Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 1 Chapter 9 Simple Interest Section 4 Discounting a Note Before Maturity
Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 2 A Note A note is a legal responsibility for one individual or firm to pay a specific amount on a specific date to another individual or firm. Notes can be bought and sold just as an automobile can be bought and sold.
Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 3 Understand the Concept of Discounting a Note For example, a company that manufactures boats, a retailer that sells the boats, and a bank may do business as follows: 1. Boat manufacturer sells boats to a retailer, accepts a promissory note instead of cash. 2. Boat manufacturer needs cash and sells the note to a bank before it matures. 3. Retailer pays the maturity value of the note to the bank when due.
Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 4 Discounting a Note
Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 5 Discounting a Note Bank Discount – bank deducts fee from maturity value of the note when it buys it from the manufacturer. Discount Period – number of days bank will hold the note until it is due. Discount Rate – percent used by bank to find the discount. Discounting the Note – finding the value of the note on a specific date before it matures.
Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 6 Finding the Proceeds when Discounting Simple Interest Notes Proceeds – amount of cash actually received by the seller on the sale of a promissory note Recourse – bank receives reimbursement from the seller if the buyer does not pay the bank when the note matures (The bank is protected against loss.)
Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 7 Calculating the Proceeds When Discounting a Simple Interest Note 1.First, understand the simple interest note by finding: (a) the due date of the original note and (b) the maturity value of the original note (M = P + I, where I = PRT)
Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 8 Calculating the Proceeds When Discounting a Simple Interest Note 2.Then discount the simple interest note. (a) Find the discount period, which is the time (e.g., number of days) from the sale of the note to the maturity date of the note (b) Find the discount using the formula B = M × D × T = Maturity value × Discount rate × Discount period (c) Find the proceeds after discounting the original note using P = M – B
Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 9 Example Jameson Plumbing takes a simple interest, 180-day note from a contractor with a face value of $64,750 and a rate of 10.5%. The company sells the note to a bank 50 days later at a discount rate of 12%. Find the proceeds to the plumbing company.
Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 10 Example (cont) Step 1Find the maturity value. Face value equals proceeds, since this is a simple interest note. Maturity value = Principal + Interest on simple interest note = $64,750 + PRT = $64,750 + $64,750 ×.105 × 180/360 = $68,149.38
Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 11 Example (cont) Step 2The note is discounted after 50 days, so the discount period is 180 – 50 = 130 days. This means that the buyer of the note will own it for 130 days before the note is paid off.
Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 12 Example (cont) Use the formula B = MDT, M = $68,149.38, D =.12, T = 130/360 Bank Discount = MDT = $68, ×.12 × 130/360 = $ Proceeds = Maturity value of note – Bank discount = $68, – $ = $65,196.24
Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 13 Example (cont) So, the following occurs: 1. A contractor signs a 180-day simple interest note with a face value of $64,750 to Jameson Plumbing. 2. After 50 days, Jameson Plumbing sells the note to a bank and receives $65, in cash. 3. The bank receives $68, on the maturity date of the loan.
Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 14 Example Page 362: exc 18
Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 15 Calculate the Proceeds When Discounting a Simple Discount Note 1. First, understand the simple discount note by finding: (a) the due date of the original note, (b) the discount of the original note using B = MDT, and (c) the proceeds from the original note using P = M – B Maturity value (face value) of the note is written on the note itself (needed in step 2b).
Copyright © 2015, 2011, and 2007 Pearson Education, Inc Then discount the simple discount note. (a) Find the discount period, which is the time (e.g., number of days) from the sale of the note to maturity date of the note. (b)Find the discount using B = MDT. (c)Find the proceeds after discounting the original note using P = M – B. Calculate the Proceeds When Discounting a Simple Discount Note
Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 17 Example Benson Automotive used excess cash to purchase a $100,000 Treasury bill with a term of 26 weeks at a 6.5% simple discount rate. However, the firm needs cash exactly 8 weeks later and sells the T- bill. During the 8 weeks, market interest rates moved up slightly so that the bill was sold at a 7% discount rate. Find (a) the initial purchase price of the T-bill, (b) the proceeds received by the firm at the subsequent sale of the T-bill, and (c) the effective interest rate received by Benson Automotive.
Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 18 Example (cont) (a) Find the discount and proceeds. B = MDT B = $100,000 ×.065 × 26/52 = $3250 The cost to the company is the maturity value minus the discount. P = M – B P = $100,000 – $3250 = $96,750 The U.S. government receives $96,750 from the sale of the T-bill.
Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 19 Example (cont) (b) Find the discount period, discount, and proceeds. T-bill is sold 26 – 8 = 18 weeks before its due date, discount period is 18 weeks.
Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 20 Example (cont) The discount at the time of the sale is as follows. B = MDT B = $100,000 ×.07 × 18/52 = $ The proceeds equal the maturity value less the discount at the time of sale. P = M – B P = $100,000 – $ = $97,576.92
Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 21 Example (cont) (c) Benson Automotive paid $96,750 to buy the T-bill and received $97, for it 8 weeks later. Interest received = $97, – $96,750 = $826.92
Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 22 Example (cont) The company would have earned 6.5% on the T- bill had it left the Treasury bill invested until maturity. Instead, the company sold it after market interest rates rose, but before the T-bill matured. This caused the company to end up with an effective interest rate somewhat less than 6.5%.