An insurance company issued a $95 million one-year, zero-coupon note at 8 percen

Question

An insurance company issued a $95 million one-year, zero-coupon note at 8 percent add-on annual interest (paying one coupon at the end of the year) and used the proceeds plus $15 million in equity to fund a $110 million face value, two-year commercial loan at 10 percent annual interest. Immediately after these transactions were (simultaneously) undertaken, all interest rates went up 2 percent.

What is the market value of the insurance company’s loan investment after the changes in interest rates? (Do not round intermediate calculations. Enter your answer in millions rounded to 3 decimal places. (e.g., 32.16))

Using duration, what is the new expected value of the loan if interest rates are predicted to increase to 12 percent from the initial 10 percent? (Do not round intermediate calculations. Enter your answer in millions rounded to 3 decimal places. (e.g., 32.16))

Explanation / Answer

Answer: Market value :

We will calculate the present value of the future amounts we will recieve and divide it by the interest rate prevalent to get the current market value

commercial loan repyament structure has been assumed as interest payments at the end of each year and principal payment at the end of 2nd year in one go. ( loan repayment structure has not been mentioned thats why followed this). answer will vary drastically based on the loan repyament structure but Logic will remain same

PV formula = cash flow /(1 + interest rate/100)^(no of year)

Expected value :

Probability : 50% (not exactly given for increase in rates hence assumed 50%)

Expected value : value of loan at 10% * probability + Value of loan at 12% * probability

Expected value : 110*0.5 + 106.28*0.5 = 108.14 million

year 1 2 2 cash flow 11 11 110 Present value 9.821429 8.769133 87.69133 market value 106.2819

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