You are evaluating a proposed expansion of an existing subsidiary located in Switzerland. The cost of the expansion would be SF 32.4 million. The cash flows from the project would be SF 9 million per year for the next five years. The dollar required return is 15 percent per year, and the current exchange rate is SF 1.72. The going rate on Eurodollars is 9 percent per year. It is 8 percent per year on Euroswiss.
We can use relative purchasing power parity to calculate the dollar cash flows at each time. The equation is:
E[St] = (SFr 1.720)[1 + (0.08 – 0.09)]t
E[St] = 1.720 (0.99)t
So, the cash flows each year in U.S. dollar terms will be:
t SFr E[St] US$
0 –32.4M 1.7200 $-18,837,209.30
1 +9M 1.7028 $5,285,412.26
2 +9M 1.6858 $5,338,800.26
3 +9M 1.6689 $5,392,727.54
4 +9M 1.6522 $5,447,199.54
5 +9M 1.6357 $5,502,221.75
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And the NPV is:
NPV = –$18,837,209.30 + $5,285,412.26/1.15 + $5,338,800.26/1.152 + $5,392,727.54 /1.153 + $5,447,199.54/1.154 + $5,502,221.75/1.155
NPV = $-808,462.07
The problem for me is, I cant figure out what numbers replace 9M in the column in order to times the SF and ES to get the US dollars. Whats the formula or where am I just not looking at?
The M here stands for Million hence 9M = 9 Million.
In order to calculate the cash flows in US dollars, you need to multiply the Swiss franc (SF) cash flows by the expected exchange rate (E[St]). The expected exchange rate is calculated using the relative purchasing power parity formula, as shown in the equation you provided.
For each year, you can calculate the expected exchange rate using the formula E[St] = 1.720 (0.99)t.
To calculate the cash flows in US dollars:
1. Multiply the cash flows in Swiss francs (SF) by the expected exchange rate (E[St]) for each year.
For example, in the first year, the cash flow is SF 9 million:
US dollar cash flow = SF 9 million * E[St]
Using the given exchange rate of SF 1.72 and the formula E[St] = 1.720 (0.99)^0, the expected exchange rate E[St] is 1.720.
So, US dollar cash flow in the first year = SF 9 million * 1.720 = $15,480,000.
Similarly, you can calculate the US dollar cash flows for the remaining years using the respective expected exchange rates calculated using the formula E[St] = 1.720 (0.99)t.
Hope this helps! Let me know if you have any further questions.
To calculate the cash flows in U.S. dollars, you'll need to multiply the Swiss franc (SF) cash flows by the exchange rate at each time period. In this case, the exchange rate is given as SF 1.72 per U.S. dollar.
The cash flows each year in U.S. dollar terms can be calculated using the formula:
Cash Flows in USD = Cash Flows in SF * Exchange Rate
For example, in year 0, the cash flow in Swiss francs is -SF 32.4 million. To convert it into U.S. dollars, you will multiply it by the exchange rate:
Cash Flow in USD (year 0) = -SF 32.4 million * 1.72 = -$55,828,800
Similarly, for the cash flows in the subsequent years, you would multiply the cash flows in Swiss francs by the exchange rate at each time period.
So, for example, in year 1, the cash flow in Swiss francs is +SF 9 million. To convert it into U.S. dollars, you will multiply it by the exchange rate:
Cash Flow in USD (year 1) = +SF 9 million * 1.7028 = +$15,351,708.40
Repeat the above calculation for each year's cash flow in Swiss francs to get the corresponding cash flow in U.S. dollars.
Once you have the cash flows in U.S. dollars for each time period, you can use them to calculate the Net Present Value (NPV) using the formula provided in the question.