Question

7.6)A bond has a $1,000 par value, 8 years to maturity, and a 7% annual coupon and sells for $980.

1. What is its yield to maturity (YTM)? Round your answer to two decimal places.

      %

2. Assume that the yield to maturity remains constant for the next five years. What will the price be 5 years from today? Do not round intermediate calculations. Round your answer to the nearest cent.

   $  

Answer 1

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

= [$ 70+ ( $ 1,000- $ 980) /8] /[( $ 1,000+ $ 980)/2] *100

=72.5/990*100

= 7.32%%

Note : Coupon = Rate * Face Value

= 7% * $ 1,000

= $ 70

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

where,

Par Value = $ 1,000

Market Price = $  980

Annual rate = 7% and

Maturity in Years = 8Years

Hence the yield to maturity = 7.34%

Answer = 7.34%

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b. Current Price = $ 980

Price 5 years from today:

Price of bond = Coupon * PVIFA (n,i)+ face value * PVIF (n,i)

Price of bond= 70* PVIFA (3 , 7.34%) + 1000 * PVIF ( 3 ,7.34%)

Price of bond = 70* 2.6080989401498+ 1000*0.8085655377930

= 991.13

Hence the correct answer is $ 991.13