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 FX operating exposure to the British

Question

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 [latex]\underline{FX \ operating \ exposure \ to \ the \ British \ pound \ is \ 1.50}[/latex], 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:[latex]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\%[/latex], 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 [latex] G R P^{\$}=5 \% [/latex] . (a) Find LVI’s intrinsic business value in British pounds. (b) Find LVI’s intrinsic business value in U.S. dollars.

Accepted Answer

(a) [latex]E^*(x^{\$/£}) = 3\% – 5\% + 0.30(5\%) = –0.5\%[/latex]. Using equation (8.1), [latex]1+{k_i}^\$=(1+{k_i}^€)(1+E^*(x^{\$/€}))+({\xi _{i€}}^\$ -1){\sigma _€}^2[/latex] given [latex]{\xi_{O€}}^\$= 1.50[/latex], LVI’s cost of capital in British pounds is found by solving [latex]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[/latex].

(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) [latex]V_B^{*\$}=X_0^{*\$/€}(V_B^€)[/latex] 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: [latex]\$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[/latex].

Question 8.P.12: The British firm LVI will generate uncertain future operatin...

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