TD Bank has the following assets and liabilities as of year-end. All assets and liabilities are currently priced at par and pay interest annually. Assets Amount($millions) Annual Rate Liabilities Amount ($ millions) Annual Rate
2-years loans $40 8% 3-years GIC $60 7%
3-years loans $60 8% 5-years term deposit $30 6%
Equity $10
Total $100 Total $100

Required:
a. What is the change in the value of its assets if all interest rates decrease by 1 percent?
b. What is the change in the value of its liabilities if all interest rates decrease by 1 percent?
c. What is the effect on the value of the Fi's equity if interest rates decrease by 1 percent?

a) Change of $2.6 million

b) Change of $3.3 million.

c) Decrease in equity by $0.7 million

Explanation:

a) Determine change in value of assets when interest rates decrease by 1%

i) 2-year loans

Principal Amount = $40  , Annual rate = 8%

Value of asset = P +  interest =  $40 + 6.4 = $46.4

Interest earned = PRT = (40 * 8 * 2) / 100 = $6.4

Given that Annual rate = 8 - 1 = 7%

value of asset = P + interest = $45.6

interest = ( 40 * 7 * 2 ) / 100 = $5.6

change in 2-year loan assets = 46.4 - 45.6 = $0.8 million

ii) 3-year loan assets

Principal amount = $60 , annual rate = 8%

Value of asset = P + interest = 60 + 14.4 = $74.4

interest earned = PRT = ( 60 * 8 * 3 ) / 100 = $14.4

When Annual rate = 8 - 1 = 7%

value of asset = P + interest = 60 + 12.6 = $72.6

interest = ( 60 * 7 * 3 ) / 100 = $12.6

Change in 3-years loan assets = 74.4 - 72.6 = $1.8

∴Total change in value of assets = 1.8 + 0.8 = $2.6 million

B) Change in value of liabilities when interest rates fall by 1%

i) 3-years GIC liability

Principal amount = $60 , interest rate = 7%

Value of liability = P + interest = $72.6

interest = ( 60 * 7 * 3 ) / 100 = $12.6

When interest rate = 7 - 1 = 6%

Interest = ( 60 * 6 *3 ) / 100 = $10.8

value = 60 + 10.8 = $70.8

change in 3 years GIC liability = 72.6 - 70.8 = $1.8

ii) 5 - years term deposit liability

principal amount = $30 , interest rate = 6%

value of liability = P + interest accrued = 30 + 9 = $39

Interest accrued = ( 30 * 6 * 5 ) / 100 = $9

when Interest rate = 6 - 1 = 5%

value of liability = P + interest accrued = 30 + 7.5 = $37.5

interest accrued = ( 30 * 5 * 5 ) / 100 = $7.5

change in 5-years term deposit liability = 39 - 37.5 = $1.5

∴ Total change in value of liabilities = 1.8 + 1.5 = $3.3 million

c) Effect on the value of FI's equity is that there will be an DECRESE in equity because of the Increase in Liability value more than increase in asset value

Equity = asset - liability

           = 2.6 - 3.3 = -$0.7 million