Explain the ideas of equations (13.2) and (13.3) on p.301 in order to evaluate the net present value (NPV) of a foreign project.

What are the main differences?

a. Explain the ideas of equations (13.2) and (13.3) on p.301 in order to evaluate the net present value (NPV) of a foreign project.

What are the main differences?

b. Now, assume that appreciates against Cr 20% for each period (instead of 25% in your text/lecture note example), but all other values are the same from the example.

(i) Find the NPV of the Wendys project based on Recipe #1 using equation (13.2). Hint: the expected cash flows in Cr (E[CF_t^Cr]) will be the same as in Exhibit 13.5. Why? Do NOT present Table, but utilize the equation.

(ii) Find the NPV of the Wendys project based on Recipe #2 using equation (13.3). Hint: first estimate the future exchange rates and then the expected cash flows in pounds E[CF_t]. Do NOT present Table, but utilize the equation.

PLEASE EXPLAIN THE ANSWER

13.2 AN EXAMPLE: WENDY'S RESTAURANT IN NEVERLAND Wendy lives in London and is considering opening a restaurant in Neverland, an imaginary world in which markets are perfect and the international parity conditions hold. Neverland is governed by the dread pirate Captain Hook, a vindictive tyrant with a consuming jealousy of Wendy and her friend Peter. We'll deal with Hook's influence on project value in Section 13.4. For now, let's consider Wendy's investment proposal in its most basic form. The details of Wendy's Neverland project appear in Exhibit 13.2. Wendy will purchase one of Captain Hook's ships and convert it into a restaurant to satisfy the appetites of the many pirates on the island. The ship is ship-shape and Wendy (with a little help from Peter) can have the galley ready for business right away (at t = 0). Wendy will invest the equity capital, Peter will serve as the local manager, and Lost Boys will provide the labor. Interest rates and expected inflation rates are shown in Exhibit 13.3. The parity conditions hold (this is an imaginary world), so real required returns on a particular asset should be the same in both British pounds (Wendy's domestic currency) and Neverland crocs. The real required return on risk-free government bills is equal in the two currencies, at RF = RECT = 1 percent. The spot exchange rate between the croc and the pound is Cr4.00/. According to the Fisher equation, the 20 percent nominal required return on comparable investments in the United Kingdom includes expected inflation and a real required return, according to (1+if) = (1 + E[p{})(1 +R$) = (1.0891)(1.1018) = 1.20, or if = 20 percent. Because the parity conditions hold, the real required return of R = 10.18 percent on restaurant projects in the United Kingdom must equal EXHIBIT 13.2 Wendy's Proposed Restaurant Project in Neverland The project lasts four years, at which time Wendy grows up. (Only Peter stays young forever.) All cash flows except the initial investment occur at the end of the year. An initial investment of Cr40,000 (10,000) will purchase the ship. An additional Cr24,000 (6,000) will be needed for inventory. Increases in other current asset accounts are offset by increases in current liabilities, so the increase in net working capital (current assets minus current liabilities) also is Cr24,000. Expected annual sales during the 4-year life of the project are Cr30,000, Cr60,000, Cr90,000, and Cr60,000 in nominal terms. Variable costs (wages for Peter and the Lost Boys) are 20 percent of sales. Peter has negotiated with a Lost Boy named Tootles to clean the ship each evening for a salary of Cr1,881 payable at the end of the first year. Tootles has negotiated a cost-of-living increase into this contract such that his salary will increase each year at the croc rate of inflation. (Although Tootles is lost, he is not stupid.) The ship will be owned by Wendy's wholly owned subsidiary in Neverland. Neverland's tax code calls for the ship to be depreciated on a straight-line basis over four years to a zero salvage value. The ship and inventory will be sold at the end of the project and are expected to retain their respective real values of Cr40,000 and Cr24,000 in time-zero crocs. Income taxes are 50 percent in Neverland. Capital gains on the sale of the ship and inventory at the end of the project also are taxed at 50 percent. No additional taxes are due as Wendy repatriates the project's cash flows back to London. The second approach takes the perspective of the parent corporation and dis- counts expected cash flows in the parent's domestic currency at the required return in the domestic currency. Expected cash flows from the project first are translated into the domestic currency at expected future spot rates of exchange according to E[CF, 41 = E[CF, s,d/f). Project value is then the discounted present value of this domestic currency cash flow stream over the life of the project, V.]id = E[CF,fs, d/f)/(1+id)t (13.3) where Vlid is the domestic value of the foreign project given discounting is done in the domestic currency. There are two complementary approaches to the valuation of a foreign project. The first approach values the project in the foreign (or local) currency and then translates this foreign currency project value into the parent's domestic currency at today's spot rate of exchange. This