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Present Value of a Gold Mine in Three Years

Suppose you just inherited an gold mine. This gold mine is believed to have three years worth of gold deposit. Here is how much income this gold mine is projected to bring you each year for the next three years:

Year 1: $49,000,000
Year 2: $61,000,000
Year 3: $85,000,000

Compute the present value of this stream of income at a discount rate of 7%. Remember, you are calculating the present value for a whole stream of income, i.e. the total value of receiving all three payments (how much you would pay right now to receive these three payments in the future). Your answer should be one number - the present value for this gold mine at a 7% discount rate but you have to show how you got to this number.

Now compute the present value of the income stream from the gold mine at a discount rate of 5%, and at a discount rate of 3%. Compare the present values of the income stream under the three discount rates and write a short paragraph with conclusions from the computations.

Solution Preview

PV for stream of income - one year each only at 7% 

PV = $49,000,000 / (1.07) + $61,000,000 / (1.07)^2 + $ 85,000,000 / (1.07)^3 

PV = $45,794,392.52 + $53,279,762.42 + $69,385,319.54 
PV = $168,459,474.55 

PV for stream of income - one year each only at 5% 

Using the same amounts but at a rate of 5% 

PV = ...

Solution Summary

This solution shows step-by-step computations are provided in the form of text and an excel file that includes the working out, explanation of results and checking final answers using Excel functions.