Chapter 31, Problem 15QP

Capital Budgeting You are evaluating a proposed expansion of an existing subsidiary located in Switzerland. The cost of the expansion would be SF 25 million. The cash flows from the project would he SF 6.9 million per year for the next five years. The dollar required return is 12 percent per year, and the current exchange rate is SF 1.17. The going rate on Eurodollars is 6 percent per year. It is 5 percent per year on Swiss francs.

1. a. What do you project will happen to exchange rates over the next four years?
2. b. Based on your answer in (a), convert the projected franc flows into dollar flows and calculate the NPV.
3. 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 explain: Exchange rate after 4 years.

Exchange rate:

Exchange rate is used to define the value of one currency against the other currency. Exchange rate has two main components one is the currency used to compare that is domestic currency and other is the currency used to compare against that is foreign currency.

Answer to Problem 15QP

Exchange rate is projected to decline.

Explanation of Solution

Implicitly, it is assumed that interest rates won’t change over the life of the project, but the exchange rate is projected to decline because the ES rate is lower than the ED rate.

Conclusion

So, in next four years exchange rate is to be declined.

Summary Introduction

To calculate: NPV and converting of franc flows into dollar flows.

Explanation of Solution

Calculation of Cash flow by using relative purchasing power parity:

Given,

Current exchange rate is SF1.17.

Going rate on Eurodollar is 6% per year.

Going rate on Swiss francs is 5% per year.

Time period is 1, 2,3,4,5 years.

Formula to calculate relative purchasing power parity is,

$E\left(S_t\right)=S_0\times {\left[1+\left(h_{FC}-h_{US}\right)\right]}^t$ (1)

Where,

• ${\text{h}}_{\text{US}}$ is U.S’s inflation rate.
• $h_{FC}$ is foreign currency inflation rate.
• $S_0$ is spot rate.
• $\text{E}\left({\text{S}}_{\text{t}}\right)$ is purchasing power parity.
• $t$ is time period.

Substitute SF1.17 for Current exchange rate, 6% per year for rate on ED, 5% rate on Swiss francs and 0 for Time period in equation (1).

$\begin{array}{c}E\left(ST\right)=\left(SF1.17\right){\left[1+\left(0.05-0.06\right)\right]}^0\\ =\left(SF1.17\right){\left[1-0.01\right]}^0\\ =SF1.17{\left(0.99\right)}^0\\ =SF1.17\end{array}$

So, relative purchasing power parity for year 0 is SF1.17.

Calculation of relative purchasing power parity for year 1:

Substitute SF1.17 for Current exchange rate, 6% per year for rate on ED, 5% rate on Swiss francs and 1 for Time period in equation (1).

$\begin{array}{c}E\left(ST\right)=\left(SF1.17\right){\left[1+\left(0.05-0.06\right)\right]}^1\\ =\left(SF1.17\right){\left[1-0.01\right]}^1\\ =SF1.17{\left(0.99\right)}^1\\ =SF1.1583\end{array}$

So, relative purchasing power parity for year 1 is SF1.1583.

Calculation of relative purchasing power parity for year 2:

Substitute SF1.17 for Current exchange rate, 6% per year for rate on ED, 5% rate on Swiss francs and 2 for Time period in equation (1).

$\begin{array}{c}E\left(ST\right)=\left(SF1.17\right){\left[1+\left(0.05-0.06\right)\right]}^2\\ =\left(SF1.17\right){\left[1-0.01\right]}^2\\ =SF1.17{\left(0.99\right)}^2\\ =SF1.1467\end{array}$

So, relative purchasing power parity for year 2 is SF1.1467.

Calculation of relative purchasing power parity for year 3:

Substitute SF1.17 for Current exchange rate, 6% per year for rate on ED, 5% rate on Swiss francs and 3 for Time period in equation (1).

$\begin{array}{c}E\left(ST\right)=\left(SF1.17\right){\left[1+\left(0.05-0.06\right)\right]}^3\\ =\left(SF1.17\right){\left[1-0.01\right]}^3\\ =SF1.17{\left(0.99\right)}^3\\ =SF1.1352\end{array}$

So, relative purchasing power parity for year 3 is SF1.1352.

Calculation of relative purchasing power parity for year 4:

Substitute SF1.17 for Current exchange rate, 6% per year for rate on ED, 5% rate on Swiss francs and 4 for Time period in equation (1).

$\begin{array}{c}E\left(ST\right)=\left(SF1.17\right){\left[1+\left(0.05-0.06\right)\right]}^4\\ =\left(SF1.17\right){\left[1-0.01\right]}^4\\ =SF1.17{\left(0.99\right)}^4\\ =SF1.1239\end{array}$

So, relative purchasing power parity for year 4 is SF1.1239.

