Chapter 17, Problem 17P

FOREIGN CAPITAL BUDGETING Sandrine Machinery is a Swiss multinational manufacturing company. Currently, Sandrine’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 $2,000 and a cash inflow the following year of $2,400. Sandrine estimates that its risk-adjusted cost of capital is 10%. Currently, 1 U.S. dollar will buy 0.94 Swiss franc. In addition, 1-year risk-free securities in the United States are yielding 3%, while similar securities in Switzerland are yielding 1.50%.

1. a. If this project was 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?
2. b. What is the expected forward exchange rate 1 year from now?
3. c. If Sandrine undertakes the project, what is the net present value and rate of return of the project for Sandrine?

Summary Introduction

To determine: The net present value and rate of return from the given project under U.S. based company.

Introduction:

Multinational Company:

It refers to such company, which operates its activities in the home country and in one or more foreign countries. The head office is always situated in the home country of the company.

Net Present Value (NPV):

It is that amount, which indicates the difference reported on subtraction of the cash outflows from the cash inflows.

The rate of Return:

It refers to that rate, which indicates the proportion of amount, which an investor gets as income annually from an investment.

Explanation of Solution

Given information:

The initial investment (cash outflow) is $2,000.

The cash inflow is $2,400.

The risk-adjusted cost of capital is 10% or 0.10.

The exchange rate of 1 U.S. dollar is 0.94 Swiss francs.

The period of the project is 1 year.

Net present value

Formula to calculate net present value:

$\text{NPV}=\text{Present value of cash inflow}-\text{Present value of cash outflow}$

Substitute $2,181.81 for the present value of cash inflow (working note) and $2,000 for the present value of cash outflow in the above formula.

$\begin{array}{c}\text{NPV}=\$2,181.81-\$2,000\\ =\$181.81\end{array}$

Rate of return

The formula to calculate the rate of return,

$\text{Rate of return}=\left(\frac{\text{Cash inflow}}{\text{Cash outflow}}-1\right)\times 100$

Substitute $2,400 for cash inflow and $2,000 for cash outflow in the above formula.

$\begin{array}{c}\text{Rate of return}=\left(\frac{\$2,400}{\$2,000}-1\right)\times 100\\ =\left(1.2-1\right)\times 100\\ =0.2\times 100\\ =20\%\end{array}$

Working Note:

The present value of cash inflow

$\begin{array}{c}\text{Present value of cash inflow}=\frac{\text{Cash inflow}}{{\left(1+\text{r}\right)}^{\text{n}}}\\ =\frac{\$2,400}{{\left(1+0.10\right)}^1}\\ =\frac{\$2,400}{1.10}\\ =\$2,181.81\end{array}$

Conclusion

Hence, the net present value is $181.81 and rate of return is 20% or 0.20.

Summary Introduction

To determine: The expected forward exchange rate for 1 year.

Introduction:

Forward Exchange Rate:

This rate indicates the pre-decided rate of exchange for currencies of two countries for a date in nearby future.

Explanation of Solution

Given information:

The exchange rate (spot rate) of 1 U.S. dollar is 0.94 Swiss francs.

The interest rate in Switzerland is 1.5% or 0.015.

The interest rate in the United States is 3% or 0.03.

The period of the project is 1 year.

The equation of interest rate parity,

$\frac{\text{Forwad exchange rate}}{\text{Spot exchange rate}}=\frac{\left(1+{\text{r}}_{\text{Swiss}}\right)}{\left(1+{\text{r}}_{\text{US}}\right)}$

Where,

• ${\text{r}}_{\text{Swiss}}$ is interest rate in Switzerland.
• ${\text{r}}_{\text{US}}$ is interest rate in the U.S.

Substitute 0.94 for spot exchange rate, 0.015 for ${\text{r}}_{\text{Swiss}}$, 0.03 for ${\text{r}}_{\text{US}}$ in the above formula.

$\begin{array}{l}\frac{\text{Forwad exchange rate}}{0.94}=\frac{\left(1+0.015\right)}{\left(1+0.03\right)}\\ \frac{\text{Forwad exchange rate}}{0.94}=\frac{\left(1.015\right)}{\left(1.03\right)}\\ \text{Forwad exchange rate}=\frac{\left(1.015\right)}{\left(1.03\right)}\times 0.94\\ \text{Forwad exchange rate}=0.9262\end{array}$

Conclusion

Hence, the 1-year forward rate is 0.9262 francs per dollar.

Summary Introduction

To determine: The net present value and rate of return from the given project under S company.

Introduction:

Net Present Value (NPV):

It is that amount, which indicates the difference reported on subtraction of the cash outflows from the cash inflows.

The rate of Return:

It refers to the rate, which indicates the proportion of amount the investor gets as income annually from an investment.

Explanation of Solution

Given information:

The initial investment (cash outflow) is $2,000.

The cash inflow is $2,400.

The risk-adjusted cost of capital is 10% or 0.10.

The spot exchange rate of 1 U.S. dollar is 0.94 Swiss francs.

The forward exchange rate of 1 U.S. dollar is 0.9262 Swiss francs.

The period of the project is 1 year.

Firstly, convert the amount of cash flows into the Swiss franc which is given in terms of dollars.

Convert amount on basis of the exchange rate as follow:

Year	Cash flow ($)	Cash flow (Swiss franc) $\left(\text{Cash flow in }\$\times \text{Exchange rate}\right)$
0	$2,000	$\left(\$2,000\times 0.94=1,880\right)$
1	$2,400	$\left(\$2,400\times 0.9262=2,222.88\right)$

Net present value

Formula to calculate net present value:

$\text{NPV}=\text{Present value of cash inflow}-\text{Present value of cash outflow}$

Substitute 2,020.8 Swiss francs for the present value of cash inflow (working note), and 2,000Swiss francs for the present value of cash outflow (above table) in the above formula

$\begin{array}{c}\text{NPV}=2,020.8\text{ francs}-1,880\text{ francs}\\ =140.8\text{ francs}\end{array}$

Rate of return

The formula to calculate the rate of return,

$\text{Rate of return}=\left(\frac{\text{Cash inflow}}{\text{Cash outflow}}-1\right)\times 100$

Substitute 2,222.88 Swiss francs for cash inflow, and 1,880 Swiss francs for cash outflow in the above formula.

$\begin{array}{c}\text{Rate of return}=\left(\frac{2,222.88}{1,880}-1\right)\times 100\\ =\left(1.1823-1\right)\times 100\\ =0.1823\times 100\\ =18.23\%\end{array}$

Working Note:

The present value of cash inflow

$\begin{array}{c}\text{Present value of cash inflow}=\frac{\text{Cash inflow}}{{\left(1+\text{r}\right)}^{\text{n}}}\\ =\frac{\$2,222.88}{{\left(1+0.10\right)}^1}\\ =\frac{\$2,222.88}{1.10}\\ =2,020.8\text{ Swiss francs}\end{array}$

Conclusion

Hence, the net present value is 140.8 francs and rate of return is 18.23% or 0.1823.