Question 8.2: The Eurozone firm DYA will generate one operating cash flow,...
The Eurozone firm DYA will generate one operating cash flow, expected to be €1 million at time 1. From the perspective of U.S. dollars, DYA’s FX operating exposure to the euro is 1 and cost of capital is 8.50%. XYZ Company, a U.S. multinational, is evaluating the acquisition of DYA. Assume {r_f}^\$ = 3\% \ and \ {r_f}^€ = 6\% , the currency beta of the euro is 0.20, and the actual time-0 spot FX rate of 1.50 $/€ is the time-0 intrinsic spot FX rate. Assume the global CAPM RAUIRP condition with GRP^\$ = 5\%. XYZ forecasts that the time-1 spot FX rate will be the intrinsic spot FX rate. (a) Find DYA’s intrinsic business value in euros. (b) Find the expected time-1 intrinsic spot FX rate. (c) Find DYA’s intrinsic business value in U.S. dollars. (d) Show that the intrinsic business values in euros and U.S. dollars are equivalent given the time-0 intrinsic spot FX rate.
(a) E^*(x^{\$/€}) = 3\% – 6\% + 0.20(5\%) = -2\%. Using equation (8.1), 1+{k_i}^\$=(1+{k_i}^€)(1+E^*(x^{\$/€}))+({\xi _{i€}}^\$ -1){\sigma _€}^2 , given {\xi_{O€}}^\$ = 1 , DYA’s {k_O}^€ is found by solving (1 + {k_O}^\$) = (1 + {k_O}^€) \times (1 + E^*(x^{\$/€})); so \ {k_O}^€ = 0.1071, or \ 10.71\%. {V_B}^€ = €1 \ million/1.1071 = €0.9032 \ million. (b) The expected time-1 intrinsic spot FX rate, E^*({X_1}^{\$/€}),is \ 1.50 \ \$/€(1 – 0.02) = 1.47 \$/€. (c) DYA’s expected time-1 operating cash flow in U.S. dollars is 1.47 $/€(€1 million) = $1.47 million. So {V_B}^\$ is $1.47 million/1.085 = $1.355 million. (d) At the time-0 intrinsic spot FX rate of 1.50 $/€, {V_B}^€ is equivalent to {V_B}^\$ , because 1.50 $/€(€0.9032 million)= $1.355 million.