Studdy AI Logo
Math  /  Algebra

QuestionM CODE 01 Aboom Financial has assets of GH\450millionandliabilitiesofGH$405mittion.Durationoftheassetsis5yearsanddurationoftheliabilitiesis3years.Ifinterestratesrisefrom 450 million and liabilities of GH\$405 mittion. Duration of the assets is 5 years and duration of the liabilities is 3 years. If interest rates rise from 10 \%to to 11.5 \%$, what will be the potential loss of the institution's net worth?

Studdy Solution

STEP 1

1. The assets and liabilities are subject to interest rate changes.
2. The duration is a measure of interest rate sensitivity.
3. The change in interest rates affects the market value of assets and liabilities.
4. The net worth is calculated as the difference between the market value of assets and liabilities.

STEP 2

1. Calculate the change in interest rates.
2. Calculate the percentage change in the value of assets and liabilities using duration.
3. Calculate the change in the market value of assets and liabilities.
4. Determine the potential loss in the institution's net worth.

STEP 3

Calculate the change in interest rates: Δi=11.5%−10%=1.5%=0.015\Delta i = 11.5\% - 10\% = 1.5\% = 0.015

STEP 4

Calculate the percentage change in the value of assets using the duration formula: ΔVA=−Duration of Assets×Δi=−5×0.015=−0.075\Delta V_A = -\text{Duration of Assets} \times \Delta i = -5 \times 0.015 = -0.075
Calculate the percentage change in the value of liabilities using the duration formula: ΔVL=−Duration of Liabilities×Δi=−3×0.015=−0.045\Delta V_L = -\text{Duration of Liabilities} \times \Delta i = -3 \times 0.015 = -0.045

STEP 5

Calculate the change in the market value of assets: ΔAssets=ΔVA×Initial Assets=−0.075×450=−33.75 million GH$\Delta \text{Assets} = \Delta V_A \times \text{Initial Assets} = -0.075 \times 450 = -33.75 \text{ million GH\$}
Calculate the change in the market value of liabilities: ΔLiabilities=ΔVL×Initial Liabilities=−0.045×405=−18.225 million GH$\Delta \text{Liabilities} = \Delta V_L \times \text{Initial Liabilities} = -0.045 \times 405 = -18.225 \text{ million GH\$}

STEP 6

Calculate the potential loss in net worth: ΔNet Worth=ΔAssets−ΔLiabilities=−33.75−(−18.225)=−15.525 million GH$\Delta \text{Net Worth} = \Delta \text{Assets} - \Delta \text{Liabilities} = -33.75 - (-18.225) = -15.525 \text{ million GH\$}
The potential loss of the institution's net worth is:
−15.525 million GH$ \boxed{-15.525 \text{ million GH\$}}

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord