1) Without taking into account the time value of money, the projects ranked according to the cash flow are as follows:
3 , 5 , 8 , 4 , 1 , 7 , 6 , 2
Based strictly on cash flow, the project that can generate the most excess cash over initial investments will be ranked first.
2) Criteria used are the no. of years that the investment amount was recovered and the discount rate.
There are several evaluation methods: Accounting Rate of Return A project is considered acceptable if it is expected to produce an average profit relative to the level of investment at a rate at least equal to the firm’s desired return on investment.
ARR = Average Profit / Initial Investment
Payback Method Measure of the expected time before the initial investment will be recovered. Accept the project if payback is faster than the targeted payback. This method ignores the time value of the cash flows and their riskiness.
Internal Rate of Return An investment project will be acceptable if IRR is greater than or equal to the required rate of return for that project. The higher the IRR, the better.
Present Value Index Known as “profitability index”. PVI was introduced for the purpose of ranking investment alternatives in the sense that it provides an indication of which alternative produces the highest return relative to the size of the investment. The highest PVI will be chosen.
PVI = PV of Inflows / PV of Outflows
Net Present Value NPV greater than or equal to zero indicates an acceptable project that at least earns the firm’s required rate of return. For ranking projects, the project with the highest NPV is preferred since it has the highest value. The 2 highlighted methods are better measures. They take into account the time value of money as well as the riskiness. 3) NPV Method & IRR Method
n CFt NPV = ?  t = 0 (1 + r)t
n CFt IRR: 0 = ?  t = 0 (1 + IRR)t
Refer to excel worksheet for detailed calculations. Both NPV and IRR give the same results.
Project 3 is preferred, as it has a higher NPV value (maximise shareholders’ wealth).
Rank by Cash Flow = 3, 5, 8, 4, 1, 7, 6, 2 Rank by NPV & IRR = 3, 4, 8, 7, 5, 1, 6, 2
4) It could be onetime construction project.
c) IRR Method
n CFt 0 = ?  t = 0 (1 + IRR)t
Investment A
10,000 25,000 25,000 380,000 0 =  170,000 +  +  +  +  (1 + IRR) (1 + IRR)2 (1 + IRR)3 (1 + IRR)4
IRR = 29.34%
Investment B
10,000 6,000 10,000 8,000 0 =  18,000 +  +  +  +  (1 + IRR) (1 + IRR)2 (1 + IRR)3 (1 + IRR)4
IRR = 32.01%
Choose Investment B, as it gives a higher internal rate of return.
d) Profitability Index
Present Value of Inflows PVI =  Present Value of Outflows
Investment A
10,000 25,000 25,000 380,000 PV of inflows =  +  +  +  (1.15) (1.15)2 (1.15)3 (1.15)4
= 261,303
261,303 PVI =  170,000
= 1.5371
Investment B
10,000 6,000 10,000 8,000 PV of inflows =  +  +  +  (1.15) (1.15)2 (1.15)3 (1.15)4
= 24,382
24,382 PVI =  18,000
= 1.3546
Choose investment A, as it provides a higher PVI (ie. higher return) than investment B. e)
• Ignore the payback method, as it does not take into account the time value of cashflows and their riskiness.
• Both the Profitability Index method and NPV method indicate that Investment A is superior to Investment B.
• The IRR for both investments exceed the required return of 15% and will result in positive NPV (maximises shareholders’ wealth).
• Conflicting recommendations occur because of the differences in the size of the investments. Always use the NPV rule when mutually exclusive projects differ in size (wealth has more value than IRR).
• Cashflow timing may also cause recommendations to differ. This occurs because of reinvestment rate assumption: 1) the IRR method assumes the future cash flows will earn the project’s IRR; 2) the NPV method assumes the future cash flows will earn the required return.
In equilibrium, required return = expected return. In the long run, reinvested cash flow can earn the cost of capital (the required return), but not the higher IRR, because the new idea or investment will be copied by every other player in the market (no longer gives positive NPV).
Therefore the NPV assumption that reinvestment rate = cost of capital is a better assumption.
CHOOSE INVESTMENT A
