Question 8.1: A U.S. multinational’s Japanese division has an FX operating...
A U.S. multinational’s Japanese division has an FX operating exposure to the yen of 1.60 and a hurdle rate in U.S. dollars of 9%. The risk-free rates are 5% in U.S. dollars and 2% in yen, and the volatility of the yen is 0.08. Assume the linear approximation RA-UIRP condition (global CAPM) in U.S. dollars. The currency beta of the yen is –0.10 and GRP^\$ = 5\%. (a) Find the division’s hurdle rate in yen. (b) How close to the correct hurdle rate is the simple interest rate differential linear approximation?
(a) Using equation (5.3): E^*(x^{\$/¥}) = {r_f}^\$ – {r_f}^€ + {\beta_€}^\$(GRP^\$), E^*(x^{\$/¥}) = {r_f}^\$ – {r_f}^¥ + {\beta_¥}^\$(GRP^\$) = 0.05 – 0.02 – 0.10(0.05) = 0.025, or \ 2.50\%.Using equation (8.1),1+{k_i}^\$=(1+{k_i}^€)(1+E^*(x^{\$/€}))+({\xi _{i€}}^\$ -1){\sigma _€}^2 , 1.09 = (1 + {k_O}^¥)(1 + 0.025) + (1.60 – 1)0.08^2 ; so the division’s {k_O}^¥ \ is \ 1.08616/1.025 – 1 = 0.0597, or \ 5.97\%. (b) {k_O}^¥ = {k_O}^\$ – ({r_f}^\$ – {r_f}^¥) = 0.09 – (0.05 – 0.02) = 0.06, or \ 6\%.