L4 - Discounted Cash Flows

# L4 - Discounted Cash Flows - Financial Management Fall 2010...

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Financial Management Fall 2010 Lecture 4: Discounted Cash Flows (II) Professor Erica Li Ross School of Business

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Growing Annuities ! g = 5% 2 3 4 5 6 . 7 78390: 78390: 4 78390: .;3 # 2 3 4 5 6 . 322 32< 332=4< 322839<>: .;3 #?32>
3 Formulas for growing annuity ! @A" B,\$-0 %C !D \$/ .A" /*," */ .A*. %C *--E\$.+= ! !D %C F#%1\$-0 G--E\$.+ ? ! !D %C F#%1\$-0 !"#)".E\$.+ ? ! FV t = PV (1 + r ) t

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Value of a new drug ! Pharmaceutical company Pfizer has developed a new drug which is patented for the next 17 years. The profits will be 2 million for the first year and you estimate it will grow by 5% each year for the next 17 years. Once the patent expires, you expect profits to be zero because of competition. What is the PV of this product if the interest rate is 10% / year? ! This is a growing annuity with " g = " r= " C= " T= ! PV = \$21.86M
U.S. government debt ! U.S. government debt reaches 11.8T, 91% of GDP ! Government income = taxes: approx. 20% of GDP ! Assume GDP grow at 2% (-3.6% in 2009) and government saves 5% of its income per year (US government is currently having a deficit) for annual payments ! Allow the government infinitely many years to pay back the debt

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U.S. government debt ! Can US government avoid default on the debt? Assume that interest rate is 5% annually compounding.
APR vs. EAR ! APR: annual percentage rate is also called as the stated (or quoted) rate ! Frequency of compounding: how many times that the interest is compounded within a year, denoted as m # Monthly compounding: m = 12 # Quarterly compounding: m = 4 # Semiannual compounding: m = 2 # Annual compounding: m = 1 ! Period rate = APR/m ! EAR: effective annual rate = (1+ period rate) m -1 ! When does APR = EAR? m = 1 (annual compounding) 7

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8 APR vs. EAR ! L%E A*M" * /*M\$-0 *’’%E-.N .A" \$-."#"/. #*." \$/ \$- .A" *’’%E-. -%1= Q%1 ,E’A 1\$II +%E A*M" *. .A" " G--E*I )"#’"-.*0" #*." 8 G!R " "*#- \$- * +"*# ? 34=VW> Interest rate per month = 12% 12 = 1% Ending balance: \$1 " (1 + 1%) 12 = \$1.1268 EAR = 1.1268 # 1 = 12.68%
! The APR quoted on a Chase Credit card is 18%. Monthly payment is required. What is the EAR on this credit card? " m= 12

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L4 - Discounted Cash Flows - Financial Management Fall 2010...

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