# 1

1. Compute the net present value of Ariel-Mexico’s recycling equipment in pesos by discounting incremental peso cash flows at a peso discount rate. How should this NPV be translated into Euros? Assume expected future inflation for France is 3% per year?

Groupe Ariel is willing to invest in the installation of new automated machinery to recycle and remanufacture toner- and printer cartridges, in one of its wholly owned subsidiary in Monterrey, Mexico.
To assess the impact of this whole project, the cash flows were calculated to determine in what way this project would impact their financials. Incremental cash flows for the next ten years are calculated. In order to calculate the net operating cost, revenue from the sale of old machinery is subtracted the purchase and installation cost of new machinery. Tax is added in the revenue of the old machine because the sale price is lower than the book value of the machine.
For the incremental cash flows from 2009 to 2018, the cost saving due to the replacement is being adjusted by the tax savings on depreciation. The tax savings on depreciation were found, by adding the tax benefits of the new equipment that is being bought, and by subtracting the tax benefits of the old equipment that is being sold.
Discount rate of 12.9 is calculated with the help of the formula.
iMXN= (1+i France) x (1+? Mexico / 1+?France ) – 1
This discount rate is calculated by assuming that the purchasing power parity holds during the whole period. Afterwards, these incremental cash flows were added to the NPV function in Excel using a 12.19% discount rate to arrive at the Project Net Present Value in 1.48 m MXN. Lastly in order to find the find the NPV in euro, this number was divided by the spot exchange rate of MXN 15.99/ EUR, to arrive at the NPV €92,495 for this project in euro.
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2. Compute the NPV in Euros by translating the project’s future peso cash flows into Euros at expected future spot exchange rates. Note that Ariel’s Euro hurdle rate for a project of this type was 8%. Assume that annual inflation rates are expected to be 7% in Mexico and 3% in France.

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In this approach the NPV is to be calculated by converting the whole cash flow from pesos in euros at the future spot exchange rate. For this method, a derivation of the PPP equation was used to compute the projected future exchange rates;
Future exchange raten = (1+? Mexico /1+?France) x Spot rate n
This theory was used to predict expected future spot rates by adding 1 to the expected inflation rates of MXN and EUR and then taking their ratio. This ratio is then multiplied by the exchange rate of every year to predict exchange rates for the following 10 years. The cash flows in pesos are than converted euros by dividing by the relevant exchange rate. Once the cash flows were obtained then their present value can be calculated by using the hurdle rate of 8% as the discount rate. The value of the Project NPV was €92,495, which was equal to the one founded using the spot exchange rate because of the presumption of the PPP equation.
This variation produces the same NPV as the original method of simply converting the MXN NPV into euro NPV after discounting, which proves accuracy of the PPP theory.

3. Compare the two sets of calculations and the corresponding NPVs. How and why do they differ? Which approach should Arnaud Martin use?

In this case, the NPV’s that were calculated by both approaches are the exact same. Basically, it means that if purchasing power parity holds for the entire period of the investment there will be no difference between either of the approaches. A lower cost of capital rate, as in the case in France (8%) should deliver a higher NPV, however, the depreciation of the MXN offset this effect in the same proportion, thus delivering same results. In other words, the IPC holds. From an IRR point of view – as expected from a higher hurdle rate and equal NPV- the CFs MXN show a higher indicator.
If the PPP assumption would not exist and interest rates stay the same, depending on whether the euro depreciates or appreciates against the peso, the euro value NPV of the project would be greater or respectively less than the peso value.
We believe that the second approach (computing NPV by converting the whole cash flow from pesos in euros) is more accurate because the appropriate exchange rates are used when transferring cash flows from Pesos into Euros thus taking into account the possible economic changes in the upcoming years. As many analysts had also predicted a real depreciation of the peso against both the U.S. dollar and the Euro over the next five years. For example, one international business publication noted “Mexico’s rising external financing requirement and the fading impact of the U.S. stimulus package can only increase pressure on Mexico’s currency.”

4. Suppose Mexican inflation is projected at 3% instead of 7% per year (assume French inflation remains at 3%). How does this affect the NPV calculations?

In the case that the inflation rate for both Mexico and France was same at 3%, we had to calculate the incremental cost savings of materials, direct labor and overhead at the lower Mexican inflation rate of 3% for both processes. Under parity conditions, equal inflation rates for the next 10 years also implies stable spot rates for the next 10 years. The discount rates of the both countries would also be equal at 8 % assuming PPP holds.
As for NPV calculations in pesos by discounting incremental peso cash flows at a peso discount rate, it was 1.77 m MXN, and when converted into Euro NPV by dividing it by the spot exchange rate it’s at €110,728. It indicates that the value of the project increases as the inflation rate is decreased. In case of computing NPV after converting the cash flows into euro from peso at an expected future exchange rate, the NPV is the same as of the first approach at €110,728.
From a business point a view, lower inflation in Mexico delivers lower savings in the operation. On the other hand, lower inflation brings a lower cost of capital impacting positively on the NPV MXN results. In relation to CFs in EUR, lower and equal inflation MXN vs. EUR means stable spot rate, and again impacting positively on the NPV EUR.

5. Suppose Ariel expects a significant real depreciation of the peso against the Euro. How should Martin incorporate such an expectation into his NPV analysis? (For simplicity you may continue with the assumption that inflation is expected to be 3% in both countries.) What is its effect on the concluded NPV under each of the approaches in questions 1 and 2?

In case that inflation rate for both countries remain same but peso depreciates against euro the two originally predicted NPVs ;ill no longer equal.

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