Question 8.P.12: The British firm LVI will generate uncertain future operatin...
The British firm LVI will generate uncertain future operating cash flows in British pounds for 5 years, expected to be £1 million per year. XYZ Co. is a U.S. firm considering the acquisition of LVI. XYZ estimates that from the U.S. dollar perspective, LVI’s \underline{FX \ operating \ exposure \ to \ the \ British \ pound \ is \ 1.50}, and the cost of capital is 9.50%. XYZ forecasts that the spot FX rate will gradually converge to the intrinsic spot FX rate by year 5, as follows:E({X_1}^{\$/£}) = 1.45 \$/£; E({X_2}^{\$/£}) = 1.50 \$/£; \ E({X_3}^{\$/£}) = 1.52 \$/£; E({X_4}^{\$/£}) = 1.54 \ \$/£; E({X_5}^{\$/£}) = E^*({X_5}^{\$/£}). Assume \ {r_f}^\$ = 3\%, {r_f}^£ = 5\%, the currency beta of the British pound is 0.30, the volatility of the British pound is 0.08, and the intrinsic time-0 spot FX rate is 1.60 $/£. Assume the global CAPM RA-UIRP condition with G R P^{\$}=5 \% . (a) Find LVI’s intrinsic business value in British pounds. (b) Find LVI’s intrinsic business value in U.S. dollars.
(a) E^*(x^{\$/£}) = 3\% – 5\% + 0.30(5\%) = –0.5\%. Using equation (8.1), 1+{k_i}^\$=(1+{k_i}^€)(1+E^*(x^{\$/€}))+({\xi _{i€}}^\$ -1){\sigma _€}^2 given {\xi_{O€}}^\$= 1.50, LVI’s cost of capital in British pounds is found by solving 1.095 – 0.50(0.08)^2 = (1 + {k_O}^£)(1 – 0.005); so \ {k_O}^£ = 1.0918/0.995 – 1 = 0.0973, or \ 9.73\%. LVI’s \ {V_B}^£ = £1 \ million/1.0973 + 1 \ million/1.0973^2 + 1 \ million/1.0973^3 + 1 \ million/1.0973^4 + 1 \ million/1.0973^5 = £3.82 \ million.
(b) If the expected British pound cash flows are converted to U.S. dollars at the expected intrinsic spot FX rates, we use equation (8.3) V_B^{*\$}=X_0^{*\$/€}(V_B^€) to get a present value of (1.60 $/£)(£3.82 million) = $6.11 million. Because 3% + 0.30(5%) = 4.50% is the required rate of return in U.S. dollars on a risk-free pound-denominated bond, the present value in U.S. dollars of the differences between the actual forecasted cash flows and those converted at the expected intrinsic spot FX rates is equal to: \$0.142 \ million/1.045 + 0.084 \ million/1.045^2 + 0.056 \ million/1.045^3 + 0.028 \ million/1.0454 = \$0.23 \ million. \ So \ LVI’s \ {V_B}^\$ = \$6.11 \ million + 0.23 \ million = \$6.40 \ million.