Calculation of relative purchasing power parity for year 5:

Substitute SF1.17 for Current exchange rate, 6% per year for rate on ED, 5% rate on Swiss francs and 5 for Time period

$\begin{array}{c}E\left(ST\right)=\left(SF1.17\right){\left[1+\left(0.05-0.06\right)\right]}^5\\ =\left(SF1.17\right){\left[1-0.01\right]}^5\\ =SF1.17{\left(0.99\right)}^5\\ =SF1.1126\end{array}$

So, relative purchasing power parity for year 5 is SF1.1126.

Cash flow each year in U.S dollars

Year	Amount of cash flow from project (SF)	Relative purchasing power parity	Cash Flow amount ($)
0	-25,000,000	1.1700	-21,367,521.37
1	6,900,000	1.1583	5,957,005.96
2	6,900,000	1.1467	6,017,177.73
3	6,900,000	1.1352	6,077,957.31
4	6,900,000	1.1239	6,139,350.82
5	6,900,000	1.1127	6,201,364.46

Table (1)

Calculation of NPV

Given,

Cash flow in year 1 is $5,957,005.96.

Cash flow in year 2 is $6,017,177.73.

Cash flow in year 3 is $6,077,957.31.

Cash flow in year 4 is $6,139,350.82.

Cash flow in year 5 is $6,201,364.46.

Initial cash flow $- is 21,367,521.37.

Discount rate is 12%.

Time period is 1, 2, 3, 4, 5years.

Formula to calculate NPV

$NPV={\displaystyle \sum _{im}^n\frac{C{F}_i}{{\left(1+r\right)}^i}-C_0}$

Where,

• NPV is net present value.
• i is number of years.
• $C_0$ is initial cash flow.
• CF is cash flow in particular year.
• r is discount rate.

Substitute $5,957,005.96 for Cash flow in year 1, $6,017,177.73 for Cash flow in year 2, $6,077,957.31 for Cash flow in year 3, $6,139,350.82 for Cash flow in year 4, $6,201,364.46 for Cash flow in year 5, -$21,367,521.37 for Initial cash flow, 12% for Discount rate and 1, 2, 3,4,5 years for Time period.

$\begin{array}{c}NPV=\left[\begin{array}{l}\frac{\$5,957,005.96}{{\left(1+.12\right)}^1}+\frac{\$6,017,177.73}{{\left(1+.12\right)}^2}+\frac{\$6,077,957.31}{{\left(1+.12\right)}^3}\\ +\frac{\$6,139,350.82}{{\left(1+.12\right)}^4}+\frac{\$6,201,364.46}{{\left(1+.12\right)}^5}-\$21,367,521.37\end{array}\right]\\ =\left[\begin{array}{l}\$5,318,755.321+\$4,796,857.246+\$4,326,169.967\\ +\$3,901,668.436+\$3,518,820.737-\$21,367,521.37\end{array}\right]\\ =\$494,750.33\end{array}$

Conclusion

So, the net present value is $494,750.33.

Summary Introduction

To calculate: require return in franc flows, NPV in francs and in dollars.

Explanation of Solution

Calculation of rearranging of purchasing power parity to get the required return in Swiss franc:

Given,

Current exchange rate is SF1.12.

Going rate on Eurodollar is 6% per year.

Going rate on Swiss francs is 5% per year.

Formula to calculate relative purchasing power parity is,

$RSF=S_0\times \left[1+\left(h_{FC}-h_{US}\right)\right]-t$

Here,

• $h_{US}$ is US inflation rate.
• $h_{FC}$ is foreign currency inflation rate.
• $S_0$ is spot rate.
• $RSF$ is relative purchasing power parity.

Substitute SF1.12 for Current exchange rate, 6% per year for going rate on ED, 5% per year for going rate on Swiss francs and 1 for time period.

$\begin{array}{c}E\left(ST\right)=\left(SF1.12\right)\left[1+\left(0.05-0.06\right)\right]-1\\ =SF\left(1.12\right)\left[1-0.09\right]-1\\ =1.1088-1\\ =0.1088\end{array}$

So, the relative purchasing power parity is 10.88%.

Calculation of NPV in Swiss franc:

Given,

Initial investment is -SF25, 000,000.

Cash flow in year 1 is SF6, 900,000.

Relative purchasing power parity is 10.88%.

Time period is 5 years.

Formula to calculate NPV is,

$NPV=\left[\begin{array}{l}\text{Initial}\text{investment}+\text{ Cash flow in year 1st}\\ \times \left(\text{interest}\text{rate}\text{parity}\right)\end{array}\right]$

Substitute -SF25, 000,000 for Initial investment, SF6, 900,000 for Cash flow in year 1, 3.70708 for interest rate parity.

$\begin{array}{c}NPV=-SF25,000,000+SF6,900,000\times \left(3.70708\right)\\ =-SF25,000,000+SF25,578852\\ =SF578,852\end{array}$

So NPV in franc is SF578, 852.

Converting of NPV in $ from SF,

$\begin{array}{c}NPV=\left(SF578,852\right)\left(\frac{\$1}{SF1.17}\right)\\ =\$494,745.3\end{array}$

Conclusion

So, NPV in franc is SF578, 852, while in dollar is $494,745.30.