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Consider an 8% coupon bond selling for $953.10 with three years until maturity making annual coupon payments. the interest rates in the next three years will be, with certainty, r1 = 8%, r2 = 10%, and r3 = 12%. calculate the bond's (a) yield to maturity and (b) realized compound yield

Respuesta :

raphealnwobi

Answer:

a) YTM = 9.8%

b) realized compound yield is 9.9%

Explanation:

a) PMT = 80

par value FV = 1000

coupon rate = 8%

curent price PV = 953.1

years to maturity n = 3

Yield to maturity (YTM) = [tex]\frac{PMT+(FV-PV)/n}{(FV+PV)/2}[/tex] = [tex]\frac{80+(1000-953.1)/3}{(1000+953.1)/2}[/tex]= 9.8%

b) r2 = 10% = 100%+10%=1.1

r3 = 12% = 100%+12%=1.12

Realized compound yield:First, find the future value (FV. of reinvested coupons and principal

FV =  ($80 *1.10 *1.12) + ($80 * 1.12) + $1080 = $1268.16

let a be the rate that makes the future value $1268.16

953.1(1+y)³ =$1268.16

(1+y)³=1.33

1+y=1.099

y = 0.099 = 9.9%

chilljain33

The correct statements will be that the yield to maturity of a bond with 8% coupon will be 9.8% and the realized compound yield for such bond will be 9.9%.

Bond yields can be calculated using the simple formulas of the above asked queries in the name of Yield To Maturity and realized compound yield by putting the values in the information provided below.

  • Bonds are the debt securities subscribed to by such creditors who are assured of a fixed interest rate at a predetermined rate on its maturity given that the conditions of such bond are fulfilled.

  • The Yield to Maturity can be calculated with the following formula,

  • [tex]\rm YTM= \dfrac {PTM+ (Future\ Value\ - Face\ Value)\ /2}{(Future\ Value+ Face\ Value)\ /2}[/tex]

  • Putting the values in the formula we get,

  • [tex]\rm YTM= \dfrac{80\ + (1000-953.1)\ /2}{(1000\ + 953.1)\ /2}[/tex]

  • We obtain the values as

  • [tex]\rm YTM= 0.098[/tex]

  • So, the value of Yield To Maturity interest is 9.8%.

  • Calculating the realized compound yield,

  • [tex]\rm Realized\ Compound\ Yield= Present\ value\ (1 +\ y )^{2}[/tex]

  • We get the values as ,

  • [tex]1268.16= 953.1\ \rm x\ (1+y)^2\\\\\\1.33 = (1 + y)^2\\\\\\1+y = 1.099[/tex]

  • We finally get,

  • [tex]\rm y = 0.099[/tex]

  • The realized compounded yield is 9.9%

Hence, the correct values for the Yield To Maturity is 9.8% whereas the realized compounded yield is 9.9%

To know more about bond yields, click the link below.

https://brainly.com/question/7208555

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