# Bond Valuation Problem Set The $1,000 face value bond has a coupon rate of 6%, with interest paid semi-annually, and matures in 5 years. If the bond is priced to yield 8%, what is the bond’s value today? A bond has a 8% coupon rate (with interest paid semi-annually), a maturity value of $1,000, and matures in 5 years. If the bond is priced to yield 6%, what is the bond’s current price? A bond has a face value of $1000 with a time to maturity ten years from now. The yield to maturity of the bond now is 10%. What is the price today if pays 8% coupon rate semi-annually? A 2-year zero-coupon note was issued on December 1, 2019. If its YTM is 1.95%, what is its current market value?

**QUESTION**

__BOND VALUATION PROBLEM SET 1__

__Bond Value:__

- The $1,000 face value bond has a coupon rate of 6%, with interest paid semi-annually, and matures in 5 years. If the bond is priced to yield 8%, what is the bond’s value today?
- A bond has a 8% coupon rate (with interest paid semi-annually), a maturity value of $1,000, and matures in 5 years. If the bond is priced to yield 6%, what is the bond’s current price?
- A bond has a face value of $1000 with a time to maturity ten years from now. The yield to maturity of the bond now is 10%. What is the price today if pays 8% coupon rate semi-annually?
- A 2-year zero-coupon note was issued on December 1, 2019. If its YTM is 1.95%, what is its current market value?

__Bond YTM:__

- The $1,000 face value bond has a coupon of 10% (paid semi-annually), matures in 4 years, and has current price of $1,140. What is the bond’s yield to maturity?

- A bond has an 8% coupon rate (semi-annual interest), a maturity value of $1,000, matures in 5 years, and a current price of $1,200. What is the bond’s yield-to-maturity?
- Suppose you invest in zero coupon bonds and you are looking at a five-year zero-coupon that matures on 2/22/2019, and which you want to buy on 2/22/2018. It has a face value of $1,000, and its price is $990.10. If the one-year risk-free rate is 2%, what is the bond’s YTM?
- You are looking at another 5-year zero-coupon bond which matures on 2/22/2020 paying $1,000, and its price is $983.27. If the 2-year risk-free rate is 2.25%, what is the bond’s YTM?

__Bond YTM 2 ^{nd} Series:__

- Suppose you purchase a 25-year, $1000-face value, zero coupon bond for $357.80 when issued on 3/1/2020. What is the bond’s YTM?
- Find the yield to maturity on a semiannual coupon bond you are thinking of buying today. The bond price is $1128, the coupon rate is 6.5%, the face value is $1000, and was issued on Aug 15, 2013, maturing in 13 years.
- Suppose you purchase a 25-year, $1000-face value, zero coupon bond for $357.80 when issued on 3/1/2020. What is the bond’s YTM?

- What is the yield-to-maturity of a $1,000 zero-coupon 2-year note priced at 96.79 and maturing on Dec. 15, 2019? Assume you bought the bond on February 21, 2018. Current rates are 3.5%.

__Coupon Rate/Current Yield:__

- A bond has a current price of $800, a maturity value of $1,000, and matures in 5 years. If interest is paid semi-annually and the bond is priced to yield 8%, what is the bond’s annual coupon rate?
- Consider a $1,000 par value bond with a 7% annual coupon. The bond pays interest annually. There are 2 years remaining until maturity. What is the current yield on the bond assuming that the required return on the bond is 10%?

- Consider a $1,000 par value bond with a 7% annual coupon. The bond pays interest annually. There are 2 years remaining until maturity. What is the current yield on the bond assuming that the required return on the bond is 10%?
- A bond has a current price of $800, a maturity value of $1,000 (matures in 5 years). If interest is paid semi-annually and the bond has a current yield of 8%, what is the bond’s annual coupon rate?

__Duration Duration:__

What is the duration of the following bonds (round to two decimal places)?

Terms: |
1. Bond A |
2. Bond B |
3. Bond C |
4. Bond D |

Settlement Date |
4/15/2020 | 4/15/2020 | 4/15/2020 | 4/15/2020 |

Issue Date: |
12/15/2015 | 6/1/2018 | 9/15/2012 | 3/1/2019 |

Maturity Date: |
12/15/2035 | 6/1/2023 | 9/15/2042 | 3/1/2029 |

Par Value (% of Par): |
100.00 | 100.00 | 100.00 | 100.00 |

Price Now (% of Par): |
||||

Coupon Rate: |
5.50% | 2.85% | (zero-coupon) | 2.75% |

Current Yield: |
3.62% | 1.9% | 2.5% | 2.11% |

Coupon Pmt Frequency: |
2 (Semi-annual) | 2 (Semi-annual) | 2 (Semi-annual) | 2 (Semi-annual) |

__ __

__Modified Duration:__

What is the modified duration of the bonds in the previous section (round to two decimal places)?

