Question

In: Finance

6. Smithson Co.'s Class A bonds have 10 years to go until maturity. They have a...

6. Smithson Co.'s Class A bonds have 10 years to go until maturity. They have a $1,000 face value and carry coupon rates of 8%. Approximately what do the bonds yield at the following prices?

a. $770?

b. $1,150?

c. $1,000?

Solutions

Expert Solution

Answers:

a. 12.08%

b. 5.97%

c. 8.00%

---------------------

Workings:

a. The Approximate Yield to Maturity Formula =[Coupon + ( Face Value - Market Price) / Number of years to maturity] / [( Face Value + Market Price)/2 ] *100

= [$ 80+ ( $ 1,000- $ 770) /10] /[( $ 1,000+ $ 770)/2] *100

= 103/885*100

= 11.64%

Note : Coupon = Rate * Face Value

= 8% * $ 1,000

= $ 80

Since this formula gives an approximate value, The financial calculators can be used alternatively.

where,

Par Value = $ 1,000

Market Price = $  770

Annual rate = 8% and

Maturity in Years = 10 Years

Hence the yield to maturity = 12.08%

-----

b.

The Approximate Yield to Maturity Formula =[Coupon + ( Face Value - Market Price) / Number of years to maturity] / [( Face Value + Market Price)/2 ] *100

= [$ 80+ ( $ 1,000- $ 1150) /10] /[( $ 1,000+ $ 1150)/2] *100

= 65/1075*100

= 6.05%

Note : Coupon = Rate * Face Value

= 8% * $ 1,000

= $ 80

Since this formula gives an approximate value, The financial calculators can be used alternatively.

where,

Par Value = $ 1,000

Market Price = $ 1,150

Annual rate = 8% and

Maturity in Years = 10 Years

Hence the yield to maturity = 5.97%

----------

The Approximate Yield to Maturity Formula =[Coupon + ( Face Value - Market Price) / Number of years to maturity] / [( Face Value + Market Price)/2 ] *100

= [$ 80+ ( $ 1,000- $ 1000) /10] /[( $ 1,000+ $ 1000)/2] *100

= 80/1000*100

= 8.00%

Note : Coupon = Rate * Face Value

= 8% * $ 1,000

= $ 80

Since this formula gives an approximate value, The financial calculators can be used alternatively.

where,

Par Value = $ 1,000

Market Price = $  1000

Annual rate = 8% and

Maturity in Years = 10 Years

Hence the yield to maturity = 8.00%

jeff jeffy answered 2 years ago
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