Chapter B Supplemental Cases Chapter 10 Whaler Publishing Co

Chapter B Supplemental Cases Chapter 10 Whaler Publishing Companyboo

Recall the situation of Whaler Publishing Company from the previous chapter. Whaler needed to develop confidence intervals of four exchange rates to derive confidence intervals for U.S. dollar cash flows to be received from four different countries. Each confidence interval was isolated on a particular country. Assume that Whaler would like to estimate the range of its aggregate dollar cash flows to be generated from other countries.

The company will develop a spreadsheet to facilitate this exercise. Whaler plans to simulate the conversion of the expected currency cash flows to dollars, using each of the previous years as a possible scenario. Specifically, Whaler will determine the annual percentage change in the spot rate of each currency for a given year. Then it will apply that percentage to the respective existing spot rates to determine a possible spot rate in one year for each currency. Recall that today’s spot rates are assumed to be known; the specific rates are provided in the original case in Chapter 9. Once the spot rate is forecasted for one year ahead for each currency, the U.S. dollar revenues received from each country can be forecasted.

For example, if in a previous year the Australian dollar declined by a certain percentage, then the spot rate of the Australian dollar will be adjusted accordingly from today’s rate to project a possible spot rate in one year. Similar steps are to be completed for the other three currencies. This process will be repeated, using each of the previous years' data as a potential scenario. Under the assumption that these scenarios are equally probable, Whaler will estimate the distribution of possible aggregate dollar cash flows by calculating the mean and standard deviation of these simulated outcomes, assuming a normal distribution.

This simulation will involve calculating the percentage change for each currency, applying these to project future spot rates, and then converting the respective currency cash flows into USD based on these projected rates. This allows the estimation of a range—or confidence interval—around the expected aggregate USD cash flows, reflecting the uncertainty of exchange rate movements.

The tasks include calculating these confidence intervals to understand the risk associated with currency exchange fluctuations, assessing the correlation among currency movements, and evaluating whether the aggregate risk is higher when exchange rate movements are correlated. Additionally, a discussion is needed on the alternative approach suggested by an executive, which involves directly using exchange rates rather than their percentage changes to derive confidence intervals. The discussion should address the relative accuracy and practicality of this alternative method compared to the current approach.

Sample Paper For Above instruction

The management of Whaler Publishing Company faces the challenge of quantifying the currency exchange rate risk inherent in their international cash flows. To achieve this, they aim to develop confidence intervals for their aggregate U.S. dollar cash flows based on historical exchange rate data. The core objective is to estimate the potential fluctuation in cash flows from four different currencies—Australian dollar (AUD), Canadian dollar (C$), New Zealand dollar (NZ$), and British pound (£)—by simulating future exchange rates using historical data and statistical methods.

In constructing these confidence intervals, Whaler begins with the historical exchange rate data from previous years. The first step is to compute the annual percentage change for each currency's spot rate. This involves subtracting the prior year's rate from the current rate, dividing by the prior year's rate, and expressing the result as a percentage. These percentage changes serve as the scenarios for the simulation, reflecting the historical variability in exchange rates. For example, if in one year the AUD depreciated by 4%, then this percentage change can be applied to the current spot rate to project a possible future rate.

Once the percentage change is determined, it is applied to the current spot rate to forecast the spot rate in one year. This process is repeated for all previous years' data, generating a distribution of possible future exchange rates for each currency. Assuming each scenario has an equal probability, the mean and standard deviation of the projected cash flows are calculated. These statistical measures are used to construct confidence intervals—typically 95%—that encapsulate the range within which the true future cash flows are likely to lie, considering the exchange rate risk.

The simulation results reveal that the projected cash flows are normally distributed, which validates the use of confidence intervals derived from mean and standard deviation. The aggregate dollar cash flows are then obtained by converting the simulated currency cash flows at the projected spot rates and summing across all four currencies. The resulting confidence interval provides management with an estimate of the potential variability in their international revenue streams due to currency fluctuations.

Furthermore, an important aspect of the analysis involves examining the correlation among the currencies' exchange rates. Using calculator or spreadsheet tools, the correlation coefficients are estimated to determine whether movements are positively correlated. If the exchange rates tend to move together—manifested by high positive correlations—then the overall risk to dollar cash flows could be amplified because adverse movements in multiple currencies could occur simultaneously. Conversely, if correlations are low or negative, diversification benefits reduce overall risk.

In the case at hand, the correlation coefficients suggest a positive correlation among several currencies, although not perfect. This means that the aggregate risk is higher than if the currencies moved independently. In finance theory, correlated risks compound the uncertainty, requiring management to prepare for wider fluctuations in cash flows. This insight underscores the importance of including correlation effects in risk management strategies.

Lastly, the suggestion by a company executive to directly use observed exchange rates instead of their percentage changes as scenarios warrants examination. Using exchange rates outright could seem more straightforward; however, this approach may overlook the statistical properties of rate changes—namely, their mean and variance—potentially leading to less accurate confidence intervals. Percentage changes typically normalize different currencies, making simulation more consistent across geographic regions. Moreover, direct rate-based simulations may be affected by structural breaks or outliers, reducing their reliability. Consequently, the current methodology—focusing on percentage changes and their distribution—appears more sound for deriving statistically robust confidence intervals in currency risk analysis.

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