QUESTION $1$

$[25$ marks$]$

ABC Ltd$,$ a United Kingdom multinational firm, is contemplating making a foreign capital expenditure in South Africa. The initial cost of the project is ZAR$50$ million. The annual cash flows over the five$-$year economic life of the project are estimated to be ZAR$13$ million, ZAR$18$ million, ZAR$25$ million, ZAR$10$ million, and ZAR$9$ million. ABC Ltd$\text{'}$s cost of capital in pounds $()$ is $7\mathrm{.}5$ percent. The long$-$run inflation rate is forecasted to be $4$ percent per annum in the U$.$K$.$ and $12$ percent in South Africa. The current spot foreign exchange rate is $ZA\frac{R}{}=15\mathrm{.}56.$

Required:

$($a$)$ Calculate the NPV in ZAR using the ZAR equivalent cost of capital according to the Fisher Effect and then convert the ZAR NPV to $$ at the current spot exchange rate.

$(5)$

$($b$)$ Convert all cash flows from ZAR to $$ at Purchasing Power Parity forecasted exchange rates and then calculate the NPV at the pound cost of capital.

$($c$)$ What is the NPV in pounds if the actual pattern of ZAR$/$ exchange rates is: $S(0)=15\mathrm{.}56,S(1)=14\mathrm{.}56,S(2)=16\mathrm{.}72,S(3)=15\mathrm{.}78,S(4)=16\mathrm{.}54,$ and $S(5)=16\mathrm{.}32?$

Explain the difference between the actual and the forecasted NPV$.$

$(8)$