Question

Moon Software Inc. is planning to issue a 10-year, noncallable bonds to raise a total of $3 million. The bond is with a 10-year maturity and a $1000 par value. The bond has a coupon rate of 6.25% and is compounded annually.

In addition, following information is collected:

1) A share of 5 year 4.25% coupon Treasury note is sold at $1028.58.

2) A share of 10 year 4.25% coupon Treasury note is sold at $1022.1.

3) Moon software Inc. has an outstanding 5-year noncallable bond, with a coupon rate of 10%, compounded semi-annually. The bond is valued at par.

Q: How many 10-year bonds must the firm issue to raise $3,00,000? Assume Moon's default risk remains unchanged, and round your final answer up to a whole number of bonds.

Answer 1

Default Risk Premium Calculation:

Treasury Note: Tenure = 5 years, Coupon Rate = 4.25 %, Price = $ 1028.58, Par Value = $ 1000

Let the yield to maturity be y

Annual Coupon = 0.0425 x 1000 = $ 42.5

Therefore, 1028.58 = 42.5 x (1/y) x [1-{1/(1+y)^(5)}] + 1000 / (1+y)^(5)

Using EXCEL's Goal Seek Function to solve the above equation, we get:

y = 0.03615 or 3.615 %

Existing Bond: Coupon = 10%, Par Value = $ 1000, Bond Price = Par Value = $ 1000, As bond price equals its par value, the bond's Yield should equal its coupon rate

Therefore, Yield of 5 - Year Corporate Bond = 10 %

Default Risk Premium = 10 - 3.615 = 6.385 %

10-Year Treasury Note Yield :

Tenure = 10 years, Coupon = 4.25 %, Bond Price = $ 1022.1

Annual Coupon = 0.0425 x 1000 = $ 42.5

Let the yield to maturity be y

Therefore, 1022.1 = 42.5 x (1/y) x [1-{1/(1+y)^(10)}] + 1000 / (1+y)^(10)

Using EXCEL's Goal Seek Function to solve the above equation, we get:

y = 0.03978 or 3.978 %

Yield of About to be Issued Bond: Expected Yield of 10-Year Corporate Bond = Yield of 10 Year Treasury Bond + Default Risk Premium = 3.978 + 6.385 = 10.363 %

Bond Coupon = 6.25 % and Par Value = $ 1000

Annual Coupon = 0.0625 x 1000 = $ 62.5

Bond Tenure = 10 years

Therefore, Bond Price = 62.5 x (1/0.10363) x [1-{1/(1.10363)^(10)}] + 1000 / (1.10363)^(10) = $ 751.167

Target Amount to be Raised = $ 3000000

Therefore, Number of Bonds Required = 3000000 / 751.167 = 3993.78 ~ 3994