Question

Hands Insurance Company issued a $90 million, 1-year, zero-coupon note at 8 percent add-on annual interest...

Hands Insurance Company issued a $90 million, 1-year, zero-coupon note at 8 percent add-on annual interest (paying one coupon at the end of the year). The proceeds were used to fund a $100 million, 2-year commercial loan at 10 percent annual interest. Immediately after these transactions were simultaneously closed, all market interest rates increased 1.5 percent (150 basis points).

a.      What is the true market value of the loan investment and the liability after the change in interest rates?

with the steps of calculating please (finance formulas)

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Answer #1

Answer a(i):

Market value of loan investment:

Loan amount = $100 million = $100,000,000

Annual Interest = 100000000 * 10% = $10,000,000

New market rate of interest = 11.50%

Market value of loan after change in interest = 10000000 * PV of $1 annuity for 2 years at 11.50% + 100000000 + PV of $1 for 2 years at 11.50%

= 10000000 * (1 - 1 / (1 + 11.50%)^2) / 11.50% + 100000000 * 1/(1+11.50%)^2

= $97,448,169.08

True market value of the loan investment = $97,448,169.08

Answer a(ii):

Market value of the liability:

Bond issued for $90 million for one year at 8 percent add-on annual interest

Liability (after one year) before change in interest = 90000000 * (1 + 8%) = 97200000

Market value of liability after change in interest by 1.50% = 97200000 / (1 + 9.50%) = $88,767,123.29

Market value of liability after change in interest = $88,767,123.29

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