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# S6 - -= = = = =-m and therefore IRR 1 = x 1 – 1 = 10 and...

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H AAS S CHOOL OF B USINESS U NIVERSITY OF C ALIFORNIA AT BERKELEY UGBA 103 A VINASH V ERMA S OLUTION TO H OMEWORK 6 Consider the capital budgeting project mentioned on slide 16 of L3 (Lecture 3), where we are given that cash flows at t=0, at t=1, and at t=2 are C 0 = –\$10 million, C 1 = \$23 million, and C 2 = –\$13.2 million respectively. Slide 17 of L3 shows numerically and graphically that the two solutions for the internal rate of return (IRR) are 10% and 20%. These solutions can be worked out using the quadratic formula, as follows: Recall that by definition, IRR is given by: 1 2 0 2 0 (1 ) (1 ) C C C IRR IRR + + = + + Multiplying each term by 2 (1 ) IRR + , we get: 2 0 1 2 (1 ) (1 ) 0 C IRR C IRR C + + + + = Defining x ≡ (1+ IRR ), a C 0 , b C 1 , and c C 2 , we can express this equation in the standard form of a quadratic equation: 2 0 ax bx c + + = The two solutions to the quadratic equation are: 2 2 1 1 0 1 0 4 4 2 2 C C C C b b ac x a C - - - - = = Using the specific numbers for the three cash flows denominated in \$m, we get: 2 2 1 1 0 1 0 1.1 4 23 23 4*( 10)*( 13.2) 23 529 528 23 1 1.2 2 2*( 10) 20 20 C C C C x C - - - - - - ( - -

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Unformatted text preview: -= = = = =--m and therefore, IRR 1 = x 1 – 1 = 10%, and IRR 2 = x 2 – 1 = 20%. H OMEWORK Q UESTIONS : 1. Suppose we are given that C = –\$1 million; C 1 = \$6 million; and C 2 = –\$6.75 million. Work out the two solutions for the IRR. We are given that a = –1, b = 6, and c = –6.75. Therefore, b 2 – 4 ac = 9, and x 1 = 1.5, and x 2 = 4.5, which in turn leads to IRR 1 = 50%, and IRR 2 = 350%. These are shown in the graph below: 2. Suppose we are given that C = –\$20 million; C 1 = \$48 million; and C 2 = –\$28.4875 million. Work out the two solutions for the IRR. We are given that a = –20, b = 48, and c = –28.4875. Therefore, b 2 – 4 ac = 25, and x 1 = 1.075, and x 2 = 1.325, which in turn leads to IRR 1 = 7.5%, and IRR 2 = 32.5%. These are shown in the graph below: Solution to Homework 6 Solution to Homework 6...
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S6 - -= = = = =-m and therefore IRR 1 = x 1 – 1 = 10 and...

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