The X Bank is a commercial bank that mainly engage in taking deposits and makes loans to corporations. The deposit attracted at the end of year 2017 is $ 100 Million SGD, and the deposit is expected to rise by 10% until 2022. The current deposit rate is 0.5% above LIBOR. X lends to corporations at an average of LIBOR + 3%, and the total amount is currently $ 120 Million, and is expected to grow by 20% per year over the next five years.
1. How much does X need to raise at the end of 2017, assuming that X will have sufficient amount of funds for the next five years. Suppose it can make an annual 3% profit from the proceedings.
2. The management of X decides to issue a 5 year bond. The annual coupon rate is 2%, and the YTM of this bond is expected to be 5%. What is the face value of this bond? What is the duration of the bond?
To answer these questions, we need to calculate the future values of the deposits and loans based on the given growth rates. Let's break it down step by step:
1. Calculation for the deposit amount at the end of 2022:
Given:
- Initial deposit at the end of 2017 = $100 million SGD
- Expected annual growth rate = 10%
To find the deposit amount at the end of 2022, we need to calculate the compound interest for five years:
Deposit at the end of 2022 = Initial deposit * (1 + growth rate)^number of years
Deposit at the end of 2022 = $100 million * (1 + 0.1)^5
Calculating this value will give us the total deposit amount at the end of 2022.
2. Calculation for the loan amount at the end of 2022:
Given:
- Initial loan amount = $120 million
- Expected annual growth rate = 20%
Similar to the deposit calculation, we can find the loan amount at the end of 2022 using compound interest:
Loan amount at the end of 2022 = Initial loan amount * (1 + growth rate)^number of years
Loan amount at the end of 2022 = $120 million * (1 + 0.2)^5
Calculating this value will give us the total loan amount at the end of 2022.
3. Calculation for the amount X needs to raise:
Given: X wants to have sufficient funds for the next five years.
We need to find the difference between the projected loan amount and the projected deposit amount at the end of 2022:
Amount X needs to raise = Loan amount at the end of 2022 - Deposit amount at the end of 2022
Calculating this difference will give us the amount X needs to raise.
4. Calculation for the annual profit:
Given: X is expected to make a 3% profit from the proceedings.
We can calculate the annual profit as a percentage of the amount X needs to raise:
Annual profit = Amount X needs to raise * 3%
Calculating this value will give us the annual profit.
Now, let's move on to question 2:
To determine the face value and duration of the bond, we need to understand the formulas used in bond valuation:
1. Face value: The face value of a bond is the amount that the bondholder will receive when the bond reaches maturity.
2. Duration: The duration of a bond is a measure of its sensitivity to changes in interest rates.
In this case, we are given the annual coupon rate (2%) and the expected yield to maturity (YTM) of the bond (5%). Using these values, we can calculate the face value and the duration.
To calculate the face value of the bond, we need to use the present value formula:
Face value = Coupon payment / (YTM / number of payments per year)
In this case, the bond is 5-year, so the number of payments per year is 1.
Now that you have the basic understanding of how to calculate the answers to these questions, you can use the given information and formulas to calculate the exact values.