bond amortization - change in interest rates

This question comes from one of the Schweser mocks.

Company issued a 5-year, $50 million face, 6% semiannual bond when market interest rates were 7%. The market yield of the bonds was 8% at the beginning of the next year. What is the interest expense that the company should report for the first half of the second year of the bond’s life (third semiannual period).

I understand that you have to get the PV of the bond at the beginning of the second year, then multiply that by the interest rate. The solutions does this but it uses 3.5% instead of 4.0%. " The subsequent change in the market rate has no effect on the amortization of the discount." Why is this?

The effective interest rate method uses carrying values, not market values. The market value can bounce around all it wants to, but the issuer is basically locked in to amortizing the discount @ 7% over the life of the bond.

Bonds payable are shown at par value with any premium or discount amortized over the life of the bonds; they are not shown at market value. As breadmaker says, the only market rate that matters is the one at issuance.

Can you please show how you solved this question

N = 8, since there’s 4 years left at the beginning of the second year.

I/Y = 3.5% / PMT = 1,500,000 / FV = 50,000,000

Calculate PV. You’ll get $48,281,511.12. This is the PV (principal) at the beginning of the second year. Multiply this by 3.5% to get the interest owed for the semiannual period.

One bond’s price (and BV) at issuance:

n = 10, i = 3.5%, PMT = 30, FV = 1,000, calculate PV = 958.42.

(That’s just for practice; you don’t need that number, but it’s good to have against which to check your work.)

One bond’s BV one year after issuance (assuming they’re amortizing the discount using the effective rate, not straight-line):

n = 8, i = 3.5%, PMT = 30, FV = 1,000, calculate PV = 965.63.

Interest expense, first half of year 2 = 965.63 × 3.5% = 33.80, per bond, or $50,000,000 ÷ $1,000 × $33.80 = $1,689,852.89 total.

$1,500,000.00 is coupon, $189,852.89 is amortization of the discount.

It’s the _ BV _, not the PV.

Is it correct to say the PV at time 1?

Only if market rates at time 1 are the same as market rates at time 0.