Question 23.5: Use the Law of One Price to infer the pound WACC from Ityesi...

PLAN
We can use Eq. 23.6 to compute the pound WACC. The market data we need is:

r_£^∗=\frac{1+r_£}{1+r_\$}(1+r^∗_\$)-1          (23.6)

r_£ = 0.07,  r_\$ = 0.04,  r_\$^∗ = 0.068.

EXECUTE
Applying Eq. 23.6, we have

r_£^∗=\frac{1+r_£}{1+r_\$}(1+r^∗_\$)-1=\left(\frac{1.07}{1.04} \right) (1.068 )-1 = 0.0988

The pound WACC is 9.88%.
We can now use Ityesi’s pound WACC to calculate the present value of the pound free cash flows in Table 23.3:

\frac{11.25}{1.0988}+\frac{11.25}{1.0988^2}+\frac{11.25}{1.0988^3}+\frac{11.25}{1.0988^4} = £35.75 million

The NPV in pounds of the investment opportunity is £35.75 – £17.5 = £18.25 million. Converting this amount to dollars at the spot rate gives £18.25 million × $1,6/£ = $29.20 million, which is exactly the NPV we calculated before.

EVALUATE
The U.S. and U.K. markets are integrated and our simplifying assumptions for the WACC valuation method are valid.