If you were offered the chance of an investment in a business and you were promised a return of $18,000 per year forever. The first payment is one year from today. What is the maximum amount you would be prepared to pay for such an investment if you required a return of 7.98%?

Round your answer to TWO decimal places & ignoring $ sign.

Question

If you were offered the chance of an investment in a business and you were promised a return of $18,000 per year forever.  The first payment is one year from today.  What is the maximum amount you would be prepared to pay for such an investment if you required a return of 7.98%?

Round your answer to TWO decimal places & ignoring $ sign.

BlackTom AI · Accepted Answer

The problem asks for the maximum amount you'd pay today for a perpetuity that pays 18,000 each year forever, with the first payment one year from today, given a required return (discount rate) of 7.98%.

First, recognize this as a perpetuity valued at present value: PV = Annual Payment / Discount Rate, provided the payments continue forever and the first payment is one period from now.

Plug in the numbers: PV = 18,000 / 0.0798.

To compute, you can scale up to avoid decimals: 18,000 / 0.0798 = 18,000,000 / 79.8. Multiplying 79.8 by 225,000 yields 17,955,000, which is slightly short of 18,000,000. The remaining amount is 45,000; dividing 45,000 by 79.8 gives about 563.0. Therefore, 225,563 plus a small fraction brings the product to 18,000,000.

Carrying out the precise division, 18,000 / 0.0798 = 225,563.909... Repeating appropriately, and rounding to two decimal places yields 225,563.91.

Thus, the maximum amount you should be willing to pay today (the present value) is 225,563.91 when rounded to two decimals.

A few checks to confirm understanding: because this is a perpetuity, the value is simply the annual cash flow divided by the discount rate; if the discount rate were higher, the present value would be lower, and if it were lower, the present value would be higher. Also, since the first payment occurs one year from today, there is no need for a separate adjustment for an immediate payment.

Note on rounding: the instruction asks to round to two decimals and ignore the dollar sign, which is why the final value is written as 225563.91 rather than including a currency symbol.

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