The British firm LVI expects operating cash flows for 5 years of £1 million per year. XYZ Co., a U.S. firm, is considering the acquisition of LVI. XYZ estimates that from the U.S. dollar perspective, LVI’s FX operating exposure to the British pound is 1 and the cost of capital is 9.50%. Assume

Question

The British firm LVI expects operating cash flows for 5 years of £1 million per year. XYZ Co., a U.S. firm, is considering the acquisition of LVI. XYZ estimates that from the U.S. dollar perspective, LVI’s FX operating exposure to the British pound is 1 and the cost of capital is 9.50%. Assume ${r_f}^\$ = 3\%,{r_f}^£ = 5\%$ , the currency beta of the British pound is 0.30, the intrinsic time-0 spot FX rate is 1.60 $/£, and the actual time-0 spot FX rate is 1.40 $/£. Assume the global CAPM RA-UIRP condition with $GRP^\$ = 5\%$ . XYZ’s managers forecast the spot FX price of the British pound will gradually converge to the intrinsic spot FX rate by year 5, as follows: $E({X_1}^{\$/£} ) = 1.45 \ \$/£; \ E({X_2}^{\$/£}) = 1.50 \ \$/£; E({X_3}^{\$/£ }) = 1.52 \ \$/£; \ E({X_4}^{\$/£} ) = 1.54 \ \$/£; \ E({X_5}^{\$/£}) = E^*({X_5}^{\$/£} )$ . (a) Find LVI’s intrinsic business value in British pounds. (b) Make a table in the format of Exhibit 8.1. (c) Find LVI’s intrinsic business value in U.S. dollars.

Exhibit 8.1. Five-Year Project Scenario

N	$E^*({X_N}^{\$/€})$	$E({X_N}^{\$/€})$	$E^*({O_N}^\$)$	$E({O_N}^\$)$	$E({O_N}^\$)- E^*({O_N}^\$)$
1	0.985 $/€	0.90 $/€	$1,970	$1,800	–$170
2	0.970 $/€	0.91 $/€	$1,940	$1,820	–$120
3	0.956 $/€	0.92 $/€	$1,912	$1,840	–$72
4	0.941 $/€	0.93 $/€	$1,882	$1,860	–$22
5	0.927 $/€	0.927 $/€	$1,854	$1,854

Exhibit 8.1. Five-Year Project Scenario

N	[latex]E^*({X_N}^{\$/€})[/latex]	[latex]E({X_N}^{\$/€})[/latex]	[latex]E^*({O_N}^\$)[/latex]	[latex]E({O_N}^\$)[/latex]	[latex]E({O_N}^\$)- E^*({O_N}^\$)[/latex]
1	0.985 $/€	0.90 $/€	$1,970	$1,800	–$170
2	0.970 $/€	0.91 $/€	$1,940	$1,820	–$120
3	0.956 $/€	0.92 $/€	$1,912	$1,840	–$72
4	0.941 $/€	0.93 $/€	$1,882	$1,860	–$22
5	0.927 $/€	0.927 $/€	$1,854	$1,854

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, LVI’s \ {k_O}^£ \ is \ 1.095/(1 – 0.005) – 1 = 0.10, or \ 10\%. LVI’s \ {V_B}^£ \ is \ £1 \ million/1.10 + 1 \ million/1.10^2 + 1 \ million/1.10^3 + 1 \ million/1.10^4 + 1 \ million/1.10^5 = £3.79 \ million[/latex].

(b)

N	[latex]E^*({X_N}^{\$/€})[/latex]	[latex]E({X_N}^{\$/€})[/latex]	[latex]E^*({O_N}^\$)[/latex]	[latex]E({O_N}^\$)[/latex]	[latex]E({O_N}^\$)- E^*({O_N}^\$)[/latex]
1	1.592 $/€	1.45 $/€	$1.592 m	$1.560 m	$0.142 m
2	1.584 $/€	1.50 $/€	$1.584 m	$1.50 m	$0.084 m
3	1.576 $/€	1.52 $/€	$1.576 m	$1.52 m	$0.056 m
4	1.568 $/€	1.54 $/€	$1.568 m	$1.54 m	$0.028 m
5	1.560 $/€	1.56 $/€	$1.560 m	$1.56 m

(c) Converting the expected British pound cash flows to U.S. dollars at the expected intrinsic spot FX rates, we get a present value of [latex]\$1.592 \ million/1.095 + 1.584 \ million/1.095^2 + 1.576 \ million/1.095^3 + 1.568 \ million/1.095^4 + 1.56 \ million/1.095^5 = \$6.06 \ million[/latex]. Or, using equation (8.3), [latex]V_B^{*\$}=X_0^{*\$/€}(V_B^€)[/latex] , 1.60 $/£(£3.79 million) = $6.06 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/1.045^4 = \$0.29 \ million. \ So \ LVI’s \ {V_B}^\$ \ is \ \$6.06 \ million + 0.29 \ million = \$6.35 \ million.[/latex]

Question 8.P.9: The British firm LVI expects operating cash flows for 5 year...

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