is algebraically expressed as Vedlif = S, d/f [E,E[CF,41/(1+if)] or Vedlif = Sod/vof (13.2) where Vof = E[CF,f1/(1+if)' is the value of the project in the foreign (or local) cur- rency based on all incremental cash flows over the life of the project including the initial investment at t = 0. The net present value Vodlif is the foreign currency project value (i.e., given discounting is done in the foreign currency) translated to the domes- tic currency at today's spot exchange rate. 13.2 AN EXAMPLE: WENDY'S RESTAURANT IN NEVERLAND Wendy lives in London and is considering opening a restaurant in Neverland, an imaginary world in which markets are perfect and the international parity conditions hold. Neverland is governed by the dread pirate Captain Hook, a vindictive tyrant with a consuming jealousy of Wendy and her friend Peter. We'll deal with Hook's influence on project value in Section 13.4. For now, let's consider Wendy's investment proposal in its most basic form. The details of Wendy's Neverland project appear in Exhibit 13.2. Wendy will purchase one of Captain Hook's ships and convert it into a restaurant to satisfy the appetites of the many pirates on the island. The ship is ship-shape and Wendy (with a little help from Peter) can have the galley ready for business right away (at t = 0). Wendy will invest the equity capital, Peter will serve as the local manager, and Lost Boys will provide the labor. Interest rates and expected inflation rates are shown in Exhibit 13.3. The parity conditions hold (this is an imaginary world), so real required returns on a particular asset should be the same in both British pounds (Wendy's domestic currency) and Neverland crocs. The real required return on risk-free government bills is equal in the two currencies, at RF = RECT = 1 percent. The spot exchange rate between the croc and the pound is Cr4.00/. According to the Fisher equation, the 20 percent nominal required return on comparable investments in the United Kingdom includes expected inflation and a real required return, according to (1+if) = (1 + E[p{})(1 +R$) = (1.0891)(1.1018) = 1.20, or if = 20 percent. Because the parity conditions hold, the real required return of R = 10.18 percent on restaurant projects in the United Kingdom must equal EXHIBIT 13.2 Wendy's Proposed Restaurant Project in Neverland The project lasts four years, at which time Wendy grows up. (Only Peter stays young forever.) All cash flows except the initial investment occur at the end of the year. An initial investment of Cr40,000 (10,000) will purchase the ship. An additional Cr24,000 (6,000) will be needed for inventory. Increases in other current asset accounts are offset by increases in current liabilities, so the increase in net working capital (current assets minus current liabilities) also is Cr24,000. Expected annual sales during the 4-year life of the project are Cr30,000, Cr60,000, Cr90,000, and Cr60,000 in nominal terms. Variable costs (wages for Peter and the Lost Boys) are 20 percent of sales. Peter has negotiated with a Lost Boy named Tootles to clean the ship each evening for a salary of Cr1,881 payable at the end of the first year. Tootles has negotiated a cost-of-living increase into this contract such that his salary will increase each year at the croc rate of inflation. (Although Tootles is lost, he is not stupid.) The ship will be owned by Wendy's wholly owned subsidiary in Neverland. Neverland's tax code calls for the ship to be depreciated on a straight-line basis over four years to a zero salvage value. The ship and inventory will be sold at the end of the project and are expected to retain their respective real values of Cr40,000 and Cr24,000 in time-zero crocs. Income taxes are 50 percent in Neverland. Capital gains on the sale of the ship and inventory at the end of the project also are taxed at 50 percent. No additional taxes are due as Wendy repatriates the project's cash flows back to London. The second approach takes the perspective of the parent corporation and dis- counts expected cash flows in the parent's domestic currency at the required return in the domestic currency. Expected cash flows from the project first are translated into the domestic currency at expected future spot rates of exchange according to E[CF, 41 = E[CF, s,d/f). Project value is then the discounted present value of this domestic currency cash flow stream over the life of the project, V.]id = E[CF,fs, d/f)/(1+id)t (13.3) where Vlid is the domestic value of the foreign project given discounting is done in the domestic currency. There are two complementary approaches to the valuation of a foreign project. The first approach values the project in the foreign (or local) currency and then translates this foreign currency project value into the parent's domestic currency at today's spot rate of exchange. This is algebraically expressed as Vedlif = S, d/f [E,E[CF,41/(1+if)] or Vedlif = Sod/vof (13.2) where Vof = E[CF,f1/(1+if)' is the value of the project in the foreign (or local) cur- rency based on all incremental cash flows over the life of the project including the initial investment at t = 0. The net present value Vodlif is the foreign currency project value (i.e., given discounting is done in the foreign currency) translated to the domes- tic currency at today's spot exchange rate