Question

For example, assume Olivia wants to earn a return of 12.00% and is offered the opportunity to purchase a $1,000 par value bond that pays a 10.00% coupon rate (distributed semiannually) with three years remaining to maturity. The following formula can be used to compute the bond's intrinsic value: A A Intrinsic Value = A (1+C)3 (1+C) ' (1+C)2 (1+0)4' А (1+ C)5. (1+C)6 ' (1+C)6 2017 Complete the following table by identifying the appropriate corresponding variables used in the equation. Unknown Variable Value Variable Name Bond's semiannual coupon payment B Bond's par value $1,000 Semiannual required return - reasonable to expect that Olivia's potential bond investment is currently exhibiting an intrinsic value Based on this equation and the data, it is less than $1,000. Now, consider the situation in which Olivia wants to earn a return of 8.00%, but the bond being considered for purchase offers a coupon rate of 10.00%. 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 (rounded to the nearest whole dollar) is its par value, so that the bond is Given your computation and conclusions, which of the following statements is true? When the coupon rate is greater than Olivia's required return, the bond's intrinsic value will be less than its par value. O A bond should trade at a par when the coupon rate is greater than Olivia's required return. O When the coupon rate is greater than Olivia's required return, the bond should trade at a premium. When the coupon rate is greater than Olivia's required return, the bond should trade at a discount.

Answer 1

Answer a.

Unknown Variable A:

Annual Coupon Rate = 10.00%
Semiannual Coupon Rate = 5.00%

Bond’s Semiannual Coupon Payment = 5.00% * $1,000
Bond’s Semiannual Coupon Payment = $50.00

Unknown Variable B:

Bond’s Par Value = $1,000

Unknown Variable C:

Annual Required Return = 12.00%

Semiannual Required Return = 6.00%

Answer b.

Based on this equation and the data, it is reasonable to expect that Olivia’s potential bond investment will exhibit an intrinsic value less than $1,000.

Answer c.

Annual Required Return = 8.00%
Semiannual Required Return = 4.00%

Time to Maturity = 3 years
Semiannual Period to Maturity = 6

Price of Bond = $50/1.04 + $50/1.04^2 + $50/1.04^3 + $50/1.04^4 + $50/1.04^5 + $50/1.04^6 + $1,000/1.04^6
Price of Bond = $50 * (1 - (1/1.04)^6) / 0.04 + $1,000 * (1/1.04)^6
Price of Bond = $1,052

Now, consider the situation in which Olivia wants to earn a return of 8.00%, but the bond being considered for purchase offers a coupon rate of 10.00%. 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 $1,052 is greater than its par value, so that the bond is trading at a premium.

Answer d.

When the coupon rate is greater than Olivia’s required return, the bond should trade at a premium.