1. AcF 214 Tutorial Week 3

2. Question 6.23 Use the incremental IRR rule to choose between projects A & B. Cost of capital 7%. To calculate the incremental IRR subtract A from B (i.e. A is the basic project and B-A is the incremental project): A: -10 +2 +2 +2 B: -10 +1.5 +1.5(1.02) +1.5(1.02) 2 0 1 2 3 B-A: 0 1.5 - 2 +1.5(1.02) -2 +1.5(1.02) 2 -2

3. Hence: So the incremental IRR for B-A is 8%. This rate is above the cost of capital so we should take B!! If r<8% take the incremental project B, otherwise take the basic project A.

4. A B

5. Question 6.32 5 projects - Resource Constraints (a) Capital Budget: $60 million. How to prioritise the projects? First, calculate Profitability Index: The PI rule selects projects V, III, II. (Total NPV = 60.2+22+19 = 101.2) These are also the optimal projects to undertake (as the budget is used up fully after selecting the projects according to PI). Proj.Initial Capital NPVPI = (NPV/Resource Consumed) I1010.110.1/10 = 1.01 II1519.019.0/15 = 1.27 III1522.022.0/15 = 1.47 IV2025.025.0/20 = 1.25 V3060.260.2/30 = 2.01

6. (b) Number of research scientists: 12 Firstly, calculate NPV per Headcount: The PI rule selects IV, II, III, and I. The total NPV of those 4 projects is 25+19+22+10.1 = $76.1 million. Proj.# of research scientists NPVNPV/Headcount I210.110.1/2 = 5.1 II319.019.0/3 = 6.3 III422.022.0/4 = 5.5 IV325.025.0/3 = 8.3 V1260.260.2/12 = 5.0

7. (b) Number of research scientists: 15 The PI rule still selects IV, II, III, and I. However, projects IV and V generate a total NPV of $85.2 million compared to the previous NPV of $76.1 million. Thus, choose IV and V. PI rule might not work when resources are not used fully. Proj.# of research scientists NPVNPV/Headcount I210.110.1/2 = 5.1 II319.019.0/3 = 6.3 III422.022.0/4 = 5.5 IV325.025.0/3 = 8.3 V1260.260.2/12 = 5.0

8. Question 7.10 Consider: Investment: $25m, Required Working Capital: $10m (constant between years 0 and 9), Overhead: $1m (a) Free cash flows: 012…910 = Net income4,875 + Overhead (after tax at 35%)650 + Depreciation2,500 – Capex25,000 – ΔNWC10,000–10000 FCF–35,0008,025 … 18,025

9. (b) NPV if the cost of capital equals 14%?

10. Question 7.23 (a) NPV in the base-case scenario: (b) Initial Sales 90 100110 change FCF/year -6.50.06.5 NPV20.5 57.394.0 (c) Growth Rate0%2%5% NPV57.372.598.1

11. (d) NPV is positive for discount rates below the IRR of 20.55%: