Question

The nominal annual risk-free rate is

2.2% in the U.S. and 3.5% in Brazil.
What should be the one-year forward
premium or discount according to interest rate parity?

Answer 1

The one-year forward premium or discount should be 1.3% according to interest rate parity.

Step-by-step explanation:

Interest rate parity is the theory that suggests the exchange rates between two countries will equalize based on the difference in interest rates between those countries. According to interest rate parity, the forward exchange rate should reflect the difference in interest rates.

In this case, the interest rate in the U.S. is 2.2% and in Brazil is 3.5%, resulting in a difference of 1.3%. Therefore, the one-year forward premium or discount should be 1.3%.

If the interest rate in Brazil is higher, the forward exchange rate will be at a premium.

Answer 2

Interest rate parity determines the forward premium or discount based on the interest rate differential between two countries. For bond valuation, the present value is calculated using the discount rate which adjusts when interest rates change, thereby affecting the bond's market value.

Step-by-step explanation:

To calculate the one-year forward premium or discount according to interest rate parity, we need to consider the nominal annual risk-free rate in the U.S. (2.2%) and Brazil (3.5%). The concept of interest rate parity suggests that the difference in interest rates between two countries will be equal to the differential between the forward exchange rate and the spot exchange rate for their currencies.

To determine the forward premium or discount, we use the following formula:
(Forward Exchange Rate - Spot Exchange Rate) / Spot Exchange Rate = Interest Rate Domestic - Interest Rate Foreign.
In this case, we would need additional information about the current spot exchange rate to finalize the calculation.

For the bond valuation, consider a two-year bond. The bond pays $240 of interest each year and returns the principal of $3,000 at the end of two years. The present value of the bond can be calculated using the discount rate that reflects its yield to maturity. At an 8% discount rate, the bond's present value is the sum of the present value of all future cash flows. The same calculation is then redone with an elevated discount rate of 11% due to a rise in interest rates, resulting in a decreased present value.

To calculate the present value (PV) of future cash flows, we use the formula:
PV = C/(1+r)^t, where C is the cash flow, r is the discount rate, and t is the time period.

For the first year's interest payment of $240 at an 8% discount rate:
PV = $240 / (1+0.08)^1 = $222.22. For the combined second year's interest and principal payment:
PV = ($240 + $3000) / (1+0.08)^2 = $2,777.78. Thus, the bond's present value is $3,000 when the discount rate is 8%. When the discount rate rises to 11%, the present values would be lower:

First year's interest payment at 11% discount rate:
PV = $240 / (1+0.11)^1 = $216.22. For the second year's payments at 11% discount rate:
PV = ($240 + $3000) / (1+0.11)^2 = $2,645.28. Thus, the bond's present value would decrease with the higher discount rate, reflecting the higher opportunity cost of capital.