Chapter 31, Problem 1P

You are a U.S. investor who is trying to calculate the present value of a ∊ [&|euroSer|&]5 million cash inflow that will occur one year in the future. The spot exchange rate is S = $1.25/€ [&|euroSer|&] and the forward rate is F₁ = $1.215/ € . You estimate that the appropriate dollar discount rate for this cash flow is 4% and the appropriate euro discount rate is 7%.

1. a. What is the present value of the ∊[&|euroSer|&]5 million cash inflow computed by first discounting the euro and then converting it into dollars?
2. b. What is the present value of the ∊[& |euroSer| &] 5 million cash inflow computed by first converting the cash flow into dollars and then discounting?
3. c. What can you conclude about whether these markets are internationally integrated, based on your answers to parts a and b?

Summary Introduction

To determine: The present value of the cash inflow computed by first discounting the euro and then converting it into dollars.

Introduction: The present value is an amount that an individual makes as an investment at present in order to generate the cash flow in the future. The present value of the cash flows can be computed by adding the cash flow of every stream.

Answer to Problem 1P

The present value of the cash inflow, first discounting and then converting into the dollar is $5,841,121.50.

Explanation of Solution

The given information:

Cash inflow: €5,000,000.

Spot exchange rate: $1.25/€

Forward rate $\left(F_1\right)$: $1.215/€

Dollar discounted cash flow rate: 4.00%

Euro discount rate: 7.00%.

The formula for calculating the present value by first discounting the euro and then converting it into dollars is as follows:

$\text{Present}\text{value}=\left(\frac{\text{Cash}\text{flow}}{\left(\text{1}+\text{EuroRate}\right)}\right)\times \text{Spot}\text{exchange}\text{rate}$

Calculation of the present value of the cash inflow computed by first discounting the euro and then converting it into dollars is as follows:

For converting it into the dollar, multiply the present value by spot exchange rate as shown below:   

$\begin{array}{c}\text{Present}\text{value}=\left(\frac{\text{Cash}\text{flow}}{\left(\text{1}+\text{EuroRate}\right)}\right)\times \text{Spot}\text{exchange}\text{rate}\\ =\left(\frac{€5,000,000}{\left(1+7.00\%\right)}\right)\times 1.25\\ = \$ 4,672,897.20\times 1.25\\ = \$ 5,841,121.50\end{array}$

Therefore, the present value of the cash inflow is $5,841,121.50.

Summary Introduction

To determine: The present value of the cash inflow computed by first converting the cash flow into dollars and then discounting.

Answer to Problem 1P

The present value of the cash inflow, first converting into the dollar and then discounting is $5,841,121.50.

Explanation of Solution

Given information:

Cash inflow: €5,000,000.

Spot exchange rate: $1.25/€

Forward rate $\left(F_1\right)$: $1.215/€

Dollar discounted cash flow rate: 4.00%

Euro discount rate: 7.00%.

The formula for calculating the present value by first converting into cash flow, then into the dollar, and discounting is as follows:

$\text{Present}\text{value}=\left(\frac{\text{Cash}\text{flow}\times \text{Forward}\text{rate}}{\left(\text{1}+\text{Dollar discount Rate}\right)}\right)$

Calculation of the present value of the cash inflow computed by first converting into cash flow, then into dollar, and discounting is as follows:

For converting the cash flow into the dollar, multiply the cash flow by forward rate as shown below:   

$\begin{array}{c}\text{Present}\text{value}=\left(\frac{\text{Cash}\text{flow}\times \text{Forward}\text{rate}}{\left(\text{1}+\text{Dollar discount Rate}\right)}\right)\\ =\left(\frac{€5,000,000\times 1.215}{\left(1+5.00\%\right)}\right)\\ = \frac{6,075,000}{1.04}\\ = \$ 5,841,346.15\end{array}$

Therefore, the present value of the cash inflow is $5,841,346.15.

Summary Introduction

To determine: Whether the markets are internationally integrated, basic of part A and part B.

Answer to Problem 1P

Answer: Yes, the markets are internationally integrated, basic of part A and part B.

Explanation of Solution

Yes, the markets are internationally integrated, basic of part A and part B because, the present value of the cash inflow in part A and part B is approximately identical to each other.