There was a write-down of $6.94 in the book value in the year ending May 1, 2000.
How can you calculate the write-up or write-down in the book value in the year ending May 1, 2000?
We need to compare the bond's purchase price with its redemption value on that date.
The bond was purchased on May 1, 1995, with a par value of 1000 and annual coupons at 5.375%. The effective annual interest rate was 5%. This means that the bondholder receives an annual coupon payment equal to 5.375% of the par value, or $53.75.
The bond is redeemable on May 1, 2010, at 1100. To calculate the number of years until redemption, we subtract the purchase year (1995) from the redemption year (2010): 2010 - 1995 = 15 years.
Now, we need to calculate the annual coupon payment in the year ending May 1, 2000. This year is 5 years after the purchase year, so we divide the annual coupon payment by the effective annual interest rate to account for the compounding effect:
Annual coupon payment in the year ending May 1, 2000 = $53.75 / (1 + 0.05)⁵ = $39.09 (rounded to two decimal places)
The book value of the bond is the sum of all the present values of the future cash flows.
We can calculate the book value as follows:
Book value in the year ending May 1, 2000, = Present value of the remaining coupons + Present value of the redemption value
The remaining coupons are the annual coupon payments from May 1, 2000, to May 1, 2010. There are 10 years left until redemption. The present value of the remaining coupons can be calculated using the formula for the present value of an annuity:
Present value of the remaining coupons = Annual coupon payment x [1 - (1 + interest rate)^(-number of years)] / interest rate
Present value of the remaining coupons = $39.09 x [1 - (1 + 0.05)⁻¹⁰] / 0.05 = $321.05 (rounded to two decimal places)
The present value of the redemption value can be calculated using the formula for the present value of a single payment:
Present value of the redemption value = Redemption value / (1 + interest rate)ⁿ
where n = number of years
Present value of the redemption value = $1100 /(1 + 0.05)¹⁰ = $685.89 (rounded to two decimal places)
Therefore, the book value in the year ending May 1, 2000, is $321.05 + $685.89 = $1006.94.
To calculate the amount of the write-up or write-down in the book value, we subtract the book value from the purchase price:
Write-up or write-down = Purchase price - Book value
Write-up or write-down = $1000 - $1006.94 = -$6.94
Therefore, there was a write-down of $6.94 in the book value in the year ending May 1, 2000.