On January $2,2024,$ an Australian Copper Exploration Company was investigating the feasibility of two mutually exclusive investment projects. The first prospective investment involved a strip $($open cut$)$ mining operation in South Wales. The second investment also involved the extraction of copper, but this expenditure would be an underground site in Queensland. Preliminary drilling, sampling, and analysis of both sites and consultation with geologists, costing the company $$3600,000,$ suggested that both sites have similar copper reserves and useful lives.

The copper extraction process for the two types of mines and the equipment required for the operation of the mines are very different, however, the underground mining operation is expected to be more complex and difficult. The process of drilling underground also increases the dangers faced by employees, although it is more environmentally friendly than the pollution and soil erosion caused by open$-$cut mining operations.

For the past several months, Jonathan Smith has been involved in the development of revenue and expense projections for the two projects. For his analysis, necessary data exists from prior investments to provide relatively accurate cost data. After examining the data at hand, Smith made the following projections related to the investment costs for each project:

Strip Mining Underground Mining

Equipment $$1,750,000$ $$2,000,000$

Additional working capital requirements $200,000200,000$

Total $$1,950,000$ $$2,200,000$

Concerning these figures, experience suggests that a $10-$year life may be expected on either of the two prospective investments, with the practice being to depreciate the equipment of the MACRS over the life of the projects.

Year $10-$Year MACRS

$110\mathrm{.}00\%$

$218\mathrm{.}00\%$

$314\mathrm{.}40\%$

$411\mathrm{.}52\%$

$59\mathrm{.}22\%$

$67\mathrm{.}37\%$

$76\mathrm{.}55\%$

$86\mathrm{.}55\%$

$96\mathrm{.}55\%$

$106\mathrm{.}55\%$

$113\mathrm{.}28\%$

Both sites have no alternative productive use for the company. The projected salvage value for the strip$-$mining operation would be $$150,000$ at the project$$s end, while the equipment for the underground plant could be expected to have a residual value of $$600,000.$ The working capital requirement would arise at the time of the investment but could be released upon the termination of the project with only a negligible chance of the full amount not being recovered.

In addition to the cost estimates, the engineers, based upon studies of the subsurface formations, were able to make projections as to the revenues that could be generated from the two fields. As a result of their studies, expected earnings before taxes for the two investments would be as follows:

Years Annual expected earnings before taxes

Strip mining $14$ $$468,000$

$57$ $$299,000$

$810$ $$169,000$

Underground mining $14$ $$520,000$

$57$ $$286,000$

$810$ $$130,000$

Upon receiving this information, Jonathan Smith questioned the reliability of the anticipated earnings. In response, Benjamin Brown, head of the engineering staff at the Australian Copper Exploration Company, informed him that both projects would have to be considered riskier than the firm$$s typical investment. The analysis indicated that the expected cash flows from the underground mining operation were subject to considerably more uncertainty than those from the strip mining project. In fact, Brown considered the extraction of coal through the underground facility to be twice as risky as that of the strip mining alternative. For this reason, he recommended that the strip mining project be discounted using a cost of capital of $10$ percent rate, while the underground mining proposal be analyzed with a $14$ percent criterion. Smith questioned Brown$$s logic, in that the company$$s cost of capital had been computed to be $8$ percent. He believed that this figure better reflected the shareholders$$ required rate of return and for that reason should be used as the discount rate for both projects. The company$$s marginal corporate tax rate is $20$ percent on earnings and other cash flows.

Questions:

$1.$ Which discount rate would you use in the estimation of the project$$s NPV and why? Who is correct, Smith or Brown, and why? $(10$ points$)$

$2.$ Using Excel and the information you learned in Chapter $12,$ and if the company faces a marginal corporate tax rate of $20$ percent on earnings and other cash flows,

a$.$ Estimate the project$$s cash flows for each year $(010)$ as shown in the table used in my Chapter $12$ lecture notes. $(30$ points$)$

b$.$ Calculate the net present value $($NPV$),$ internal rate of return $($IRR$),$ modified internal rate of return $($MIRR$),$ and payback for each investment. Information on how to use these methods can be found in Chapter $11$ and Table $12\mathrm{.}1.(30$ points$)$

c$.$ Provide a recommendation to the company as to which project the firm should accept.

i$.$ Make sure to carefully explain in some detail the why of your findings and recommendation. $(10$ points$)$