BD_SM_c06

# BD_SM_c06 - Chapter 6 Investment Decision Rules 6-1...

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Chapter 6 Investment Decision Rules 6-1. Timeline: 0 1 2 3 4 –100 30 30 30 13 0 NPV= -100=\$247.22 million 1.08 0.08 ⎛⎞ ⎜⎟ ⎝⎠ The IRR solves 0 100 0 r 24.16% 1r r −= = + So, the cost of capital can be underestimated by 16.16% without changing the decision. 6-2. a. Timeline: 0 1 2 3 10 –8 –8 –8 () 3 81 NPV 10 1 \$9.895 million 0.1 1.1 =− = b. Timeline: 0 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: 5 55 PV 12.5 million 0.1 0.3 0.4 == = −−

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52 Berk/DeMarzo Corporate Finance So the value today is () 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: 0 1 2 3 6 7 16 -200,000 -200,000 -200,000 -200,000 300,000 300,000 i. 66 1 0 1 0 200,000 1 1 300,000 1 NPV=- 1- + 1- rr 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>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 0 1 2 3 N N+1 N+10 -200,000 -200,000 -200,000 -200,000 300,000 300,000 NN 1 0 200,000 1 1 300,000 1 NPV=- 1- + 1- 1+r 1+r 1+r Setting the NPV = 0 and solving for N gives 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
Chapter 6 Investment Decision Rules 53 b. i. Timeline: 0 1 2 3 6 7 16 -200,000 -200,000 -200,000 -200,000 300,000 300,000 () 66 1 0 1 0 200,000 1 1 300,000 1 NPV=- 1- + 1- rr 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: 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 = 0 1.14 4.9176 1.14 N log(1.14) log(4.9176) 0.131N 1.5928 N 12.16 years = = = = = 6-4. 10 months. 6-5. Timeline: 0 1 2 3 4 –100 30 30 30 13 0 NPV 100 \$247.22 million 1.08 0.08 =− = The IRR solves 0 100 0 r 24.16% 1r r −= = + Since the IRR exceeds the 8% discount rate the IRR gives the same answer as the NPV rule.

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54 Berk/DeMarzo Corporate Finance 6-6. Timeline: 0 1 2 3 10 –8 –8 –8 IRR is the r that solves () 3 81 NPV 0 10 1 r 1r == − + ⎛⎞ ⎜⎟ ⎝⎠ To determine how many solutions this equation has, plot the NPV as a function of r From the plot there is one IRR of 60.74% Since the IRR is much greater than the discount rate the IRR rule says write the book. Since this is a negative
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BD_SM_c06 - Chapter 6 Investment Decision Rules 6-1...

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