Problem 25 setting. A zero coupon note payable in 8 years is offered by Brown Brothers Box Company. The offering price of the note was set by the company to provide a rate of return equal to 8 percent per year compounded annually. Problem 25 questions. (a) Find the offering price of the note as a percentage of redemption value. Solution: The growth factor over the 8 years is the annual growth factor raised to the 8th power. Let A = redemption value. Let P = offer price. A = P*(1.08^8). So P/A = 1/1.08^8 = .540269 = 54%. (b) After 1 year investors would be willing to buy notes with a 7-year maturity which provided a rate of return equal to 7 percent per year compounded annually. If Audrey bought $10,000 of the Brown Brothers notes at the original price and sold them 1 year later, find her profit. (Corrected) solution: The posted solutions mistakenly take $10,000 to be the offer price. But a $10,000 note is a note with a redemption value of $10,000. So A = 10,000 P = A/1.08^8 = $5,402.69 Let Q = amount the investors pay. Q = A/1.07^7 = $6227.50 So the profit is Q - P = A*(1/1.07^7 - 1/1.08^8) = $10,000*( = $6227.50 - $5,402.69 = $824.81. (c) Find the rate of return to Audrey. Solution: The rate of return is the profit divided by the purchase price: (Q-P)/P = 824.81/5402.69 = .15266 = 15.266%. Problem 26. In the situation described in exercise 25, suppose that after 1 year interest rates have increased, and investors buying zero coupon notes with a 7-year maturity ask for return equivalent to 8.5 percent per year compounded annually. If Audrey bought $10,000 of the Brown Brothers notes at the original price and sold them 1 year later, does she have a profit or a loss? How much? Solution: Everything is the same as in problem 25, except that we should replace 1.07 with 1.085. Q-P = $10,000*(1/1.085^7 - 1/1.08^8) = $246.57; Since this number is positive, it represents a profit rather than a loss.