Question

Hands Insurance Company issued a $90 million, one-year note at 8 percent add-on annual interest (paying one coupon at the end of the year) or with an 8 percent yield. The proceeds were used to fund a $100 million, two-year commercial loan with a 10 percent coupon rate and a 10 percent yield. 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? b. What impact did these changes in market value have on the market value of the FI’s equity?What was the duration of the loan investment and the liability at the time of issuance? d. Use these duration values to calculate the expected change in the value of the loan and the liability for the predicted increase of 1.5 percent in interest rates. e. What is the duration gap of Hands Insurance Company after the issuance of the asset and note? f. What is the change in equity value forecasted by this duration gap for the predicted increase in interest rates of 1.5 percent? g. If the interest rate prediction had been available during the time period in which the loan and the liability were being negotiated, what suggestions would you have offered to reduce the possible effect on the equity of the company? What are the difficulties in implementing your ideas?

Answer 1

Solution:

a. The market value of the loan decreased by $2,551,831 to $97,448,169.

MV A = $10,000,000 x PVIFA n=2, i=11.5% + $100,000,000 x PVIF n=2, i=11.5%

MVA = $10,000,000 [(1.115^2 - 1)/(0.115*1.115^2)] + $100,000,000 (1/1.115^2)

MVA = $10,000,000 (1.70122) + $100,000,000 (0.8044)

MVA = $97,448,169

The market value of the note fall $1,232,876.71 to $88.767 million

MVL = $97,200,000 x PVIF n = 1, i = 9.5%

MVL = $97,200,000 (1/1.095)

MVL = $88,767,123.29

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b. A - L = -$2,551,830.92 – (-$1,232,876.71) = -$1,313,954.21

Increase in interest rates caused the asset to decrease in value more than the liability which caused the market value of equity to decrease by $1,313,954.21

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c. Two-year Loan (values in millions of $s)

Par value = $100 Coupon rate = 10% Annual payments R = 10% Maturity = 2 years

t CF PV of CF PV of CF x t

1 $10 $9.091 $9.091

2 $110 $90.909 $181.818

$100.000 $190.909

Duration = $190.909/$100.00 = 1.9091

The duration of the loan investment is 1.9091 years.

The duration of the liability is one year since it is a one year note that pays interest and principal at the end of the year.

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d. The approximate change in the market value of the loan for a 150 basis points change is:

= -1.909*0.015/1.10*100,000,000 = -$2,603,181.82

The expected market value of the loan using the above formula is $97,396,818.18 or $97.4 million.

= -1.0*0.015/1.08*90,000,000 = -$1,250,000

The expected market value of the note using the above formula is  $88,750,000 or $88.750 million