1.

The coupon rate is the sum of the 2.46% annual coupon and the current 6-month $LIBOR rate, which is 2.46% + 0.78% = 3.24%.

The interest paid at the end of each six-month period is calculated as follows:

For the first six-month period, the face value of the bond is multiplied by the coupon rate for that period (half of the annual coupon rate), and the result is divided by 2 to get the semi-annual interest payment.

Interest payment for the first six-month period = ($75,000,000 x 3.24%)/2 = $1,215,000

For the second six-month period, the face value of the bond is multiplied by the coupon rate for that period, which is the sum of the 2.46% annual coupon and the 0.88% six-month $LIBOR rate for that period, and the result is divided by 2 to get the semi-annual interest payment.

Interest payment for the second six-month period = ($75,000,000 x (2.46% + 0.88%))/2 = $1,252,500

For the third six-month period, the face value of the bond is multiplied by the coupon rate for that period, which is the sum of the 2.46% annual coupon and the 1.47% six-month $LIBOR rate for that period, and the result is divided by 2 to get the semi-annual interest payment.

Interest payment for the third six-month period = ($75,000,000 x (2.46% + 1.47%))/2 = $1,473,750

For the fourth six-month period, the face value of the bond is multiplied by the coupon rate for that period, which is the sum of the 2.46% annual coupon and the 2.68% six-month $LIBOR rate for that period, and the result is divided by 2 to get the semi-annual interest payment.

Interest payment for the fourth six-month period = ($75,000,000 x (2.46% + 2.68%))/2 = $1,927,500

For the fifth six-month period, the face value of the bond is multiplied by the coupon rate for that period, which is the sum of the 2.46% annual coupon and the 3.28% six-month $LIBOR rate for that period, and the result is divided by 2 to get the semi-annual interest payment.

Interest payment for the fifth six-month period = ($75,000,000 x (2.46% + 3.28%))/2 = $2,152,500

For the final six-month period, the face value of the bond is multiplied by the coupon rate for that period, which is the sum of the 2.46% annual coupon and the 4.50% six-month $LIBOR rate for that period, and the result is divided by 2 to get the semi-annual interest payment.

Interest payment for the final six-month period = ($75,000,000 x (2.46% + 4.50%))/2 = $2,610,000

Therefore, the amounts of interest that the company pays at the end of each six-month period are:

First six-month period: $1,215,000
Second six-month period: $1,252,500
Third six-month period: $1,473,750
Fourth six-month period: $1,927,500
Fifth six-month period: $2,152,500
Final six-month period: $2,610,000

2.

To calculate the inflation index for each year, we can use the following formula:

Inflation index = (1 + inflation rate) x previous year’s inflation index

Using this formula, we can calculate the inflation index for each year as follows:

Year 1: Inflation index = (1 + 0.88%) x 100 = 100.88
Year 2: Inflation index = (1 + 1.47%) x 100.88 = 102.36
Year 3: Inflation index = (1 + 2.68%) x 102.36 = 105.1
Year 4: Inflation index = (1 + 3.28%) x 105.1 = 108.54
Year 5: Inflation index = (1 + 4.50%) x 108.54 = 113.42

To calculate the coupon payment per bond for each of the five years, we can use the following formula:

Coupon payment = coupon rate x principal x inflation index

Using the inflation index values calculated above, we can calculate the coupon payment per bond for each of the five years as follows:

Year 1: Coupon payment = 4.75% x £100 x 100.88% = £4.79
Year 2: Coupon payment = 4.75% x £100 x 102.36% = £4.86
Year 3: Coupon payment = 4.75% x £100 x 105.1% = £4.99
Year 4: Coupon payment = 4.75% x £100 x 108.54% = £5.15
Year 5: Coupon payment = 4.75% x £100 x 113.42% = £5.38

Finally, to calculate the amount that the company pays bondholders when the debt matures after five years, we need to calculate the inflation-adjusted principal. The inflation-adjusted principal is calculated by multiplying the principal by the inflation index at maturity (i.e., at the end of year 5).

Inflation-adjusted principal = principal x inflation index at maturity

Using the inflation index value calculated above for year 5, we can calculate the inflation-adjusted principal as follows:

Inflation-adjusted principal = £100 x 113.56% = £113.56

Therefore, the company pays bondholders £113.56 when the debt matures after five years.

1.

The reason we add the 6-month LIBOR rate to the annual coupon rate (2.46%) to calculate the coupon rate is because the interest payment is made every six months based on the prevailing 6-month LIBOR rate at that time.

The coupon rate is therefore a combination of the fixed annual coupon rate (which remains constant throughout the bond\’s term) and the variable 6-month LIBOR rate, which changes every 6 months.

When calculating the interest payment for each 6-month period, we use the coupon rate for that period, which is the sum of the annual coupon rate and the 6-month LIBOR rate for that period.

We divide the result by 2 because interest payments are made every 6 months, so we need to calculate half of the annual interest payment for each 6-month period.

2. 

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