You are the financial planner for Johnson Controls. Assume last year’s profits were $760,000. The board of directors decided to forgo dividends to stockholders and retire high-interest outstanding bonds that were issued 5 years ago at a face value of $1,420,000. You have been asked to invest the profits in a bank. The board must know how much money you will need from the profits earned to retire the bonds in 10 years. Bank A pays 6% compounded quarterly, and Bank B pays 7% compounded annually.

To retire the bonds in 10 years, you will need to invest $1,420,000 in Bank A and $1,521,945 in Bank B.

To calculate how much money is needed to retire the bonds in 10 years, we can use the formula for the future value of an annuity.

First, we need to determine the interest rate for each bank on a quarterly basis and an annual basis, respectively.

For Bank A:
Quarterly interest rate = 6% / 4 = 1.5% = 0.015

For Bank B:
Annual interest rate = 7% = 0.07

Now, let's calculate the future value of the bonds in 10 years using the future value of an annuity formula:

Future Value = Payment per period * [(1 + Interest Rate)^(Number of periods) - 1] / Interest Rate

Future Value of Bonds = $1,420,000 * [(1 + 0.07)^10 - 1] / 0.07
Future Value of Bonds = $1,420,000 * (1.07^10 - 1) / 0.07

Thus, the future value of the bonds in 10 years is approximately $2,356,264.31.

To determine how much money you will need from the profits earned to retire the bonds in 10 years, we can calculate the future value of the bond repayment using the given interest rates for Bank A and Bank B.

Let's start with Bank A, which offers an interest rate of 6% compounded quarterly. To calculate the future value (FV) of the bond repayment, we can use the formula:

FV = PV * (1 + r/n)^(n*t)

Where:
PV = Present Value (the amount you need to calculate)
r = interest rate (in decimal form)
n = number of compounding periods per year
t = number of years

In this case, the present value (PV) is $1,420,000, the interest rate (r) is 6%, the number of compounding periods per year (n) is 4 (quarterly), and the number of years (t) is 10.

Using these values in the formula, we can calculate the future value (FV):

FV = $1,420,000 * (1 + 0.06/4)^(4*10)
FV ≈ $2,249,865.32

Therefore, if you choose Bank A, you will need approximately $2,249,865.32 from the profits earned to retire the bonds in 10 years.

Now let's calculate the future value using Bank B, which offers an interest rate of 7% compounded annually. We can use the same formula with the respective interest rate and compounding period:

FV = $1,420,000 * (1 + 0.07/1)^(1*10)
FV ≈ $2,360,489.71

So, if you choose Bank B, you will need approximately $2,360,489.71 from the profits earned to retire the bonds in 10 years.

Please note that these calculations assume that the interest rates remain constant over the 10-year period and that the interest is reinvested without withdrawals. Additionally, it's important to consider other factors such as liquidity and risk when selecting a bank for investment purposes.