The Eurozone firm DYA expects €1 million per year in operating cash flow for 5 years. XYZ Company, a U.S. firm, is considering acquiring DYA. XYZ estimates that in U.S. dollars, DYA’s FX operating exposure to the euro is 1 and the cost of capital is 8.50%. Assume r_f^$=3% and r_f^$=6%, the currency

Question

The Eurozone firm DYA expects €1 million per year in operating cash flow for 5 years. XYZ Company, a U.S. firm, is considering acquiring DYA. XYZ estimates that in U.S. dollars, DYA’s FX operating exposure to the euro is 1 and the cost of capital is 8.50%. Assume ${r_f}^\$ = 3\% \ and \ {r_f}^€ = 6\%$ , the currency beta of the euro is 0.20, the time-0 actual and intrinsic spot FX rates are 1.80 $/€ and 1.50 $/€, the global CAPM RA-UIRP condition applies, and $GRP^\$$ is 5%. XYZ forecasts that the spot FX rate will gradually converge to the intrinsic spot FX rate by year 5, as follows: $E({X_1}^{\$/€}) = 1.70 \ \$/€; \ E({X_2}^{\$/€}) = 1.60 \ \$/€; \ E({X_3}^{\$/€}) = 1.50 \ \$/€; \ E({X_4}^{\$/€}) = 1.40 \ \$/€$ . (a) Find DYA’s intrinsic business value in euros. (b) Make a table in the format of Exhibit 8.1. (c) Find DYA’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\% – 6\% + 0.20(5\%) = –2\%[/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, {k_O}^€ = 1.085/(1 – 0.02) – 1 = 0.1071, or \ 10.71\%. {V_B}^€ \ is \ €1 \ million/1.1071 + 1 \ million/1.1071^2 + 1 \ million/1.1071^3 + 1 \ million/1.1071^4 + 1 \ million/1.1071^5 = €3.723 \ 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	1.470 $/€	1.70 $/€	$1.470 m	$1.70 m	$0.230 m
2	1.441 $/€	1.60 $/€	$1.441 m	$1.60 m	$0.159 m
3	1.412 $/€	1.50 $/€	$1.412 m	$1.50 m	$0.088 m
4	1.384 $/€	1.40 $/€	$1.384 m	$1.40 m	$0.016 m
5	1.356 $/€	1.356 $/€	$1.356 m	$1.356 m

(c) With the expected intrinsic spot FX rates, the present value in U.S. dollars is [latex]\$1.47 \ million/1.085 + 1.441 \ million/1.085^2 + 1.412 \ million/1.085^3 + 1.384 \ million/1.085^4 + 1.356 \ million/1.085^5 = \$5.585 \ million[/latex]. Because 4% is the required return in U.S. dollars on a euro risk-free asset, the present value in U.S. dollars of the windfall cash flow differences is [latex] \$0.23 \ million/ 1.04 + 0.159 \ million/1.04^2 + 0.088 \ million/1.04^3 + 0.016 \ million/1.04^4 = \$0.46 \ million. {V_B}^\$ = \$5.585 \ million + 0.46 \ million = \$6.045 \ million[/latex].

Question 8.5: The Eurozone firm DYA expects €1 million per year in operati...

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