Say that the current direct exchange rate is $1.5537/£.The cash inflow in pounds is £70,000 in two years and the discount rate is 7%.During this time,the anticipated annual inflation rate is 3% per year in the United States and 5% per year in the United Kingdom.What is the present value (in U.S.dollars)of the £100,000 after conversion from pounds to dollars if you are using current and forward exchange rates?

Question

Quizplus · Accepted Answer

To calculate the present value of the cash inflow in pounds, we need to convert it to U.S. dollars using the forward exchange rate. Let's first calculate the forward exchange rate:

Forward exchange rate = Spot exchange rate x (1 + domestic interest rate) / (1 + foreign interest rate)
Forward exchange rate = 1.5537 x (1 + 0.03) / (1 + 0.05)
Forward exchange rate = 1.5011

So, for every pound, we will receive $1.5011 in two years. Therefore, the present value of the cash inflow in pounds is:

Present value = £70,000 / (1 + 0.05)^2 x 1.5011
Present value = £56,647.75 x 1.5011
Present value = $85,101.75

Now, we need to convert the £100,000 to U.S. dollars using the current exchange rate. The conversion rate is:

Conversion rate = 1 / 1.5537
Conversion rate = 0.6439

So, £100,000 is equivalent to $154,509.80. However, we need to take into account the anticipated inflation rates in both countries. To adjust for inflation, we need to use the following formula:

Adjusted cash inflow = Cash inflow x (1 + foreign inflation rate) ^ n / (1 + domestic inflation rate) ^ n

Here, n is the number of years. In our case, n is 2. So, the adjusted cash inflow is:

Adjusted cash inflow = £100,000 x (1 + 0.05) ^ 2 / (1 + 0.03) ^ 2
Adjusted cash inflow = £110,387.31

To convert this to U.S. dollars, we multiply by the current exchange rate:

Adjusted cash inflow in dollars = £110,387.31 x 0.6439
Adjusted cash inflow in dollars = $70,976.55

Therefore, the present value of the £100,000 after conversion to U.S. dollars is $70,976.55. The best choice is C.

Say That the Current Direct Exchange Rate Is $1