QUESTION 9 If $1 million face amount of commercial paper (270-day paper) is sold

Question

QUESTION 9

If $1 million face amount of commercial paper (270-day paper) is sold for $982,500, what is the simple rate of interest being paid? What is the compound annual rate? A financial manager may sell $1 million of six-month commercial paper for $950,000 or borrow $1 million for six months from a commercial bank for 10 percent annually and a 2 percent origination fee. Which set of terms is more expensive? Bank A offers the following terms for a $10 million loan: interest rate: 8 percent for one year on funds borrowed fess: 0.5 percent of the unused balance for the unused term of the loan Bank B offers the following terms for a $10 million loan: interest rate: 6.6 percent for one year on funds borrowed fees: 2 percent origination fee Which terms are better if the firm intends to borrow the $10 million for the entire year? If the firm plans to use the funds for only three months, which terms are better? A commercial bank offers you a $200,000 annual line of credit with the following terms: origination fee: $2,000 paid when the line is accepted fees" 1 percent on unused balance, paid at the end of the year interest rate: 9 percent What is the effective cost of the loan if you expect to borrow the entire $200,000 for the year? if you expect to borrow the $200,000 for only three months? Little Store buys inventory using trade credit. The terms are stated as 2/10, n30, but Little Store rides the credit and generally pays on the 40th day. Occasionally, payment is made as late as the 50th day. What is the approximate cost of the credit (a) if paid on time, (b) if paid on the 40th day, and (c) if paid on the 50th day? What is the compound cost of credit in each case? Why does the cost change? High Time's suppliers tend to offer generous terms of trade credit (2/30, n90), but High Time can also issue commercial paper, receive $0.978, and repay $1.00 at the end of 60 days. What are the compound interest rates offered by the two alternatives? What would be the impact if High Time's suppliers changed the terms to n30?

Explanation / Answer

Face value = $1mn = $1000,000 270 day paper Price = $982,500 Interest rate for a period of 270 days (life of commercial paper) = Face value/price -1 = 100,000/982,500 -1 = 1.78% This is the interest for a period of 270 days. Simple Interest rate for 365 days = 1.78*365/270 = 2.40% To calculate compound interest, we first calculate no. of periods in 1 year No. of 270 days period in 1 year = 365/270 Compound interest = (1+r)^period - 1 Here r = simple interest for specified period = 1.78% = 0.0178 Compound interest = (1+0.0178)^(365/270) - 1 = 0.0241 = 2.41% (Since commercial paper is 270 day paper which is very close to 1 year, compound interest is also very close to simple interest rate)

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