A company is planning to set aside money to repay $100 million in bonds that will be coming due in 10 years. If the appropriate discount rate is 9%,
a. how much money would the company need to set aside at the end of each year for the next 10 years to be able to repay the bonds when they come due?
b. how would your answer change if the money were set aside at the beginning of each year?
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To determine the amount of money the company would need to set aside at the end of each year for the next 10 years, we can use the concept of present value (PV). PV is the value today of a future cash flow, discounted by the appropriate interest rate.
a. If the company plans to repay $100 million in bonds in 10 years, we need to find the present value of this amount today. The formula to calculate PV is:
PV = FV / (1 + r)^n
Where:
PV = Present Value
FV = Future Value
r = Discount rate
n = Number of periods
In this case, FV is $100 million, r is 9% (or 0.09 as a decimal), and n is 10 years. Plugging in these values into the formula:
PV = 100,000,000 / (1 + 0.09)^10
PV = 100,000,000 / (1.09)^10
PV ≈ 41,734,122
Therefore, the company would need to set aside approximately $41,734,122 at the end of each year for the next 10 years in order to repay the bonds when they come due.
b. If the money were set aside at the beginning of each year, the calculation would remain the same. The only difference would be the timing of the cash flows. Instead of setting aside the amount at the end of each year, the company would do so at the beginning of each year.
So, whether the money is set aside at the end or beginning of each year, the amount to be set aside would still be approximately $41,734,122.