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**Unformatted text preview: **Chapter 3: Asset Prices and Interest Rates • 3.1: Valuing Income Streams o Future value – value of a dollar today in terms of dollars at some future time. The future value of a dollar is how many dollars it can produce in some future year. $1 Today = $(1+ i) n ; if i= 6%, then $1 today in terms of 1 yr later = $(1 + .06) 1 o Present value – value of a future dollar in terms of today’s dollars. Shows how much a future dollar is worth today. $1 in ‘n’ years= $1/(1+i) n today ↑ interest rate (i) = ↓ PV B/C the saver can trade a dollar today for more future dollars(higher int. rates mean that in future it will be ↑ so its less ↓ now) o A Series of Payments Example 1: to find the PV of 2 different payments: $3 in 2 yrs, and $5 in 4 yrs, the PV is: – PV = $3/(1 + i) 2 + $5/(1 + i) 4 Example 2: to find the PV of a series of given payments continuing given years up to $X T , PV is: – PV = $X 1 /(1 + i) 1 + $X 2 /(1+i) 2 + … +$X T /(1 + i) T o Payments Forever Perpetuity – infinite income stream To calculate the PV of a perpetuity that doesn’t have a constant growth rate forever, PV: – PV = $Z/i $Z is just a variable, like $X ($Z is the initial payment) To calculate the PV of a perpetuity with a constant growth rate forever, PV: – PV = $Z/(i – g) • 3.2: The Classical Theory of Asset Prices o Classical theory of asset prices – the price of an asset equals the PV of expected income from the asset Asset Price = PV of asset (income) – PV of an asset tells us how much we’re willing to pay now – No one really knows the price of an asset (For Ex: stocks), but classical theory says the asset prices depend on people’s expectations/best guesses of asset income o Safe interest rate (i safe ) – interest rate that savers can receive for sure; also known as the risk free rate PV with i safe is: PV = $1/(1 + i safe ) o...

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