Chapter 21, Problem 15QP

a)

Summary Introduction

To find: The changes in the exchange rate for the next four years.

Introduction:

International capital budgeting estimates the decisions on investment that are related to the changes in the rate of exchange. There are two methods under international capital budgeting which are as follows:

Home currency approach:

In this approach, “Net present value (NPV)” is ascertained on converting “foreign cash flows” in to domestic currency.

Foreign currency approach:

In this approach, “foreign discount rate” is computed to find the NPV of foreign cash flows. Then, the NPV is converted into dollars.

Explanation of Solution

Given information:

Person X is evaluating the proposed expansion of a current subsidiary that is located in Country S. The cost of expansion will be SF (Swiss franc) 21 million. The cash flows from the project are SF 5.9 million for a year and for the next 5 years. The dollar required rate of return will be 12% for a year, and the current exchange is SF 1.09. The going rate of the Eurodollar is 5% for a year and for the Euroswiss is 4%.

Explanation:

The changes in the exchange rate for the upcoming 4 years:

The exchange rate of the Euroswiss is 4% for a year and exchange rate of the Eurodollar is 5% for a year. This points out that there is a minor decline in the projected exchange rate because the market rate of Euroswiss is 4% for a year; that is lower than the Eurodollar market rate that is 5%. Therefore, the exchange rate over the next 4 years will decline for the concerned project.

b)

Summary Introduction

To convert: The projected flow of francs to the dollar flows; also calculate the NPV.

Introduction:

International capital budgeting estimates the decisions on investment that are related to the changes in the rate of exchange. There are two methods under international capital budgeting which are as follows:

Home currency approach:

In this approach, “Net present value (NPV)” is ascertained on converting “foreign cash flows” in to domestic currency.

Foreign currency approach:

In this approach, “foreign discount rate” is computed to find the NPV of foreign cash flows. Then, the NPV is converted into dollars.

Answer to Problem 15QP

The NPV is $799,795.46.

Explanation of Solution

Computation of the NPV of the project:

The following steps compute the NPV:

• At first, determine the “expected exchange rate” at time “t”.
• Secondly, determine the dollar cash flows by dividing cash flows from the project with the expected exchange rate of subsequent years.
• Finally, determine the NPV with the computed dollar cash flows.

Formula to calculate the purchasing power parity:

$\text{E}\left(S_1\right)=S_o\times {\left[1+\left(h_H-h_{US}\right)\right]}^t$

E (S₁) refers to “expected exchange rate” in t periods.

$S_0$ refers to current “spot exchange rate”.

t refers to number of years.

$h_{FC}$ refers to foreign country inflation rate.

$h_{US}$ refers to the inflation rate in Country U.

Computation of the dollar cash flows by converting the projected SF to dollars:

It is given that the current exchange rate of S Country is SF1.09, the going rate (market rate) on Eurodollar is 5% per year, and the market rate of Euroswiss is 4% per year.

$\begin{array}{c}\text{E}\left(S_1\right)=S_0\times {\left[1+\left(h_S-h_{US}\right)\right]}^t\\ =\text{SF}1.09\times {\left[1+\left(0.04-0.05\right)\right]}^t\\ =\text{SF}1.09\times {\left[1+\left(-0.01\right)\right]}^t\\ =\text{SF}1.09\times {\left(0.99\right)}^t\end{array}$

Hence, the expected exchange rate is $\text{SF}1.09\times {\left(0.99\right)}^t$.

Formula to calculate the dollar cash flows:

$\text{Dollar cash flow for initial year}=\frac{\text{Initial cost of expansion}}{\text{Expected project cost}}$

Computation of the dollar cash flows in the initial year:

It is given that the expected project rate is SF1.09×(0.99)^t and the cost of expansion is SF21,000,000.

$\begin{array}{c}\text{Dollar cash flow for initial year}=\frac{\text{Initial cost of expansion}}{\text{Expected project cost}}\\ \text{=}\frac{-\text{SF21},000,000}{\text{SF}1.09}\\ =-\$19,266,055.05\end{array}$

Hence, the dollar cash flow in year 0 is - $19,266,055.05.

