Nair Inc. bought a "growing perpetuity" bond. The bond will pay 631.85 dollars at the end of year 1 and the payment will increase by 2.5 percent each year forever thereafter. Assuming the interest rate is 11.26% (forever), what is the maximum amount that Nair Inc. will be able to charge for this bond if the firm put it on sale at the end of year 33? (Accuracy is set at the first decimal.)
To calculate the maximum amount that Nair Inc. will be able to charge for this bond, we need to determine the present value of the perpetuity, which is the value of all future cash flows discounted to the present at the given interest rate.
The perpetuity formula is:
PV = C / r
Where:
PV = Present Value
C = Cash Flow
r = Interest Rate
In this case, the cash flow (C) is the payment at the end of year 1, which is $631.85 and it will increase by 2.5 percent every year thereafter. The interest rate (r) is given as 11.26%.
First, let's calculate the cash flows for the bond in future years using the growth rate of 2.5 percent:
Year 2: $631.85 * (1 + 2.5%) = $647.33
Year 3: $647.33 * (1 + 2.5%) = $663.24
Year 4: $663.24 * (1 + 2.5%) = $679.59
...
This pattern continues indefinitely, with each year's cash flow increasing by 2.5 percent.
To find the value at year 33, we need to calculate the cash flow at year 33:
Year 33: $631.85 * (1 + 2.5%)^(33 - 1)
Next, we calculate the present value using the perpetuity formula:
PV = C / r
where C is the cash flow at year 33 and r is the interest rate. We use the formula on the cash flow at year 33 to find its present value:
PV = [ $631.85 * (1 + 2.5%)^(33 - 1) ] / 0.1126
Using a calculator to solve this expression, we find that the maximum amount Nair Inc. will be able to charge for this bond is approximately $3,806.1 (rounded to the nearest tenth), assuming a sale at the end of year 33.