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Chapter 19: Problem 17

Solitaire Machinery is a Swiss multinational manufacturing company. Currently, Solitaire's financial planners are considering undertaking a 1 -year project in the United States. The project's expected dollar-denominated cash flows consist of an initial investment of \(\$ 1,000\) and a cash inflow the following year of \(\$ 1,200 .\) Solitaire estimates that its risk-adjusted cost of capital is 14 percent. Currently, 1 U.S. dollar will buy 1.62 Swiss francs. In addition, 1-year risk-free securities in the United States are yielding 7.25 percent, while similar securities in Switzerland are yielding 4.5 percent. a. If this project were instead undertaken by a similar U.S.-based company with the same risk-adjusted cost of capital, what would be the net present value and rate of return generated by this project? b. What is the expected forward exchange rate 1 year from now? c. If Solitaire undertakes the project, what is the net present value and rate of return of the project for Solitaire?

Short Answer

Expert verified
a. NPV: $52.63, Rate of Return: 20%. b. Forward Rate: 1.663 CHF/USD. c. NPV: 289.67 CHF, Rate of Return: 23.18%.

Step by step solution

01

Calculate Net Present Value (NPV) for a U.S.-based Company

First, we need to calculate the Net Present Value (NPV) for a similar U.S.-based company. To do this we apply the NPV formula: \[ NPV = \sum \dfrac{C_t}{(1+r)^t} - C_0 \]where \(C_t\) is the cash inflow for year \(t\), \(r\) is the discount rate, and \(C_0\) is the initial investment. Given:- Initial Investment \(C_0 = \\(1000\)- Cash Inflow in year 1, \(C_1 = \\)1200\)- Discount Rate \(r = 0.14\) (risk-adjusted cost of capital)Substitute into the formula:\[ NPV = \dfrac{1200}{(1+0.14)^1} - 1000 \]\[ NPV = \dfrac{1200}{1.14} - 1000 \]\[ NPV = 1052.63 - 1000 \]\[ NPV = 52.63 \]Thus, the NPV for the U.S.-based company is \$52.63.
02

Calculate Rate of Return for a U.S.-based Company

The Rate of Return can be found using the formula:\[ Rate \ of \ Return = \dfrac{C_1 - C_0}{C_0} \]Substitute the values:- Initial Investment \(C_0 = \\(1000\)- Cash Inflow in year 1, \(C_1 = \\)1200\)\[ Rate \ of \ Return = \dfrac{1200 - 1000}{1000} = 0.2 \text{ or } 20\% \]Thus, the rate of return for the U.S.-based company is 20%.
03

Calculate Expected Forward Exchange Rate 1 Year from Now

The expected forward exchange rate can be calculated using the interest rate parity:\[ F = S \times \dfrac{1 + r_{domestic}}{1 + r_{foreign}} \]Given:- Current Exchange Rate \(S = 1.62\) CHF/USD- U.S. interest rate \(r_{domestic} = 7.25\% = 0.0725\)- Swiss interest rate \(r_{foreign} = 4.5\% = 0.045\)Substitute into the formula:\[ F = 1.62 \times \dfrac{1 + 0.0725}{1 + 0.045} \]\[ F = 1.62 \times \dfrac{1.0725}{1.045} \]\[ F = 1.62 \times 1.0263 \]\[ F \approx 1.663 \text{ CHF/USD} \]Thus, the expected forward exchange rate 1 year from now is approximately 1.663 CHF/USD.
04

Calculate NPV for Solitaire Machinery

Convert the cash flows from USD to CHF using the current and expected exchange rates to calculate the NPV for Solitaire. Year 0:- Initial CHF Investment: \(1000 \times 1.62 = 1620 \) CHFYear 1:- Expected CHF Inflow: \(1200 \times 1.663 = 1995.6 \) CHFNow, calculate NPV:- Discount rate (Swiss) \(r = 0.045\)\[ NPV = \dfrac{1995.6}{(1+0.045)^1} - 1620 \]\[ NPV = \dfrac{1995.6}{1.045} - 1620 \]\[ NPV = 1909.67 - 1620 \]\[ NPV = 289.67 \text{ CHF} \]Thus, the NPV for Solitaire is 289.67 CHF.
05

Calculate Rate of Return for Solitaire Machinery

The rate of return in terms of CHF is found similarly to Step 2:\[ Rate \ of \ Return = \dfrac{1995.6 - 1620}{1620} \]\[ Rate \ of \ Return = \dfrac{375.6}{1620} \]\[ Rate \ of \ Return \approx 0.2318 \text{ or } 23.18\% \]Thus, the rate of return for Solitaire Machinery is approximately 23.18%.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Net Present Value
Net Present Value, or NPV, is a fundamental concept in finance that helps determine the value of an investment over time. When a company makes an investment, it expects to receive cash flows in the future. However, the value of money generally changes over time due to inflation and opportunity costs. NPV answers the question: Is an investment worth more today than its costs?
The formula to calculate NPV is:\[NPV = \sum \dfrac{C_t}{(1+r)^t} - C_0\]- **\(C_t\)**: Cash inflow during the period \(t\)
- **\(r\)**: Discount rate鈥攔eflects the riskiness of the investment and the time value of money
- **\(C_0\)**: Initial investment
The NPV calculation considers all future cash inflows and discounts them back to their present value using the discount rate. If the NPV is positive, it indicates that the investment is expected to generate more money than it costs, making it a wise choice for investors.
When applied to the U.S. project by Solitaire Machinery, the expected cash inflows were discounted back at a rate of 14%, resulting in a net present value of \$52.63. This suggests that at this discount rate, the project is financially viable.
Exchange Rate
The exchange rate is the price of one currency expressed in terms of another. In international finance, understanding exchange rates is crucial as they affect how much you will earn or pay when converting one currency to another.
Exchange rates can fluctuate based on numerous factors, including economic indicators, interest rates, political stability, and market speculation. For businesses engaged in international trade, managing these fluctuations can be critical to their success. - **Spot Rate**: The current exchange rate at which a currency pair can be bought or sold.
- **Forward Exchange Rate**: An agreed-upon exchange rate for a currency pair at a future date. It is often used to hedge against the unpredictability of spot rates. In the Solitaire Machinery example, an initial exchange rate of 1 USD to 1.62 CHF was given. However, when predicting into the future, financial analysts often rely on calculated forward exchange rates, as shown in the exercise, using interest rate differentials between the two countries involved.
Interest Rate Parity
Interest Rate Parity (IRP) is a theory used in forex markets that suggests the difference in interest rates between two countries is equal to the difference between the forward exchange rate and the spot exchange rate. It is crucial for understanding how currency valuation aligns with interest rates between countries.
The formula for interest rate parity is:\[F = S \times \dfrac{1 + r_{domestic}}{1 + r_{foreign}}\]- **\(F\)**: Forward exchange rate
- **\(S\)**: Current spot exchange rate
- **\(r_{domestic}\)**: Interest rate of the domestic country
- **\(r_{foreign}\)**: Interest rate of the foreign country
In short, IRP ensures that investors won鈥檛 profit from differences in currency rates by investing in different interest rate environments.
In the exercise, IRP was used to determine the expected forward exchange rate for converting USD to CHF in the future. Given the interest rates in the U.S. (7.25%) and Switzerland (4.5%), the expected forward rate calculated was approximately 1.663 CHF/USD. This calculation essentially equalizes the returns from investing in risk-free securities in either of the two countries, assuming no arbitrage opportunities.

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