# Question

A German company manufactures a specialized piece of manufacturing equipment and leases it to a U.K. enterprise. The lease calls for five end-of-year payments of £1 million. The German firm spent €3.5 million to produce the equipment, which is expected to have no salvage value after five years. The current spot rate is €1.5/£. The risk-free interest rate in Germany is 3 percent, and in the United Kingdom it is 5 percent. The German firm reasons that the appropriate (German) discount rate for this investment is 7 percent. Calculate the NPV of this investment in two ways.

a. First, convert all cash flows to pounds, and discount at an appropriate (U.K.) cost of capital. Convert the resulting NPV to euros at the spot rate.

b. Second, calculate forward rates for each year, convert the pound-denominated cash flows into euros using those rates, and discount at the German cost of capital. Verify that the NPV obtained from this approach matches (except perhaps for small rounding errors) that obtained in part (a).

a. First, convert all cash flows to pounds, and discount at an appropriate (U.K.) cost of capital. Convert the resulting NPV to euros at the spot rate.

b. Second, calculate forward rates for each year, convert the pound-denominated cash flows into euros using those rates, and discount at the German cost of capital. Verify that the NPV obtained from this approach matches (except perhaps for small rounding errors) that obtained in part (a).

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