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# BD_SM06 - Chapter 6 Investment Decision Rules 6-1 Timeline...

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Unformatted text preview: Chapter 6 Investment Decision Rules 6-1. Timeline: 1 2 3 4 100 30 30 30 1 30 NPV=-100=\$247.22 million 1.08 0.08 The IRR solves 1 30 100 r 24.16% 1 r r- = = + So, the cost of capital can be underestimated by 16.16% without changing the decision. 6-2. a. Timeline: 1 2 3 10 8 8 8 ( 29 3 8 1 NPV 10 1 \$9.895 million 0.1 1.1 =-- = - b. Timeline: 1 2 3 4 5 6 10 8 8 8 5 5(1 0.3) 5(1 - 03) 2 First calculate the PV of the royalties at year 3. The royalties are a declining perpetuity: ( 29 5 5 5 PV 12.5 million 0.1 0.3 0.4 = = =-- 52 Berk/DeMarzo Corporate Finance So the value today is ( 29 royalties 3 12.5 PV 9.391 1.1 = = Now add this to the NPV from part a), NPV 9.895 9.391 \$503,381 = - + = - . 6-3. a. Timeline: 1 2 3 6 7 16-200,000 -200,000 -200,000-200,000 300,000 300,000 i. ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 6 6 10 6 6 10 200,000 1 1 300,000 1 NPV=- 1- + 1- r r 1+r 1+r 1+r 200,000 1 1 300,000 1 =- 1- + 1- 0.1 0.1 1.1 1.1 1.1 =\$169,482 NPV&amp;gt;0, so the company should take the project. ii. Setting the NPV = 0 and solving for r (using a spreadsheet) the answer is IRR = 12.66%. So if the estimate is too low by 2.66%, the decision will change from accept to reject. iii. The new timeline is 1 2 3 N N+1 N+10-200,000 -200,000 -200,000-200,000 300,000 300,000 ( 29 ( 29 ( 29 N N 10 200,000 1 1 300,000 1 NPV=- 1- + 1- r r 1+r 1+r 1+r Setting the NPV = 0 and solving for N gives ( 29 ( 29 ( 29 10 10 300,000 500,000- 1+r log 200,000 1.5 log 2.5- 1.1 N= = =6.85 years log 1+r log 1.1 b. Chapter 6 Investment Decision Rules 53 i. Timeline: 1 2 3 6 7 16-200,000 -200,000 -200,000-200,000 300,000 300,000 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 6 6 10 6 6 10 200,000 1 1 300,000 1 NPV=- 1- + 1- r r 1+r 1+r 1+r 200,000 1 1 300,000 1 =- 1- + 1- 0.14 0.14 1.14 1.14 1.14 =-\$64.816 ii. Since the IRR still has not changed it is still 12.66%, so if the estimate is too high by 1.34%, the decision will change iii. Setting the NPV = 0 and solving for N gives: ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 6 6 N N N N 200,000 1 1 300,000 1 NPV=- 1- + 1- =0 .14 .14 1.14 1.14 1.14 1 =-777,733.5 + 976,256.9 1- =0 1.14 976,256.9 =198,523.4 = 1.14 4.9176 1.14 N log(1.14) log(4.9176) 0.131N 1.5928 N 12.16 years = = = = = 6-4. 5000 / 500 = 10 months....
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BD_SM06 - Chapter 6 Investment Decision Rules 6-1 Timeline...

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