Question 8.5: The Eurozone firm DYA expects €1 million per year in operati...
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 |
(a) [E^*(x^{\$/€}) = 3\% – 6\% + 0.20(5\%) = –2\%.Using equation (8.1),1+{k_i}^\$=(1+{k_i}^€)(1+E^*(x^{\$/€}))+({\xi _{i€}}^\$ -1){\sigma _€}^2 , given {\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.
(b)
| N | E^*({X_N}^{\$/€}) | E({X_N}^{\$/€}) | E^*({O_N}^\$) | E({O_N}^\$) | E({O_N}^\$)- E^*({O_N}^\$) |
| 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 \$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. 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 \$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.