Question

Consider a copper mine that is expected to produce its first cash flow of $10,000 in exactly 3 years, after which annual cash flows are expected to grow at a rate of 5%. What price do investors place on the mine today, assuming they require an annual return of 15% on similar investments?

Answer 1

Let us calculate the value of perpetuity exactly 3 years from

We know the formula for perpetuity is which grows at a rate of G annually with required rate of return of Re is.

PV = D1/(Re-g)

Now D1 = 10,000 + 10,000 * 0.05 = 10,500

Hence PV = 10500/(0.15-0.05)

Hence PV = 105,000

Now this value is exactly three years from now .

Hence the present value of this value discounted for 3 years is 105000/(1+0.15)³

= 105000/1.520875 = 69039

Hence the value investors can place in the copper mine is $69039