- _________
- _________
- _________
- _________

__Miscellaneous Bond Questions:__

- A municipal bond has a coupon rate of 4.5% and just sold for 104.56. It matures on December 1, 2023. What is its tax-equivalent yield? Assume a marginal tax rate of 40% and interest is paid June 1 and December 1.
__Short answer essay__: what is the mathematical difference between duration and modified duration, and what does each one measure? (5 points)-
**ANSWER** **Bond Value**To calculate the bond’s value today, we need to determine the present value of the bond’s future cash flows, which include the coupon payments and the principal repayment at maturity. The bond has a face value of $1,000, a coupon rate of 6% (or $60 per year), and matures in 5 years. The coupon payments are paid semi-annually, so there will be 10 coupon payments in total (5 years * 2). The bond is priced to yield 8%.

Using the formula for the present value of a bond, we can calculate the bond’s value today:

PV = (C / (1 + r/n)) + (C / (1 + r/n)^2) + … + (C / (1 + r/n)^n) + (F / (1 + r/n)^n)

Where:

PV = Present value of the bond

C = Coupon payment

r = Yield to maturity (expressed as a decimal)

n = Number of compounding periods per year

F = Face value of the bondIn this case, C = $60, r = 8% (or 0.08), n = 2 (semi-annual compounding), and F = $1,000.

Using the formula, the bond’s value today is calculated as follows:

PV = (60 / (1 + 0.08/2)) + (60 / (1 + 0.08/2)^2) + (60 / (1 + 0.08/2)^3) + (60 / (1 + 0.08/2)^4) + (60 / (1 + 0.08/2)^5) + (1,000 / (1 + 0.08/2)^5)

PV ≈ $50.83 + $47.22 + $44.02 + $41.18 + $38.68 + $680.58

PV ≈ $902.21

Therefore, the bond’s value today is approximately $902.21.

2. Similarly, for the second bond, which has a coupon rate of 8% (or $80 per year), a face value of $1,000, and matures in 5 years, we can use the same formula to calculate its current price. The bond is priced to yield 6%.

Using the formula:

PV = (C / (1 + r/n)) + (C / (1 + r/n)^2) + … + (C / (1 + r/n)^n) + (F / (1 + r/n)^n)

Where:

PV = Present value of the bond

C = Coupon payment

r = Yield to maturity (expressed as a decimal)

n = Number of compounding periods per year

F = Face value of the bondIn this case, C = $80, r = 6% (or 0.06), n = 2 (semi-annual compounding), and F = $1,000.

Using the formula, the bond’s current price is calculated as follows:

PV = (80 / (1 + 0.06/2)) + (80 / (1 + 0.06/2)^2) + (80 / (1 + 0.06/2)^3) + (80 / (1 + 0.06/2)^4) + (80 / (1 + 0.06/2)^5) + (1,000 / (1 + 0.06/2)^5)

PV ≈ $74.77 + $70.66 + $66.92 + $63.53 + $60.46

+ $927.51

PV ≈ $1,263.85

Therefore, the bond’s current price is approximately $1,263.85.

3. For the third bond, which has a face value of $1,000, a time to maturity of ten years, a coupon rate of 8% (or $40 semi-annually), and a yield to maturity of 10%, we can calculate its price today using the same formula mentioned earlier.

Using the formula:

PV = (C / (1 + r/n)) + (C / (1 + r/n)^2) + … + (C / (1 + r/n)^n) + (F / (1 + r/n)^n)

Where:

PV = Present value of the bond

C = Coupon payment

r = Yield to maturity (expressed as a decimal)

n = Number of compounding periods per year

F = Face value of the bondIn this case, C = $40, r = 10% (or 0.10), n = 2 (semi-annual compounding), and F = $1,000.

Using the formula, the bond’s price today is calculated as follows:

PV = (40 / (1 + 0.10/2)) + (40 / (1 + 0.10/2)^2) + (40 / (1 + 0.10/2)^3) + … + (40 / (1 + 0.10/2)^20) + (1,000 / (1 + 0.10/2)^20)

PV ≈ $18.18 + $16.53 + $15.03 + … + $1.81 + $376.89

PV ≈ $1,122.48

Therefore, the bond’s price today is approximately $1,122.48.

4. In the case of a 2-year zero-coupon note issued on December 1, 2019, with a yield to maturity (YTM) of 1.95%, we can calculate its current market value using the formula for present value:

PV = F / (1 + r)^n

Where:

PV = Present value of the bond

F = Face value of the bond

r = Yield to maturity (expressed as a decimal)

n = Number of years until maturityIn this case, F = $1,000, r = 1.95% (or 0.0195), and n = 2 years.

Using the formula, the bond’s current market value is calculated as follows:

PV = 1,000 / (1 + 0.0195)^2

PV ≈ $961.17

Therefore, the current market value of the bond is approximately $961.17.

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