1. AcF 214 Tutorial Week 2 1

2. Question 1. Cost of plant: $100 million upfront Profits: $30 m. per year (at the end of every year) and are expected to last forever Cost of capital: 8% per year (a) Calculate the NPV. Should you go ahead with this investment? (b) What is the IRR for the investment? What is the maximum deviation allowable in the cost of capital estimate to leave the decision unchanged? 2

3. (a) NPV? Timeline: 01 234 8% –10030 NPV = –100 + 30/0.08 = $275 million. Yes, make the investment. 3

4. (b) IRR and maximum deviation in cost of capital that makes the decision unchanged? IRR: 0 = –100 + 30/IRR. IRR = 30/100 = 30% So, the cost of capital can be overestimated by 22% (30% - 8%) without changing the decision. 4

5. Question 2. Paid to write book: $10 million Earn per year if speaking: $8 million (paid at the end of the year) Cost of Capital: 10% per year 3-years to write the book (a) NPV? (b) Assume: Royalties $5 million in the first year and then royalties decrease at a rate of 30% per year in perpetuity. NPV? 5

6. (a) NPV? Timeline: 0 1 2 3 +10 - 8 - 8 - 8 6

7. (b) NPV? (consider royalties!!) Timeline: First calculate the PV of the royalties at year 3. The royalties are a declining perpetuity: +10 - 8 - 8 - 8 5 5*(1-0.3) 5*(1-0.3) 2 0 1 2 3 4 5 6 7

8. So the value today is: Now add this to the NPV from part (a): 8

9. Question 3. Duration of investment: 6 years Cost of investment: $200,000 / year Profits: $300,000 per year for 10 years Cost of Capital: 10% per year a)NPV? b)IRR? Maximum deviation in cost of capital that makes the decision unchanged? c)NPV @ r=14%? 9

10. (a) Timeline i. NPV? NPV>0, so the company should take the project. ii. IRR? Setting the NPV = 0 and solving for r (using a spreadsheet) the answer is IRR = 12.66%.Thus, the maximum deviation allowable in cost of capital estimate is 12.66-10=2.66%. 0123 6 7 16 10% -200,000 300,000 10

11. iii. The new timeline is: 0123 67 16 14% -200,000 300,000 11

12. Question 4. How many IRR in question 2(a)? Does IRR rule give the right answer? IRR is the r that solves: 0 1 2 3 +10 - 8 - 8 - 8 12

13. To determine how many solutions this equation has, plot the NPV as a function of r: 13

14.  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.  BUT this is a negative NPV project (from 2(a), so the IRR gives the wrong answer. 14

15. Question 4 - continued How many IRR in 2(b)? Does IRR rule work in this case? From 2(b) the NPV of these cash flows is : +10 - 8 - 8 - 8 5 5*(1-0.3) 5*(1-0.3) 2 0 1 2 3 4 5 6 15

16. Plotting the NPV as a function of the discount rate gives:  The plot shows that there are 2 IRRs : 7.165% and 41.568%.  The IRR gives multiple rates in this case, so it does not work. 16

17. Question 5. Investment A & B mutually exclusive A: -$10m at t=0, +$2m per year in perpetuity B: -$10m at t=0, +$1.5m at t=1, then revenues +2% per year (a) Higher IRR? (b) Higher NPV if r=7% (c) When does picking the higher IRR give the correct answer to which is the best investment ? 17

18. (a) Setting NPV A = 0 and solving for r: IRR A = 20% A: -10 +2 +2 +2 B: -10 +1.5 +1.5(1.02) +1.5(1.02) 2 0 1 2 3 18

19. Setting NPV B = 0 and solving for r: Based on the IRR you always pick project A!! 19

20. (b) NPV? Substituting r = 0.07 into the NPV formulas derived in part (a) gives: NPV A = $18.5714 million NPV B = $20 million So the NPV says take B!! 20

21. (c) Here is a plot of NPV of A & B as a function of the r: The NPV rule selects A (and so agrees with the IRR rule) for all discount rates to the right of the point where the curves cross. 21

22. So the IRR rule will give the correct answer for discount rates greater than 8%. 22