Chapter 21, Problem 15QP

Capital Budgeting [LO2] You are evaluating a proposed expansion of an existing subsidiary located in Switzerland. The cost of the expansion would be SF 16.7 million. The cash flows from the project would be SF 4.7 million per year for the next five years. The dollar required return is 12 percent per year, and the current exchange rate is SF 1.09. The going rate on Eurodollars is 5 percent per year. It is 4 percent per year on Euroswiss.

a. What do you project will happen to exchange rates over the next four years?

b. Based on your answer in (a), convert the projected franc flows into dollar flows and calculate the NPV.

c. What is the required return on franc flows? Based on your answer, calculate the NPV in francs and then convert to dollars.

Summary Introduction

To find: The changes in the exchange rate for the next 4 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 net present value of foreign cash flows. Then net present value is converted in to 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) 16.7 million. The cash flows from the project are SF 4.7 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 Eurodollars 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 Euroswiss is 4% for a year and exchange rate of 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 year that is lower than Eurodollar market rate that is 5%. Therefore, the exchange rate over next 4 years will decline for the concern project.

Summary Introduction

To convert: The projected flow of francs to the dollar flows and also calculates the net present value.

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 net present value of foreign cash flows. Then net present value is converted in to dollars.

Answer to Problem 15QP

The net present value is $698,986.258.

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) 16.7 million. The cash flows from the project are SF 4.7 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 Eurodollars is 5% for a year and for the Euroswiss is 4%.

Computation of the net present value of the project:

The following steps compute the net present value:

• At first, determine the “expected exchange rate” at time “t”.
• Secondly, determine the dollar cash flows by dividing cash flows from project with expected exchange rate of subsequent years.
• Finally, determine net present value 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 inflation rate in Country U

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

It is given that, current exchange rate of S Country is SF1.90, going rate (market rate) on Eurodollar is 5% per years, and 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, expected project rate is SF1.09×(0.99)^t and cost of expansion is SF16,700,000.

$\begin{array}{c}\text{Dollar cash flow for initial year}=\frac{\text{Initial cost of expansion}}{\text{Expected project cost}}\\ \text{=}\frac{-\text{SF}16,700,000}{\text{SF}1.09}\\ =-\$15,321,100.917\end{array}$

Hence, the dollar cash flow in the year 0 is - $15,321,100.917.

Computation of the dollar cash flows in the year 1:

It is given that, expected project rate is SF 1.09× (0.99) ^t and cash flows is SF 4,700,000.

$\begin{array}{c}\text{Dollar cash flow for year 1}=\frac{\text{Cash flows from the project}}{\text{Expected exchange rate of year 1}}\\ =\frac{\text{SF 4,700,000}}{\text{SF}1.09{\left(0.99\right)}^1}\\ =\$4,355,481.419\end{array}$

Hence, the dollar cash flow in the year 1 is $4,355,481.419.

Computation of the dollar cash flows in the year 2:

It is given that, expected project rate is SF1.09× (0.99) ^t and cash flows is SF 4,700,000.

$\begin{array}{c}\text{Dollar cash flow for year 2}=\frac{\text{Cash flows from the project}}{\text{Expected exchange rate of year 2}}\\ \text{=}\frac{\text{SF4,700,000}}{\text{SF}1.09{\left(0.99\right)}^2}\\ =\frac{\text{SF4,700,000}}{\text{SF}1.068309}\\ =\$4,399,476.181\end{array}$

Hence, the dollar cash flow in the year 2 is $4,399,476.181.

Computation of the dollar cash flows in the year 3:

It is given that, expected project rate is SF1.09× (0.99) ^t and cash flows is SF4,700,000.

$\begin{array}{c}\text{Dollar cash flow for year 3}=\frac{\text{Cash flows from the project}}{\text{Expected exchange rate of year 3}}\\ \text{=}\frac{\text{SF4,700,000}}{\text{SF}1.09{\left(0.99\right)}^3}\\ =\frac{\text{SF4,700,000}}{\text{SF}1.05762591}\\ =\$4,443,915.334\end{array}$

Hence, the dollar cash flow in the year 3 is $4,443,915.334.

Computation of the dollar cash flows in the year 4:

It is given that, expected project rate is SF1.09× (0.99) ^t and cash flows is SF 4,700,000.

$\begin{array}{c}\text{Dollar cash flow for year 4}=\frac{\text{Cash flows from the project}}{\text{Expected exchange rate of year 4}}\\ \text{=}\frac{\text{SF4,700,000}}{\text{SF}1.09{\left(0.99\right)}^4}\\ =\frac{\text{SF4,700,000}}{\text{SF}1.0470496509}\\ =\$4,488,803.368\end{array}$

Hence, the dollar cash flow in the year 4 is $4,448,803.368.

