A $1000 bond is redeemable at 104.5.The bond is bought such that yield rate bond rate.The absolute value of the sum of the book value adjustment column is $38.75.What is the price of the bond?

Question

A $1000 bond is redeemable at 104.5.The bond is bought such that yield rate > bond rate.The absolute value of the sum of the book value adjustment column is $38.75.What is the price of the bond?

Quizplus · Accepted Answer

First, we need to find the book value of the bond:
Book value = Redeemable value / (1 + yield rate) = 1045 / (1 + yield rate)

Then, we need to calculate the difference between the book value and the purchase price:
Book value adjustment = Purchase price - Book value

We know that the absolute value of the book value adjustment is $38.75. This means that either the purchase price is higher than the book value or the book value is higher than the purchase price, but by only $38.75.

Let's assume that the purchase price is higher than the book value:
Purchase price - Book value = $38.75
Purchase price - 1045 / (1 + yield rate) = $38.75
Purchase price = $38.75 + 1045 / (1 + yield rate)

We also know that the yield rate is higher than the bond rate:
Yield rate > Bond rate

At this point, we can use trial and error to find the purchase price that makes the book value adjustment equal to $38.75. However, there is a faster way to do this. We can use the fact that the bond is redeemable at 104.5 to narrow down the possible purchase prices.

If the purchase price is equal to the redeemable value, then the book value adjustment is 0:
Purchase price = 1045 / (1 + yield rate)
Book value adjustment = Purchase price - 1045 / (1 + yield rate) = 0

If the purchase price is lower than the redeemable value, then the book value adjustment is negative:
Purchase price < 1045 / (1 + yield rate)
Book value adjustment = Purchase price - 1045 / (1 + yield rate) < 0

Therefore, the purchase price must be higher than the redeemable value in order to have a positive book value adjustment of $38.75. The only answer choice that satisfies this condition is B:
Purchase price = $1006.25
Book value = 1045 / (1 + yield rate) ≈ $967.50
Book value adjustment = Purchase price - Book value ≈ $38.75 (rounded to the nearest cent)

A $1000 Bond Is Redeemable at 104