Question

Grupo Bimbo​ (Mexico).  Grupo​ Bimbo, headquartered in Mexico​ City, is one of the largest bakery companies in the world. On January​ 1st, when the spot exchange rate isPs10.82/$​, the company borrows $24.8 million from a New York bank for one year at 6.84% interest​ (Mexican banks had quoted 9.64% for an equivalent loan in​ pesos). During that​ year, U.S. inflation is 2.4% and Mexican inflation is 4.6%. At the end of the year the firm repays the dollar loan.

a. If Bimbo expected the spot rate at the end of one year to be equal to purchasing power​ parity, what would be the cost to Bimbo of its dollar loan in​ peso-denominated interest?

b. What is the real interest cost​ (adjusted for​ inflation) to​ Bimbo, in​ peso-denominated terms, of borrowing the dollars for one​ year, again assuming purchasing power​ parity?

c. If the actual spot rate at the end of the year turned out to be Ps9.64/$​, what was the actual​ peso-denominated interest cost of the​ loan?

Answer 1

Solution:

Given that Borrowing Principal = $24,800,000

Current spot rate, pesos/dollar (Ps/$) = 10.82

Mexican inflation (actual) = 4.6%

U.S. dollar inflation (actual) = 2.4%

Actual spot rate end of year (Ps/$) = 9.64

a. Using Purchasing power parity, we have

Spot (PPP) = S*(1 + Mexican inflation)/(1 + U.S. dollar inflation)

Spot (PPP) = 10.82*(1.46)/(1.24)

Spot (PPP) = 12.73

We convert the borrowing principal in Mexican pesos at the spot rate of 10.80

24,800,000 x 10.82 = 268,336,000 Mexican pesos

Now, we find the value of borrowing principal at current spot rate

$24,800,000 x 1.0684= $26,496,320

Pesos needed to repay the loan = $26,496,320x 12.73 = 337,298,153.6

Hence, the implied cost is

(Repaid/initial proceeds) – 1

(337,298,153.6/268,336,000 ) – 1

25.69%

b)

Real peso-interest = Nominal interest – Actual inflation

Real peso-interest = 25.69% - 4.6%

Real peso-interest = 21.09%

c).

We convert the borrowing principal in Mexican pesos at the spot rate of 10.80

24,800,000 x 10.82 = 268,336,000 Mexican pesos

Pesos needed to repay the loan = $26,496,320 x 9.64 = 255,424,524.8

Hence, the implied cost is

(Repaid/initial proceeds) – 1

(255,424,524.8/268,336,000 ) – 1

-4.811%

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