Question

Assume Oliver wants to earn a return of 10.50% and is offered the opportunity to purchase a $1,000 par value bond that pays a 8.75% coupon rate (distributed semiannually) with three years remaining to maturity. The following formula can be used to compute the bond’s intrinsic value:

Intrinsic ValueIntrinsic 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

Based on this equation and the data, it is _______ (unreasonable/reasonable) to expect that Oliver’s potential bond investment is currently exhibiting an intrinsic value less than $1,000.
Now, consider the situation in which Oliver wants to earn a return of 11.75%, but the bond being considered for purchase offers a coupon rate of 8.75%. 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 _______ (equal to/greater than/less than) its par value, so that the bond is ______ (trading at premium/par/discount).

Answer 1

Answer and Explanation:

1.

A is semi annual coupon=43.75

B is par or face value=1000

C is semi annual required return=5.25%

2.

Reasonable because coupon rate is less than ytm

3.

=(8.75%*1000)/11.75%*(1-1/(1+11.75%/2)^6)+1000/(1+11.75%/2)^6=925.95

4.

Less than

5.

Discount

Answer 2

For variable A

coupon rate = 8.75%

semiannually = $\frac{8.75}{2}$ = 4.375%

Semiannual coupon rate = 4.375% * 1000

= $43.75

For variable B

Bond par value = 1000

For variable C

Coupon rate = 10.5% annually

Semiannually = $\frac{10.5}{2} =5.25$%

She wants a rate of 11.75% annually

Semiannually = $\frac{11.75}{2} = 5.875%$

The time to maturity = 3 years

Semi annual period rate to maturity = 5.25

$\frac{43.75}{1.05875} +\frac{43.75}{1.05875^2} +\frac{43.75}{1.05875^3} +\frac{43.75}{1.05875^4} +\frac{43.75}{1.05875^5} +\frac{43.75}{1.05875^6} +\frac{1000}{1.05875^6}$

= 41.32+39.029+36.8634.82+32.88+31.07+709.9

= 925.948

From the data and the calculation above we can see that the intrinsic value is $925.9 which is less than the par value of $1000.

This is reasonable given that the coupon rate is lower. Rounding up the intrinsic value we see that it is lower than the par value. Therefore this is a discount.

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