Assume Sophia wants to earn a return of 5% and is offered the opportunity to pur

Question

Assume Sophia wants to earn a return of 5% and is offered the opportunity to purchase a $1000.00 par value bond that pays a 5% coupon rate (distributed semiannually) with three years remaining to maturity. The following formula can be used to compute the bonds intrinsic value:

Intrinsic value = [A/(1=C)^1]+[A/(1=C)^2]+ [A/(1=C)^3]+[A/(1=C)^4]+ [A/(1=C)^5]+[A/(1=C)^6]+ [B/(1=C)^6]

a. Complete the following table by identifying the appropriate corresponding variables used in the equation.

b. Based on this equation and data, is it reasonable to expect that Sophia’s potential bond investment is currently exhibiting an intrinsic value equal to $1000?

c. Consider the situation in which Sophia wants to earn a return of 3%, but the bond being considered for purchase offers a coupon rate of 5%. Again, assume that the bond pays semiannual interest payments and has three years to maturity. If you round the bond’s intrinsic value to the nearest whole dollar, then its intrinsic value of __________ is ____________ its par value, so that the bond is ___________________.

Unknown    Variable name variable value A ? ? B ? $1,000 C Semiannual required return ?

Explanation / Answer

a)Intrinsic value = [A/(1+C)^1]+[A/(1+C)^2]+ [A/(1+C)^3]+[A/(1+C)^4]+ [A/(1+C)^5]+[A/(1+C)^6]+ [B/(1+C)^6]

A=coupon paid semiannually=(coupon rate/2)*par value= (5%/2)*1000= .025*1000=25 we divide coupon rate by 2 as coupon rate of 5% is annual so that 5%/2 is semiannual rate.

B=par value of bond=1000

C=Semiannual required return=C/2=5%/2=2.5% so table is,

b) Put values A=25,B=1000 and C=2.5%=.025 in the equation [A/(1+C)^1]+[A/(1+C)^2]+ [A/(1+C)^3]+[A/(1+C)^4]+ [A/(1+C)^5]+[A/(1+C)^6]+ [B/(1+C)^6] to find Intrinsic value,

Intrinsic value = [25/(1.025)^1]+[25/(1.025)^2]+ [25/(1.025)^3]+[25/(1.025)^4]+ [25/(1.025)^5]+[25/(1.025)^6]+ [1000/(1.025)^6]

Intrinsic value = [24.390]+[23.795]+ [23.215]+[22.649]+ [22.096]+[21.557]+ [862.297]

Intrinsic value = 1000

Yes,since the intrinsic value obtained from equation is 1000, it is reasonable to expect that Sophia’s potential bond investment is currently exhibiting an intrinsic value equal to $1000.

c) new C=3%/2=1.5% is semiannual required return,other values being same

Put values A=25,B=1000 and C=1.5%=.015 in the equation  [A/(1+C)^1]+[A/(1+C)^2]+ [A/(1+C)^3]+[A/(1+C)^4]+ [A/(1+C)^5]+[A/(1+C)^6]+ [B/(1+C)^6] to find Intrinsic value,

Intrinsic value = [25/(1.015)^1]+[25/(1.015)^2]+ [25/(1.015)^3]+[25/(1.015)^4]+ [25/(1.015)^5]+[25/(1.015)^6]+ [1000/(1.015)^6]

Intrinsic value = [24.630]+[24.267]+ [23.908]+[23.555]+ [23.207]+[22.864]+ [914.542]

Intrinsic value =1056.973~$1057

If you round the bond’s intrinsic value to the nearest whole dollar, then its intrinsic value of __$1057__ is _greater than___its par value, so that the bond is __at premium_to the par.___

Unknown Variable name variable value A coupon paid semiannually $25 B par value of bond $1,000 C Semiannual required return 2.5%

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