Question 8.6: The Eurozone firm DYA will generate uncertain future operati...
The Eurozone firm DYA will generate uncertain future operating cash flows in euros for 5 years, expected to be €1 million per year. XYZ Company, a U.S. firm, is considering the acquisition of DYA. XYZ estimates that from the U.S. dollar perspective, DYA’s FX operating exposure to the euro is \underline{1.50} 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, \underline{the \ volatility \ of \ the \ euro \ is \ 0.10} , and the time-0 intrinsic and actual spot FX rates are 1.50 $/€ and 1.80 $/€, respectively. Assume the global CAPM RA-UIRP condition applies, and GRP^\$ is 5%. XYZ forecasts that the spot FX rate will gradually converge to the expected 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 8.2. (c) Find DYA’s intrinsic business value in U.S. dollars.
Exhibit 8.2. Five-Year Project Scenario (Short-Cut)
| N | E^*({X_N}^{\$/€}) | E({X_N}^{\$/€}) | E({X_N}^{\$/€})- E^*({X_N}^{\$/€}) | E({O_N}^\$)- E^*({O_N}^\$) |
| 1 | 0.985 $/€ | 0.90 $/€ | –0.085 $/€ | –$170 |
| 2 | 0.970 $/€ | 0.91 $/€ | –0.060 $/€ | –$120 |
| 3 | 0.956 $/€ | 0.92 $/€ | –0.036 $/€ | –$72 |
| 4 | 0.941 $/€ | 0.93 $/€ | –0.011 $/€ | –$22 |
| 5 | 0.927 $/€ | 0.927 $/€ | 0 | 0 |
(a)E^*(x^{\$/€}) = 3\% – 6\% + 0.20(5\%) = –2\%. With equation (8.1) ,1+{k_i}^\$=(1+{k_i}^€)(1+E^*(x^{\$/€}))+({\xi _{i€}}^\$ -1){\sigma _€}^2 and {\xi_{O€}}^\$ = 1.50, {k_O}^€= 1.08/(1 – 0.02) – 1 = 0.102, or \ 10.2\%. {V_B}^€ = €1 \ million/1.102 + 1 \ million/1.102^2 + 1 \ million/1.102^3 + 1 \ million/ 1.102^4 + 1 million/1.102^5 = €3.77 \ million.
(b)
| N | E^*({X_N}^{\$/€}) | E({X_N}^{\$/€}) | E({X_N}^{\$/€})- E^*({X_N}^{\$/€}) | E({O_N}^\$)- E^*({O_N}^\$) |
| 1 | 1.470 $/€ | 1.70 $/€ | 0.230 $/€ | $0.230 m |
| 2 | 1.441 $/€ | 1.60 $/€ | 0.159 $/€ | $0.159 m |
| 3 | 1.412 $/€ | 1.50 $/€ | 0.088 $/€ | $0.088 m |
| 4 | 1.384 $/€ | 1.40 $/€ | 0.016 $/€ | $0.016 m |
| 5 | 1.356 $/€ | 1.356 $/€ |
(c) Using equation (8.3), V_B^{*\$}=X_0^{*\$/€}(V_B^€), {V_B}^{* \$} = 1.50 \ \$/€ \ (€3.77) = \$5.66 \ million. Because 4% is the required rate of return in U.S. dollars on a risk-free euro-denominated bond, the present value in U.S. dollars of the differences between the actual forecasted cash flows and those converted with expected intrinsic spot FX rates is \$0.23 \ million/1.04 + 0.159/1.04^2 + 0.088/1.04^3 + 0.016/1.04^4 = \$0.46 \ million. \ So \ {V_B}^\$ = \$5.66 \ million + 0.46 \ million = \$6.12 \ million.