. [3] Suppose you are considering buying a gold deposit. It will cost $1 million per year to construct a mine so that gold can be extracted. The construction period lasts 3 years. In the fourth year, production starts. Each year the mine operates, it will yield a net return (total revenue minus total cost) of $5,000, 000. Gold can be extracted for 6 years. Interested rates are 5%. a. What is the present value of the total net return (total benefit)

The present value of the total net return (total benefit) is $21,922,868.23

Explanation:

As the yearly net return is a form of annuity cash flow.

To calculate the present value of the total net return we will use the following formula

First we need to determine the present value of net return at the end of year 3, then we will discount further to calculate the present value at year 0

Present value of net return at the end of year 3 = Yearly net return x ( 1 - ( 1 + Interest rate )^-Number of extraction years ) / Interest rate

Where

Yearly net return = $5,000,000

Interest rate = 5%

Number of extraction years = 6 years

Present value of net return at the end of year 3 = ?

Placing values in the formula

Present value of net return at the end of year 3 = $5,000,000 x ( 1 - ( 1 + 5% )^-6 ) / 5%

Present value of net return at the end of year 3 = $5,000,000 x 5.0756921

Present value of net return at the end of year 3 = $25,378,460.34

Now we need to discount the value further to calculate the present value at year 0

Present value of net return at the end of year 0 = Present value of net return at the end of year / ( 1 + Interest rate  ) ^numbers of year

Present value of net return at the end of year 0 = $25,378,460.34 / ( 1 + 5% )^3

Present value of net return at the end of year 0 = $21,922,868.23

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