Question

An AA-rated corporate bond has a yield to maturity of 10%. A U.S. Treasury security has a yield to maturity of 8%. These yields are quoted as APRs with semi-annual compounding. Both bonds pay semi-annual coupons at an annual rate of 9% (i.e., coupon rate) and have five years to maturity. The face value of both bonds is $100. a) What is the price of the Treasury bond? b) What is the price of the AA-rated corporate bond? c) What is the credit spread on the AA-bonds?

Answer 1

The correct answer for option (a) is $104.06, for option (b) is $96.14 and for option (c) is 2%.

Step-by-step explanation:

According to the scenario, the given data are as follows:

Face value of bonds = $100

Time period = 5 years

Time period (semi annual) (Nper) = 10

Coupon rate = 9%

Coupon rate (semi annual) = 4.5%

So, payment = $100 × 4.5% = $4.5

(a). Yield to maturity = 8%

So, Rate (semi annually) = 4%

So, price of treasury bond can be calculated by using financial calculator.

The attachment is attached below.

Price of treasury bonds = $104.06

(b) Yield to maturity = 10%

So, Rate (semi annually) = 5%

So, AA rated corporate bond can be calculated by using financial calculator.

The attachment is attached below.

Price of AA rated corporate bonds = $96.14

(c). Credit spread on AA bonds = AA bonds YTM - Treasury bonds YTM

= 10% - 8%

= 2%