Question

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 method of solution)

Answer 1

Given

Bonds issued = $90,000,000

Proceeds used to fund $100,000,000

Time period n= 2 years

Annual interest rate = 10%

Market rate increased by 1.5%

So interest rate will be = 10% + 1.5%= 11.5%

Let us calculate the market value of investment

          MVA = ($100,000,000 - $90,000,000)*PVIFAn=2, i=11.5% + $100,000,000* PVIFn=2, i=11.5%

Where PVIFA = [(1+i)ⁿ – 1]/[ i * (1+i)ⁿ ]

PVIFA = [(1+0.115)² – 1]/[ 0.115 * (1+0.115)² ]

= 1.701220616

PVIF = 1/ (1+i)ⁿ = 1/ (1+0.115)² = 0.8043596292

MVA = $97,448,169.08

So, the market value is $97,448,169.08

Which is $2,551,83 0.92 worth lower than the loan.

Now, liability is calculated as

At the end of one year the coupon gives amount of $90,000,000 * (1 + 0.08)¹ = $$97,200,000

So, immediately after this transaction, the liability or the market value will be

          MVL = $97,200,000* PVIFn=1, i=9.5%

Here interest rate is changed as 10% - 1.5% = 9.5%

PVIFn=1, i=9.5% = 1/ (1 + 0.095)¹ = 0.9132420091

MVL = $97,200,000* 0.9132420091 = $88,767,123.29

The market value of the note declined by $1,232,876.71 to $88,767,123.29