually.
What is the yield-to-maturity on the five-year bond? Answer: Bond 1: (five-year bond) F V = $1, 000 a m rket value = P V = 1 $ , 0 0 0 n = 5 years * 2 = 10 periods Coupon payment = $60 Because Market value = F
V , yield to maturity = coupon rate =
Coupon payment of a year = $60 2 * = 12% F ace V alue $1000
7. Refer back to Question 6. What is the effective annual yield on the five-year bond? Answer: 2
EAR = (1 + r )m − 1 = (1 + 12% ) − 1 = 1 2.36% m 2
8. Refer back to Question 6. Assume that the five-year bond and the six-year bond
have the same yield. What should you be willing to pay for the six-year bond? Answer:
Bond 2 : the same company issuer as Bond 1, at the same time F V = $1, 000 n = 6 years * 2 = 12 periods
Coupon payment = $30 semi-annual
yield to maturity of bond 2 = r = 12% = % 6 2
M arket value of bond 2 = P V = C * [1 − 1 ] + FV = 30 ] + $1,000 n n r (1+r) (1+r) 6% * 1 [ − 1 (1+6%)12 (1+6%)12 = $251.52 + $ 496.97 = $748.49
9. Suppose that you purchased a 15-year bond that pays semi-annual coupon of $20
and is currently selling at par. What would your realized annual return be if you
sold the bond five years later when the yield is 5.5%? Assume the face value of the bond is $1,000. Ans: F V = $1, 000
P rice you buy the bond = market value = P V = F V = $1, 000 n = 5 1 years * 2 = 30 periods Coupon payment = $20
T he price you sell the bond f ive years later when the yield is 5.5% =
P V = C * [1 − 1 ] + FV = $20 [ − 1 ] + $1,000 = $ + n n 283.44 $581.25 r (1+r) (1+r) 2.75% * 1 (1+2.75%)20 (1+2.75%)20 = $864.69
Realized rate of return = $20 1 * 0+864.69−1000 = . 6 5%/5years 1000 n
A nual Realized rate of return = + 6 − 1 = . 1 27% √5(1 .5%)