Question 8.P.9: The British firm LVI expects operating cash flows for 5 year...
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 |
(a)E^*(x^{\$/£}) = 3\% – 5\% + 0.30(5\%) = –0.5\%. Using equation (8.1), 1+{k_i}^\$=(1+{k_i}^€)(1+E^*(x^{\$/€}))+({\xi _{i€}}^\$ -1){\sigma _€}^2 given {\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.
(b)
| N | E^*({X_N}^{\$/€}) | E({X_N}^{\$/€}) | E^*({O_N}^\$) | E({O_N}^\$) | E({O_N}^\$)- E^*({O_N}^\$) |
| 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 \$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. Or, using equation (8.3), V_B^{*\$}=X_0^{*\$/€}(V_B^€) , 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: \$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.