Computation of the dollar cash flows in year 1:

It is given that the expected project rate is SF 1.09× (0.99) ^t and cash flows are SF 5,900,000.

$\begin{array}{c}\text{Dollar cash flow for year 1}=\frac{\text{Cash flows from the project}}{\text{Expected exchange rate of year 1}}\\ =\frac{\text{SF 5,900,000}}{\text{SF}1.09{\left(0.99\right)}^1}\\ =\$5,467,519.23\end{array}$

Hence, the dollar cash flow in year 1 is $5,467,519.23.

Computation of the dollar cash flows in year 2:

It is given that the expected project rate is SF1.09× (0.99) ^t and cash flows are SF 5,900,000.

$\begin{array}{c}\text{Dollar cash flow for year 2}=\frac{\text{Cash flows from the project}}{\text{Expected exchange rate of year 2}}\\ \text{=}\frac{\text{SF5,900,000}}{\text{SF}1.09{\left(0.99\right)}^2}\\ =\frac{\text{SF5,900,000}}{\text{SF}1.068309}\\ =\$5,522,746.70\end{array}$

Hence, the dollar cash flow in year 2 is $5,522,746.70.

Computation of the dollar cash flows in year 3:

It is given that the expected project rate is SF1.09× (0.99) ^t and cash flows are SF 5,900,000.

$\begin{array}{c}\text{Dollar cash flow for year 3}=\frac{\text{Cash flows from the project}}{\text{Expected exchange rate of year 3}}\\ \text{=}\frac{\text{SF5,900,000}}{\text{SF}1.09{\left(0.99\right)}^3}\\ =\frac{\text{SF5,900,000}}{\text{SF}1.05762591}\\ =\$5,578,532.02\end{array}$

Hence, the dollar cash flow in year 3 is $5,578,532.02.

Computation of the dollar cash flows in year 4:

It is given that the expected project rate is SF1.09× (0.99) ^t and cash flows are SF 5,900,000.

$\begin{array}{c}\text{Dollar cash flow for year 4}=\frac{\text{Cash flows from the project}}{\text{Expected exchange rate of year 4}}\\ \text{=}\frac{\text{SF5,900,000}}{\text{SF}1.09{\left(0.99\right)}^4}\\ =\frac{\text{SF5,900,000}}{\text{SF}1.0470496509}\\ =\$5,634,880.83\end{array}$

Hence, the dollar cash flow in year 4 is $5,634,880.83.

Computation of the dollar cash flows in year 5:

It is given that the expected project rate is SF 1.09× (0.99) ^t and cash flows from the project are SF 5,900,000.

$\begin{array}{c}\text{Dollar cash flow for year 5}=\frac{\text{Cash flows from the project}}{\text{Expected exchange rate of year 5}}\\ \text{=}\frac{\text{SF 5,900,000}}{1.09{\left(0.99\right)}^5}\\ =\frac{\text{SF 5,900,000}}{1.036579154391}\\ =\$5,691,798.82\end{array}$

Hence, the dollar cash flow in year 5 is $5,691,798.82.

The dollar cash flows for the subsequent years:

Year	Dollar cash flows
0	–$19,266,055.05
1	$5,467,519.23
2	$5,522,746.70
3	$5,578,532.02
4	$5,634,880.83
5	$5,691,798.82

Computation of the NPV:

$\begin{array}{c}\text{NPV}=\left(\begin{array}{c}-\text{Initial year dollar cash flows}\\ +\frac{\text{dollar cash flows in year 1}}{{\left(1+\text{estimated rate of return}\right)}^1}\\ +\frac{\text{dollar cash flows in year 2}}{{\left(1+\text{estimated rate of return}\right)}^2}\\ +\frac{\text{dollar cash flows in year 3}}{{\left(1+\text{estimated rate of return}\right)}^3}\\ +\frac{\text{dollar cash flows in year 4}}{{\left(1+\text{estimated rate of return}\right)}^4}\\ +\frac{\text{dollar cash flows in year 5}}{{\left(1+\text{estimated rate of return}\right)}^5}\end{array}\right)\\ =\left(\begin{array}{l}-\$19,266,055.05\\ +\frac{\$5,467,519.23}{{\left(1+0.12\right)}^1}+\frac{\$5,522,746.70}{{\left(1+0.12\right)}^2}\\ +\frac{\$5,578,532.02}{{\left(1+0.12\right)}^3}+\frac{\$5,634,880.83}{{\left(1+0.12\right)}^4}\\ +\frac{\$5,691,798.82}{{\left(1+0.12\right)}^5}\end{array}\right)\\ =\$799,795.46\end{array}$

