Understanding Bond Valuation and Yield to Maturity

Posted on Jan 9, 2025 in Finance

Chapter 6 Homework

1. Default Risk Premium

The default risk premium is that portion of a nominal interest rate or bond yield that represents compensation for the possibility of nonpayment by the bond issuer.

2. Bond Pricing at Par

A bond with a 5 percent coupon that pays interest semiannually and is priced at par will have a market price of $1,000 and interest payments in the amount of $25 each.

3. Bond Selling at a Premium

All else constant, a coupon bond that is selling at a premium must have a yield to maturity that is less than the coupon rate.

4. The Rose Shoppe Bond Pricing

The Rose Shoppe offers 10-year, 8 percent coupon bonds with semiannual payments and a yield to maturity of 8.24 percent. What is the market price of a $1,000 face value bond?

  • Settlement Date (SD): 1/1/2000
  • Maturity Date (MT): 1/1/2010
  • Annual Coupon Rate (ACR): 8%
  • Yield to Maturity (YTM): 8.24%
  • Face Value (% of Par): 100
  • Coupons per Year (CPY): 2
  • Using Excel’s PRICE function:
  • Bond Price (% of par): 98.39
  • Dollar price of bond: 98.39 * 10 = $983.90

5. North & South Bond Yield

The bonds issued by North & South bear a coupon rate of 7.5 percent, payable semiannually. The bonds mature in 6.5 years, sell at par, and have a $1,000 face value. What is the yield to maturity? (Yield to maturity = discount rate = required return = interest rate) = 7.50%

6. Webster’s Bond Yield

Webster’s has a 12-year bond issue outstanding that pays a coupon rate of 6.5 percent. The bond is currently priced at $938.76 and has a par value of $1,000. Interest is paid semiannually. What is the yield to maturity?

  • SD: 1/1/2000
  • MD: 1/1/2012
  • CR: 6.5%
  • Bond Price (% of Par): (938.76/1000)*100 = 93.876
  • FV (% of Par): 100
  • CPY: 2
  • Using Excel’s YIELD function: 7.27%

7. Bond Pricing with Annual Payments

How much should you pay for a $1,000 bond with a 10% coupon, annual payments, and five years to maturity if the interest rate is 12%?

  • SD: 1/1/2000
  • MD: 1/1/2005
  • ACR: 10%
  • YTM: 12%
  • FV (% of Par): 100
  • CPY: 1
  • Using Excel’s PRICE function:
  • Bond price (% of par): 92.79
  • Dollar Price of Bond: 92.79 * 10 = $927.90

8. Greenbrier Industrial Products’ Bond Yield

Greenbrier Industrial Products’ bonds have a 7.60 percent coupon and pay interest annually. The face value is $1,000 and the current market price is $1,062.50 per bond. The bonds mature in 16 years. What is the yield to maturity?

  • SD: 1/1/2000
  • MD: 1/1/2016
  • ACR: 7.60%
  • BP (% of Par): 106.25 = (1062.50/1000)*100
  • FV (% of Par): 100
  • CPY: 1
  • Using Excel’s YIELD function: 7.05%

9. Investment-Grade Bonds

Which of the following bonds would be considered to be of investment-grade? A Baa-rated bond.

Chapter 6 Excel Calculations

1. King Noodles’ Bond Pricing

King Noodles’ bonds have a 9% coupon rate. Interest is paid semiannually and the bonds have a maturity of 10 years. If the appropriate discount rate is 10% on similar bonds, what is the price of King Noodles’ bonds?

  • SD: 1/1/2000
  • MD: 1/1/2010
  • CR: 9%
  • DR or YTM: 10%
  • FV (% of Par): 100
  • CPY: 2
  • Using Excel’s PRICE function:
  • Bond price (% of par): 93.77
  • Dollar price of bond: 93.77 * 10 = $937.70

2. Dizzy Corp. Bond Yield

Dizzy Corp. bonds bearing a coupon rate of 12%, pay coupons semiannually, have 3 years remaining to maturity, and are currently priced at $940 per bond. What is the yield to maturity?

  • SD: 1/1/2000
  • MD: 1/1/2003
  • CR: 12%
  • Bond price (% of par): 94 = (940/1000)*100
  • FV (% of par): 100
  • CPY: 2
  • Using Excel’s YIELD function: 14.49%

3. Bond Pricing with Annual Coupon

What would you pay for a bond that pays an annual coupon of $45, matures in 11 years, and has a yield to maturity of 10%? (When the coupon is in $ value, divide by the price: $45/$1000 = 4.5%)

  • SD: 1/1/2000
  • MD: 1/1/2011
  • CR: 4.5%
  • YTM: 10%
  • FV (% of Par): 100
  • Frequency or coupons per year: 1
  • Using Excel’s PRICE function:
  • Bond Price (% of par): 64.28
  • Dollar price: 64.28 * 10 = $642.80

4. Bond Yield with Annual Coupon

The market price of a bond is $1,236.94, it has 14 years to maturity, and pays an annual coupon of $100. What is the yield to maturity? (When they give you the bond price in full, you need to get it in % of par: divide the full bond price by 1000 times 100: (1236.94/1000)*100)

  • SD: 1/1/2000
  • MD: 1/1/2014
  • CR: 10% = (100/1000)
  • BP (% of Par): 123.694 = (1236.94/1000)*100
  • FV (% of par): 100
  • CPY: 1
  • Using Excel’s YIELD function:
  • YTM: 7.25%