For example, assume Sophia wants to earn a return of 15.75% and is offered the o
ID: 2810840 • Letter: F
Question
For example, assume Sophia wants to earn a return of 15.75% and is offered the opportunity to purchase a $1,000 par value bond that pays a 18.00% coupon rate (distributed semiannually) with three years remaining to maturity. The following formula can be used to compute the bond's intrinsic value: Complete the following table by identifying the appropriate corresponding variables used in the equation Unknown Variable Name Variable Value $1,000 Semiannual required return Based on this equation and the data, it is less than $1,000 to expect that Sophia's potential bond investment is currently exhibiting an intrinsic value Now, consider the situation in which Sophia wants to earn a return of 21%, but the bond being considered for purchase offers a coupon rate of 18.00%. 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 bond is (rounded to the nearest whole dollar) is its par value, so that the Given your computation and conclusions, which of the following statements is true? O When the coupon rate is greater than Sophia's required return, the bond should trade at a discount. A bond should trade at a par when the coupon rate is greater than Sophia's required return when the coupon rate is greater than Sophia's required return, the bond should trade at a premium O When the coupon rate is greater than Sophia's required return, the bond's intrinsic value will be less than its par valueExplanation / Answer
Answer a.
Unknown Variable B:
Bond’s Par Value = $1,000
Unknown Variable A:
Annual Coupon Rate = 18.00%
Semiannual Coupon Rate = 9.00%
Semiannual Coupon Payment = Semiannual Coupon Rate * Bond’s Par Value
Semiannual Coupon Payment = 9.00% * $1,000
Semiannual Coupon Payment = $90
Unknown Variable C:
Annual Required Return = 15.75%
Semiannual Required Return = 7.875%
Answer b.
Based on this equation and the data, it is unreasonable to expect that Sophia’s potential bond investment is currently exhibiting an intrinsic value less than $1,000
Answer c.
Annual Required Return = 21.00%
Semiannual Required Return = 10.50%
Time to Maturity = 3 years
Semiannual Period = 6
Intrinsic Value = $90 * PVIFA (10.50%, 6) + $1,000 * PVIF (10.50%, 6)
Intrinsic Value = $90 * (1 - (1/1.105)^6) / 0.105 + $1,000 / 1.105^6
Intrinsic Value = $936
If you round the bond’s intrinsic value to the nearest whole dollar, then its intrinsic value of $936 is less than its par value, so that the bond is trading at discount.
Answer d.
When the coupon rate is greater than Sophia’s required return, the bond should trade at a premium.
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