Delta Company, a U$.$S$.$ MNC$,$ is contemplating making a foreign capital expenditure in South Africa. The initial cost of the project is ZAR$10,000.$ The annual cash flows over the five year economic life of the project in ZAR are estimated to be $3,000,4,000,5,000,6000,$ and $7,000.$ The parent firm$$s cost of capital in dollars is $9\mathrm{.}5$ percent. Long$-$run inflation is forecasted to be $3$ percent per annum in the U$.$S$.$ and $7$ percent in South Africa. The current spot foreign exchange rate is ZAR$/$USD $=3\mathrm{.}75.$

a$.$ Determine the NPV of the project in USD by converting the USD cost of capital to the equivalent ZAR cost of capital using the Interest Rate Parity.

b$.$ Determine the NPV of the project in USD by converting the ZAR cash flows to the equivalent USD cash flows using Relative PPP to forecast exchange rates.

c$.$ Are the two USD NPVs different or the same? Explain your answer.