Question

1) You own a mining company and are trying to decide which of three mines to lease to extract ore from. For mine A you pay a leasing fee of $1,040 in period 0, and then earn net profits of $400 per year for years 1-8; in year 9 you have to pay a fee of $2,500 to rehabilitate the mining site.

For mine B you pay a fee of $240 in period 0 to lease the mine and then earn $80 per year for the next 4 years. Finally, for mine C you pay a leasing fee of $400 in period 0 and then receive profits of $90 per year for years 1-6..

a) Graph the NPV profiles for all three mines (do all of your NPV calculations before graphing). (8) B) What are the IRRs (at least to the 1st decimal point) for each of the mines? (8) c) Explain in detail which mine you would choose if your goal is to maximize the NPV. Be as specific as possible. (13) d) What is the MIRR for project A using the combination approach? Assume a discount rate of 10%.

Answer 1

Ans a)

PV profiles: It provides Chart of NPV of projects at different Discount rates.

Here to calculate NPV of all Mines we have used NPV Function in Excel .

Arguments are : NPV(Rate, Cash Flows in Periods) [Rate : It is discount Rate , periods Cash flow from Year 01 to till end of the Project]

Further we Have add Cash flow of Year 0 with NPV Function to Calculate NPV of All Mines in different discount rates.

Excel Calculn :

Next We draw charts of NPV profiles of all 03 Mines :

X Axis - Discount Rates

Y Axis - NPV

Ans b)

IRR Calculation :

To Calculate we have used Excel IRR Function.  

We have to keep in Mind unlike NPV function IRR consider cash flow from Year 0. So we do not need to add Cash flow of year zero seperately.

Project A	Project B	Project C
7.55%	12.59%	9.31%

Ans C)

To maximize the NPV we need to choose project accordingly what is the expected discount rate of the project. I.E. whats is the return investor looking for from the project.

From the given table of NPV profile: If the Investor looking for a Discount rate Below 6% No doubt Project C will be the best choice.

If the discount rate Increases project B will be preferred till 8% return.

Over 8% to till around 21% discount rate Project A will be preferred.

Ans D)

To calculate MIRR we have used MIRR Function

Here We have to Provide Cash flows from Year 0. Investment Rate and Reinvestment Rate of Cash flows..

Investment Rate and Reinvestment Rate of Cash flows are 10%.

So MIRR of Project a is 10.195% given a discount rate of 10%.