Question

Harmony is a South African mining company that exports 20 ounces of gold to the US. Gold is priced in US dollars but Harmony’s workers are paid in rand (the currency in South Africa). The current price of gold is 1,777 dollars per ounce. The current exchange rate is 18.64 rand (R) per $1. Harmony’s current mining costs are R14 per ounce. Expected one-year inflation rates are 2 in the US and 5 in South Africa (in %).

If the exchange rate in one year is consistent with PPP, what is the gold price that would maintain Harmony’s profits constant in real terms? SHOW YOUR WORK.

Answer 1

Calculation of Profit per ounce:

1ounce = $1,777

1$ = 18.64 Rand

Selling price in Rand = $1,777x18.64

= 33,123.28 Rands

Cost of mining per ounce = (14) Rands

Profit per ounce = 33,109.28

Profit of 20 ounces = 33,109.28x20

= 662,185.60 Rands

Calculation of Exchange rate after one year using Purchasing power parity:

Inflation in US = 2%

Inflation in South africa = 5%

1$(1+r) = 18.64(1+r)

1(1.02) = 18.64 (1.05)

1$ = 18.64 (1.05)/(1.02)

1$ = 19.19 Rand

Calculation of Gold price to maintain Harmony's profits constant:

Gold Price = $1,777

Gold Price in Rand = 33,123.28 Rands

Exchange rate after 1 year

1$ = 19.19 Rand

Gold Price = 33,123.28/19.19

Price of Gold in Dollars = $1,726.07

Gold price should be $1,726.07 after one year to maintain Harmony's profits constant.