Ec 1745 Fall 2008 Problem Set 1

Tarun Singh 1745 Problem Set 1 1. A) FV = 1000((1+r)4)t FV = 1000((1.02)4)3 = $1268.24 B) PV = 100/(r) PV = 100/.08 = $1250 The future value of the scenario in A is greater than the present value of the perpetuity in B. 2. A) PV = 10/(r) PV = 10/(.1) = $100 @ r=10% PV = 10/(.07) = $142.8 @ r=7% B) PV = D1 + (D/(r-g)) PV = (5/(.10-.04)) = $83.33 @ r=10% and g=4% PV = (5/(.07-.04)) = $166.67 @ r=7% and g=4% C) PV = (D/(r-g))(1-(((1+g)t)/((1+r)t)))+(D((1+g)t)/r)/((1+r)t) PV = (5/(.1-.2))(1-(((1.2)5)/((1.1)5)))+(5((1.2)5)/.1)/((1.1)5) = $104.51 @ r=10% and g=20% PV = (5/(.07-.2))(1-(((1.2)5)/((1.07)5)))+(5((1.2)5)/.07)/((1.07)5) = $156.50 @ r=7% and g=20% Thus stock C is more valuable when r=10% and stock B is more valuable when r=7% 3. $2000000 = C(1+r)t $2000000 = C(1.15)30 C = $30266.11 4. A) NPV = -100+75/(1+r)+50/((1+r)2)–50/((1+r)3)+75/((1+r)4)+50/((1+r)5) NPV = -100+75/(1.07)+50/((1.07)2)–50/((1.07)3)+75/((1.07)4)+50/((1.07)5) = $65.82 @ r=7% B) NPV = -100+75/(1+r)+50/((1+r)2)–50/((1+r)3)+75/((1+r)4)+50/((1+r)5)

r NPV in $ 7.00% 65.81695 5.00% 74.46716 10.00 % 54.21047 15.00 % 37.88909 20.00 % 24.54990 25.00 % 13.50400 30.00 % 4.24584 35.00 % -3.60092 40.00 -10.3201 % 0 45.00 -16.1285 % 0 50.00 -21.1934 % 0

The Internal Rate of Return is the interest rate at which the NPV=0. The graph and the table above show that the IRR is in between 30% and 35%, and the graph suggest that it is probably around 33%. Note: NPV for the different interest rates were calculated in Excel