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# L1.T4.10. Time value of money

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
AIMs: Describe and contrast individual and market expressions of the time value of money. Define discount factor and use a discount function to compute present and future values. Define the “law of one price”, support it using an arbitrage argument, and describe how it can be applied to bond pricing.

Questions:

10.1. Three different U.S. Treasury notes pay semi-annual coupons and mature in exactly one year; i.e., each pays the next coupon in six months and matures six months subsequently. The price of Bond A with a coupon rate of 2.0% per annum is $99.02 and the price of Bond C with a coupon rate of 7.0% per annum is$103.91. If Bond B has a coupon rate of 4.0% per annum, what is the price of Bond B? (this is a variation on an actual previous exam question)
a. $99.12 b.$100.56
c. $100.98 d.$101.12

10.2. Assume that a U.S. Treasury bill will pay $1,000 in one year and the security is default free (there is absolutely no credit risk). The price of this bill today is given by P(0). Which of the following statements, according to Tuckman, is most true about individual versus market expressions of the theory of the time value of money? a. Rational, well-informed individuals are each willing to pay a DIFFERENT price, P(0); and therefore the market should exhibit various (DIFFERENT) fair prices for the security b. Rational, well-informed individuals should arrive at the SAME willingness-to-pay price, P(0); and therefore the market should reflect this (SAME) price upon which all participants agree c. Rational, well-informed individuals are each willing to pay a DIFFERENT price, P(0); but the market should reflect only one (SAME) fair price d. Rational, well-informed individuals should arrive at the SAME willingness-to-pay price, P(0); but the market should reflect various (DIFFERENT) prices 10.3. The first U.S. Treasury bond has a price of$99.98, matures in six months, and pays a semi-annual coupon at a rate of 3.0% per annum. The second U.S. Treasury bond has a price of $101.11, matures in one year, and pays a semi-annual coupon at a rate of 4.0% per annum. What are, respectively, the six-month and one-year discount factors? a. d(0.5) = 0.9790, d(1.0) = 0.9830 b. d(0.5) = 0.9850, d(1.0) = 0.9720 c. d(0.5) = 1.0020, d(1.0) = 0.9830 d. d(0.5) = 0.9650, d(1.0) = 1.0340 10.4. Assume the following discount function, which is a set of discount factors: d(0.5) = 0.990, d(1.0) = 0.970, d(1.5) = 0.960, d(2.0) = 0.950. A U.S. Treasury bond pays a semi-annual coupon at a rate of 5.0% per annum and matures with a face value of$1,000 in eighteen months (T = 1.5 years). What is the price of the bond?
a. $985.00 b.$1,002.00
c. $1,015.00 d.$1,033.00