Question

(10-12) After discovering a new gold vein in the Colorado mountains, CTC Mining Corporation

must decide whether to go ahead and develop the deposit. The most cost-effective method of

mining gold is sulfuric acid extraction, a process that could result in environmental damage.

Before proceeding with the extraction, CTC must spend $900,000 for new mining equipment

and pay $165,000 for its installation. The gold mined will net the firm an estimated $350,000

each year for the 5-year life of the vein. CTC’s cost of capital is 14%. For the purposes of this

problem, assume that the cash inflows occur at the end of the year.

1. What are the project’s NPV and IRR?

              b. Should this project be undertaken if environmental impacts were not a consideration?

              c. How should environmental effects be considered when evaluating this, or any other,

                  project? How might these concepts affect the decision in part b?

Answer 1

(a)- Project’s Net Present Value and IRR

Project’s Net Present Value (NPV)

Period	Annual Cash Flow ($)	Present Value factor at 14%	Present Value of Cash Flow ($)
1	3,50,000	0.8771930	3,07,017.54
2	3,50,000	0.7694675	2,69,313.63
3	3,50,000	0.6749715	2,36,240.03
4	3,50,000	0.5920803	2,07,228.10
5	3,50,000	0.5193687	1,81,779.03
TOTAL			12,01,578.34

Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment

= $12,01,578.34 – [$900,000 + $165,000]

= $1,36,578.34

Project’s Internal Rate of Return (IRR)

Step – 1, Firstly calculate NPV at a guessed discount Rate, Say 19% (R1)

Period	Annual Cash Flow ($)	Present Value factor at 19%	Present Value of Cash Flow ($)
1	3,50,000	0.8403361	2,94,117.65
2	3,50,000	0.7061648	2,47,157.69
3	3,50,000	0.5934158	2,07,695.53
4	3,50,000	0.4986688	1,74,534.06
5	3,50,000	0.4190494	1,46,667.28
TOTAL			10,70,172.21

Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment

= $10,70,172.21 - $10,65,000

= $5,172.21

Step – 2, NPV at 19% is positive, Calculate the NPV again at a higher discount rate, Say 20% (R2)

Period	Annual Cash Flow ($)	Present Value factor at 20%	Present Value of Cash Flow ($)
1	3,50,000	0.8333333	2,91,666.67
2	3,50,000	0.6944444	2,43,055.56
3	3,50,000	0.5787037	2,02,546.30
4	3,50,000	0.4822531	1,68,788.58
5	3,50,000	0.4018776	1,40,657.15
TOTAL			10,46,714.25

Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment

= $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 x (0.20 – 0.19)]

              $5,172.21 – (-$18,285.750

= 0.19 + [$51.72 / $23,457.96]

= 0.19 + 0.0022

= 0.1922 or

= 19.22%

“Project’s Internal Rate of Return (IRR) = 19.22%”

Requirement (b)

“YES”. The Project should be accepted, since the NPV is Positive $1,36,578.34 and the IRR (19.22%) is greater than the Cost of Capital (14%)

Requirement (c)

The CTC Mining Corporation must deduct the cost relating to the environmental damage from the expected cash flows to get a better estimate of the benefits from the Project and if such costs are high, then it may lead to the rejection of the Investment proposals.

NOTE

The Formula for calculating the Present Value Factor is [1/(1 + r)ⁿ], Where “r” is the Discount/Interest Rate and “n” is the number of years.