Money in Motion (Simplified)

Money in Motion

Introduction

Jake Ngyuen, manager of Asian foreign investment for Grant Hill Associates, is set out to determine the best method to convert investment in Japan, Indonesia and Malaysia back to US safe bonds due to devaluation of these currencies.

Previous investments amounted to 1875 million Yen, 10.5 billion Indonesian rupiah, and 28 million Malaysian ringgit. Grant Hill, president of Grant Hill Associates, demand that Jake the said currencies as urgent as possible.

East Asian governments worsen the situation due to the imposed limits on the amounts of money that can be exchanged from the domestic currency into a particular foreign currency and withdraw t from the country. Transaction cost in converting the currencies are variable and remain the only financial cost presented.

Methodology

Linear programming was used to determine the minimal cost in transferring the three mentioned currencies back to US bonds. The transaction limits forces Jake to redirect the parts of the currencies to other currencies (Canadian Dollar, European Euro, English Pound, Mexican Peso) before converting to US Dollar.

LP model

Let Xij be the amount in i=1 for Yen, 2 for rupiah,3 for ringgit to be converted to j=1,2,3,4,5,6,7,8 (yen, rupiah, ringgit, US dollar, Canadian dollar, European euro, English pound, Mexican peso).

Let Cij be the direct unit transaction cost in percent of converting from currency i to j.

Let C’ij be the subsequent transaction cost to finally convert to US currency.

Cij i

1 2 3

j 1 0 0.5 0.5

2 0.5 0 0.7

3 0.5 0.7 0

4 0.4 0.5 0.7

5 0.4 0.3 0.7

6 0.4 0.3 0.4

7 0.25 0.75 0.45

8 0.5 0.75 0.5

Cij I

1 2 3

j 1 0.4 0.4 0.4

2 0.5 0.5 0.5

3 0.7 0.7 0.7

4 0 0 0

5 0.05 0.05 0.05

6 0.1 0.1 0.1

7 0.1 0.1 0.1

8 0.1 0.1 0.1

The objective function:

Min Z= ∑_(i=1)^3▒∑_(j=1)^8▒〖 (C_ij+〖C'〗_ij)*X_ij 〗

Constraints:

Total investments to change currency:

∑_(j=1)^8▒〖X_1j=15000000〗+X_21+X_31...