Question

A salt mine you inherited will pay you $25,000 per year for 25 years, with the first payment being made today. If you think a fair return on the mine is 7.5%, how much should you ask for it if you decide to sell it?

A. $284,595

B. $299,574

C. $314,553

D. $330,281

E. $346,795

Answer 1

In determining the fair value of the salt mine, the present value of the annuity needs to be calculated. Considering a 7.5% annual discount rate, the present value of the cash flows over 25 years amounts to $314,553. Therefore, the correct answer is C. $314,553.

Step-by-step explanation:

To calculate the present value of the annuity, we use the formula for the present value of an ordinary annuity:

`\[PV = C * \left(1 - \frac{1}{{(1 + r)^n}}\right) / r\]`

Where:

-
`\(PV\)`is the present value of the annuity,

-
`\(C\)` is the annual cash flow (in this case, $25,000),

-
`\(r\)` is the discount rate per period (7.5% or 0.075), and

-
`\(n\)` is the number of periods (25 years).

Substituting these values, we get:

`\[PV = 25,000 * \left(1 - \frac{1}{{(1 + 0.075)^(25)}}\right) / 0.075\]`

Calculating this expression results in the present value of the annuity, which is $314,553.36. Therefore, the fair value of the salt mine, based on a 7.5% return, is approximately $314,553.

In financial terms, this represents the amount an investor would be willing to pay today to receive the annual cash flows from the salt mine over the next 25 years at a 7.5% return. The chosen answer, C. $314,553, accurately reflects this valuation based on the given parameters.