(b) (15 marks) Suppose the balance sheet of the Spacia Bank can be divided as follows: Assets Liabilities Rate-sensitive $90 million $100 million $40 million $40 million Fixed-rate $90 million Bank Capital (i) (3 marks) Use the gap analysis to calculate the change in the bank’s profit if the interest rate decreases from 9% to 6%. (ii) (7 marks) Suppose that the average duration of its assets is four years, while the average duration of its liabilities is six years. Use the duration analysis to calculate the approximate change of the bank's net worth as a percentage of the total original asset value if the interest rate decreases from 9% to 6%. (iii) (5 marks) Given your answers above, suggest what the bank manager can do to reduce the interest rate risk the bank faces when the interest rate is too high and is likely to fall in the near future.

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i) Here, we have to calculate change in Bank's profit. Decrease in interest rate = 9% - 6% = 3% given : Rate sensitive assets = $90 millions             Rate sensitive liabilities = $100 millions if there is a decrease in interest rate, income on assets will decrease. Calculation : the income on assets decreases by = 3% x $90 millions of rate-sensitive assets = $2.7 millions if there is a decrease in interest rate, payment on liabilities will also decrease. Calculation : the payment on liabilities will decrease by = 3% x $100 millions of rate-sensitive liabilities = $3 millions Hence, change in bank's profit = change in payment of liabilities - change in income on assets = $3 millions - $2.7 millions = $0.3 millions (Bank's profit increase because liabilities decrease much more than the decrease in income) or using gap analysis directly, we can obtain the same result. Gap = Rate sensitive assets - Rate sensitive liabilities = $90 millions - $100 millions = -$10 millions Change in bank profits = gap x Change in interest rate = -$10 millions x (-3%) = $0.3 millions (increase)   ii) Duration analysis Average duration of assets = 4 years average duration of liabilities = 6 years % change in market value of security = - (%change in interest rate) x duration in years change in interest rate = -3% Change in market value of assets = - (-3%) x 4 = 12% (of asset value i.e.. $180 millions) = $21.6 millions Change in market value of liabilities = - (-3%) x 6 = 18% (of liabilities value i.e.. $140 millions) = $25.2 millions The net results is, net worth change = market value of assets - market value of liabilities = $21.6 millions - $25.2 millions = -$3.6 millions net worth change as a percentage of total asset value = (-$3.6 millions / $180 millions) x 100 = -2% (or decline of 2%)   iii) Banks can either go for increasing the duration of their assets (say giving more long term assets and lesser short term assets) or alternatively can decrease the duration of their liabilities, if feasible. example : say average duration of assets rises by 1 year i.e.. the average duration of assets becomes 5 years, the change in market value of asset will become = - (-3%) x 5 = 20% of $180 millions = $36 millions and keeping the duration of duration of liabilities the same, net worth change = $36 - $25.2 = $10.8 ( increase) % change in net worth = ($10.8 / $180) millions x 100 = 6% (increase) ...