Question

use paper and dont do it on excel

4) After discovering a new gold vein in the Colorado Mountains, CTC Mining Corp. must decide whether to mine the deposit. The most cost-effective method of mining gold is sulfuric acid extraction, a process that results in environmental damage. To go ahead with the extraction, CTC must spend $900,000 for new mining equipment and pay $165,000 for the installation. The gold mined will net the firm an estimated $350,000 cach year over the 5-year life of the vein. CTC's cost of capital is 14%. For purposes of this problem, assume that the cash inflows occur at the end of the year.What are the NPV and IRR of this project?If CTC expects to be fined $1 million by the government for environmental damage 11 years after the mine is closed, what is the NPV? a) $136,578, 19.22%; $13,686

Answer 1

(a)- Project’s NPV and IRR

Project’s NPV

Net Present Value of the Project = Total Present Value of Annual after-tax cash inflows - Initial Investment

= $350,000[PVIFA 14%, 5 Years] – [$900,000 + 165,000]

= [$350,000 x 3.433080] - $1,065,000

= $ 1,201,578.34 – $1,065,000

= $136,578.34

Project’s IRR

Step – 1, Firstly calculate NPV at Say 19%

Net Present Value [NPV] = Present Value of Annual cash flows – Initial Investment

= $350,000[PVIFA 19%, 5 years] – $10,65,000

= [$350,000 x 3.057634] – 10,65,000

= $ 10,70,172.21 – 10,65,000

= $ 5,172.21

Step – 2, NPV at 19% is positive, Calculate the NPV again at a higher rate, Say 20%

Net Present Value [NPV] = Present Value of Annual cash flows – Initial Investment

= $350,000[PVIFA 20%, 5 years] – $10,65,000

= [$350,000 x 2.99061] - 10,65,000

= $ 10,46,714.25 – 10,65,000

= -$18,285.75 (negative NPV)

Therefore IRR = R1 + [NPV1(R2-R1)]

                                   NPV1-NPV2

= 0.19 + [5,172.21(0.20 – 0.19)]

              $5,172.21 – (-$18,285.75)

= 0.19 + 0.022

= 0.1922

= 19.22%

Project’s IRR = 19.22%”

(b)

Amount of fine = $1,000,000

Fine expected after 11 years from end of project

thus, it is 16 years away from today.

Present value of Fine = 1,000,000/(1+0.14)^16 = 122,891.65

New NPV = NPV without fine - Present value of Fine

New NPV = 1,36,578.34 - 122,891.65

New NPV = $13,686.69

Hope this will help, please do comment if you need any further explanation. Your feedback would be highly appreciated.