Answer to Question #226727 in Financial Math for Nick

Question

Ghana’s inflation is forecasted to be 10.2% over the coming year whilst that of South Africa is forecasted to be 6.5%. The current exchange rate between Ghana Cedi and the South African Rand is 0.32 ZAR per 1 GHS. a) How should we quote the exchange rate between Ghana Cedi and the South African Rand (ZAR) in a year’s time to avoid arbitrage? (5 marks) b) A Ghanaian company is importing goods worth ZAR 20m in a year’s time, how much GHS will the company require to import the goods? (5 marks) c) If the actual rate at the end of the year is 0.35 ZAR per 1GHS, what is the absolute forecast error for the forecast in (a)? (5 marks)

Answer 1

a)

$forward\space rate = spot\space rate\times\frac{1+inflation\space in\space ghana }{ 1+inflation in South africa}$

$= 0.32\times \frac{1+10.2\%}{1+6.5\%}$

= 0.33 ZAR per 1 GHS(rounded to two decimals)

b)

$GHS\space require = \frac{20\space million }{0.32}$

= 62.5 million GHS (rounded to two decimals)

c)

when actual rate = 0.35

$GHS\space required = \frac{20million}{ 0.35}$

= 57.14million

$absolute\space fore\space cast\space error (in\space percentage) = \frac{actual\space value - expected\space value}{ actual\space value}$

= (57.14 - 60.61) / 57.14

= 6.06%(rounded to two decimals)