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# Estimate interest rates, inflation adjustment, pure interest rate

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Part a)
You have been assigned to estimate the interest rates that your company may have to pay when borrowing money in the near future. The following information is available.

kPR = 2%
MR = 0.1% for a 1 year loan increasing by 0.1% for each additional year
LR = 0.05% for a 1 year loan increasing by 0.05% for each additional year
DR = 0 for a 1 year loan, 0.2% for a 2-year loan, increasing 0.1% for each additional year Expected Inflation Rates

Year 1 = 7%
Year 2 = 5%
Year 3 and thereafter = 3%

a. Calculate the inflation adjustment (INFL) for a 5-year loan.

b. Calculate the appropriate interest rate for a 5-year loan.

Part b)
Olde-Style Baking Inc. manufactures gourmet baking products, and needs to borrow money to get through a brief cash shortage. Sales have been slow over the last few months and lenders have decided that the firm is risky. The CFO has asked you to estimate the interest rate Olde-Style should expect to pay for a one-year loan. Assume a 4% default risk premium, and assume liquidity and maturity risk premiums are each 1%. Inflation is expected to be 3% over the next twelve months. Economists believe the pure interest rate is currently about 4%.

Part c)
BrandyWine Company just issued a two-year bond at 11%. Inflation is expected to be 2% next year and 3% the year after. BrandyWine estimates its default risk premium at about 1.8% and its maturity risk premium at about 1%. Because it's a relatively small and unknown firm, its liquidity risk premium is about 2% even on relatively short debt like this.

a. What is the average inflation rate over the two years?
b. What pure interest rate is implied by these assumptions?

Part d)
Calculate the annual nominal rate (APR) in the following situations.

a. You borrow \$1000 and repay \$1110 in one year.
b. You lend \$2,850 and are repaid \$3,324.24 in two years.
c. You lend \$920 and are repaid \$2,015.83 in five years with quarterly compounding.
d. You borrow \$20,500 and repay \$29,330.76 in three years with monthly compounding.

#### Solution Preview

Given that,
kPR = 2%
MR = 0.1% for a 1 year loan increasing by 0.1% for each additional year
LR = 0.05% for a 1 year loan increasing by 0.05% for each additional year
DR = 0 for a 1 year loan, 0.2% for a 2-year loan, increasing 0.1% for each additional year Expected Inflation Rates

Year 1 = 7%
Year 2 = 5%
Year 3 and thereafter = 3%

Inflation adjustment for 5 year loan is:
INFL=(7%+5%+3%+3%+3%)/5=4.2%
Appropriate interest rate for 5 year ...

#### Solution Summary

The expert estimates the interest rate, inflation adjustment and pure interest rates in the near future.

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