Hence, the NPV is $799,795.76.

c)

Summary Introduction

To find: The required return of franc flows based on this, compute the NPV and convert it into dollars.

Introduction:

International capital budgeting estimates the decisions on investment that are related to the changes in the rate of exchange. There are two methods under international capital budgeting which are as follows:

Home currency approach:

In this approach, “Net present value (NPV)” is ascertained on converting “foreign cash flows” in to domestic currency.

Foreign currency approach:

In this approach, “foreign discount rate” is computed to find the NPV of foreign cash flows. Then, the NPV is converted into dollars.

Answer to Problem 15QP

The required return of franc flows is 10.88%, the NPV is SF 871,300, and the net present value in dollars is $799,357.80.

Explanation of Solution

Formula to calculate the return on franc flows:

$\text{Required return of SF}=\left(\begin{array}{c}\text{1+Rate of retun on dollar}\\ \left[1+\left(\begin{array}{l}\text{Market rate of Euroswiss}\\ -\text{Market rate of Eurodollar}\end{array}\right)\right]-1\end{array}\right)$

Computation of the return on franc flows:

$\begin{array}{c}\text{Required return of SF}=\left(\begin{array}{c}\text{1+Rate of retun on dollar}\\ \left[1+\left(\begin{array}{l}\text{Market rate of Euroswiss}\\ -\text{Market rate of Eurodollar}\end{array}\right)\right]-1\end{array}\right)\\ =1+0.12\left[1+\left(0.04-0.05\right)\right]-1\\ =1.12\left[1+\left(-0.01\right)\right]-1\\ =\left[1.12\times 0.99\right]-1\end{array}$

$\begin{array}{c}=1.1088-1\\ =0.1088\end{array}$

Hence, the required return of SF is 0.1088. Now, “required return of SF” is multiplied with 100 to change into percentage $\left(0.1088\times 100\right)$ . Hence, “required return of SF” is 10.88%.

Formula to calculate the NPV in francs:

$\text{NPV}=\left[\begin{array}{c}-\text{Initial cost of expansion}\\ +\left(\text{Cash flows from the project}\times \text{Present value of <x-custom-btb-me data-me-id="2167" class="microExplainerHighlight">annuity</x-custom-btb-me>}\right)\end{array}\right]$

Computation of the NPV in francs:

It is given that the cost of expansion is SF21,000,000, cash flows is SF5,900,000, number of years is 5, present value of annuity (table value) is 3.707, and computed return of SF is 10.88%.

$\begin{array}{c}\text{NPV}=\left[\begin{array}{c}-\text{Initial cost of expansion}\\ +\left(\text{Cash flows from the project}\times {\text{Present value of annuity}}_{10.88\%\text{ 5 years}}\right)\end{array}\right]\\ =-\text{SF21,000,000}+\left[\text{SF5,900,000}\times 3.707\right]\\ =-\text{SF21,000,000}+\text{SF21,871,300}\\ =\text{SF871,300}\end{array}$

Hence, the NPV is SF 871,300.

Computation of the NPV in dollars:

It is given that the current exchange rate is SF1.09% and computed NPV is SF 871,300.

$\begin{array}{c}\text{NPV}=\frac{\text{NPV}}{\text{Current exchange rate }}\\ =\frac{\text{SF871,300}}{\text{SF1}\text{.09}}\\ =\$799,357.80\end{array}$

Hence, the NPV is $799,357.80.