# The capital gain/loss

This is the question guys,

An investor purchases a nine-year, 7% annual coupon payment bond at a price equal to par value. After the bond is purchased and before the first coupon is received, interest rates increase to 8%. The investor sells the bond after five years. Assume that interest rates remain unchanged at 8% over the five-year holding period.

Question

The capital gain/loss per 100 of par value resulting from the sale of the bond at the end of the five-year holding period is closest to a:

1. loss of 8.45.
2. loss of 3.31.
3. gain of 2.75.

#### Solution

B is correct. The capital loss is closest to 3.31 per 100 of par value. After five years, the bond has four years remaining until maturity and the sale price of the bond is 96.69.

The investor purchased the bond at a price equal to par value (100). Because the bond was purchased at a price equal to its par value, the carrying value is par value. Therefore, the investor experienced a capital loss of 96.69 – 100 = –3.31.

*** I dont understand the solution. My idea is

• Selling price: 96.69
• Coupon earn after 5yrs: 41.07 (PV=0, N=5, I/Y=8, PMT=7)
=> Total: 137.75
While the value of bond at t=5 will be calculated by:
PV=-100, PMT=7, I/Y=8. N=5
=> FV= 105.87
So gain: 31.88

This is interest, not capital gains.

I got it. Thanks. @S2000magician : “the capital loss is measured from the bond’s carrying value, the point on the constant-yield price trajectory, and not from the original purchase price”.

Does it mean that i have to calculate the carrying value with old YTM(i/r) and selling price (when i/r changes)?

If im not wrong, it’s also applied for reinvestment coupon?

At what price did you buy the bond?

it’s par value but i meant in other cases for instance: discount/premium

In those cases you’ll amortize the discount/premium, but the capital gain is still calculated as the sale price less the carrying value. Interest doesn’t come into it.