Question 23.5: Use the Law of One Price to infer the pound WACC from Ityesi...
Use the Law of One Price to infer the pound WACC from Ityesi’s dollar WACC. Verify that the NPV of Ityesi’s project is the same when its pound free cash flows are discounted at this WACC and converted at the spot rate.
PLAN
We can use Eq. 23.6 to compute the pound WACC. The market data we need is:
r^{\ast }_{£} =\frac{1+r_{£} }{1+rx_{\$} } (1+r^{\ast }_{\$} )-1 (23.6)
r_{£} =0.07, r_{\$} =0.04, r^{\ast }_{\$} =0.068 .
Finally, we’ll need the spot exchange rate ($1.60/£) to convert the pound NPV to dollars.
EXECUTE
Applying Eq. 23.6, we have
r^{\ast }_{£} =\frac{1+r_{£} }{1+r_{\$} } (1+r^{\ast }_{\$})-1=(\frac{1.07}{1.04} )(1.068)-1=0.0988The pound WACC is 9.88%.
We can now use Ityesi’s pound WACC to calculate the present value of the pound free cash flows in Table 23.3:
| TABLE 23.3 Expected Dollar Free Cash Flows from Ityesi’s U.K. Project | ||||||
| 1 | Year | 0 | 1 | 2 | 3 | 4 |
| 2 | Dollar Free Cash Flow ($ million) | |||||
| 3 | Pound FCF (£ million) | -17.500 | 11.250 | 11.250 | 11.250 | 11.250 |
| 4 | Forward Exchange Rate ($/£) | 1.6000 | 1.5551 | 1.5115 | 1.4692 | 1.4280 |
| 5 | Dollar Value of Pound FCF (3 \times 4) | -28.000 | 17.495 | 17.004 | 16.528 | 16.065 |
\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 \times $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.