Computation of the dollar cash flows in the year 5:

It is given that, expected project rate is SF 1.09× (0.99) ^t and cash flows from the project is SF 4,700,000.

$\begin{array}{c}\text{Dollar cash flow for year 5}=\frac{\text{Cash flows from the project}}{\text{Expected exchange rate of year 5}}\\ \text{=}\frac{\text{SF 4,700,000}}{1.09{\left(0.99\right)}^5}\\ =\frac{\text{SF 4,700,000}}{1.036579154391}\\ =\$4,534,144.818\end{array}$

Hence, the dollar cash flow in the year 4 is $4,534,144.818.

The dollar cash flows for the subsequent years:

Year	Dollar cash flows
0	–$15,321,100.917
1	$4,355,481.42
2	$4,399,476.18
3	$4,443,915.33
4	$4,488,803.37
5	$4,534,144.82

Computation of the net present value:

$\begin{array}{c}\text{NPV}=\left(\begin{array}{c}-\text{Initial year dollar cash flows}\\ +\frac{\text{dollar cash flows in year 1}}{{\left(1+\text{estimated rate of return}\right)}^1}\\ +\frac{\text{dollar cash flows in year 2}}{{\left(1+\text{estimated rate of return}\right)}^2}\\ +\frac{\text{dollar cash flows in year 3}}{{\left(1+\text{estimated rate of return}\right)}^3}\\ +\frac{\text{dollar cash flows in year 4}}{{\left(1+\text{estimated rate of return}\right)}^4}\\ +\frac{\text{dollar cash flows in year 5}}{{\left(1+\text{estimated rate of return}\right)}^5}\end{array}\right)\\ =\left(\begin{array}{l}-\$15,321,100.917\\ +\frac{\$4,355,481.419}{{\left(1+0.12\right)}^1}+\frac{\$4,399,476.181}{{\left(1+0.12\right)}^2}\\ +\frac{\$4,443,915.334}{{\left(1+0.12\right)}^3}+\frac{\$4,488,803.368}{{\left(1+0.12\right)}^4}\\ +\frac{\$4,534,144.818}{{\left(1+0.12\right)}^5}\end{array}\right)\\ =\left(\begin{array}{l}-\$15,321,100.917+\$3,888,822.695+\$3,542,662.096\\ +\$3,163,091.157+\$2,852,715.690\\ +\$2,572,795.537\end{array}\right)\\ =\$698,986.258\end{array}$

Hence, the net present value is $698,986.258.

Summary Introduction

To find: The required return of franc flows and based on this compute the net present value and convert 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 net present value of foreign cash flows. Then net present value is converted in to dollars.

Answer to Problem 15QP

The required return of franc flows is 10.88%, the net present value is SF 722,900, and the net present value in dollars is $663,211.0091.

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) 16.7 million. The cash flows from the project are SF 4.7 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 Eurodollars is 5% for a year and for the Euroswiss is 4%.

Explanation:

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 net present value in francs:

$\text{NPV}=\left[\begin{array}{c}-\text{Initial cost of expansion}\\ +\left(\text{Cash flows from the project}\times \text{Present value of annuity}\right)\end{array}\right]$

Computation of the net present value in francs:

It is given that, cost of expansion is SF16,700,000, cash flows is SF4,700,000, number of years is 5, present value of annuity(table value) is  3.707 and computed return of SF is 10.88%.

$\begin{array}{c}\text{NPV}=\left[\begin{array}{c}-\text{Initial cost of expansion}\\ +\left(\text{Cash flows from the project}\times {\text{Present value of annuity}}_{10.88\%\text{ 5 years}}\right)\end{array}\right]\\ =-\text{SF16,700,000}+\left[\text{SF4,700,000}\times 3.707\right]\\ =-\text{SF16,700,000}+\text{SF}17,422,900\\ =\text{SF722,900}\end{array}$

Hence, the net present value is SF 722,900.

Computation of the net present value into dollars:

It is given that, current exchange rate is SF1.09% and computed NPV is SF 722,900.

$\begin{array}{c}\text{NPV}=\frac{\text{NPV}}{\text{Current exchange rate }}\\ =\frac{\text{SF722,900}}{\text{SF1}\text{.09}}\\ =\$663,211.0091\end{array}$

Hence, the net present value is $663,211.0091.