Question 8.4: Extend the previous example of XYZ and DYA. DYA’s owners are...
Extend the previous example of XYZ and DYA. DYA’s owners are asking €800,000 for the business. The time-0 actual spot FX rate is 1.80 $/€, whereas the time-0 intrinsic spot FX rate is 1.50 $/€. XYZ’s managers believe that the current misvaluation of the euro will \underline{not} be fully corrected when the time-1 cash flow arrives. Instead, managers forecast a time-1 spot FX rate of 1.65 $/€. (a) Find the NPV in euros of the proposed acquisition. (b) Find the NPV in U.S. dollars of the proposed acquisition.
(a) The acquisition’s NPV^€ is the same as before, €903,200 – 800,000 = €103,200. (b) The expected time-1 operating cash flow in U.S. dollars is 1.65 $/€ (€1 million) = $1.65 million. Of this expected cash flow, there is a $1.47 million component based on the expected time-1 intrinsic spot FX rate, and a $0.18 million component that is a forecasted windfall FX gain. Because the currency beta of the euro is 0.20, the discount rate for the FX windfall component is 3% + 0.20(5%) = 4%, using the global CAPM. {V_B}^\$ is thus $1.47 million/1.085 + 0.18 million/1.04 = $1.355 million + 0.173 million = $1.528 million. Because I^\$ is (1.80 $/€)(€800,000) = $1.44 million, NPV^\$ = $1.528 million – 1.44 million = $0.088 million.