Question

BMW is taking on new project and came up with the following projected cash flows. Compute a) Profitability Index b) NPV c) IRR for the project. Use a discount rate of 10%. Discuss the results by explaining what each of the methods mean and your decision on going forward with the project.

Year	Cash flow ($)
0	(850,000)
1	350,000
2	350,000
3	250,000
4	200,000
5	200,000

Answer 1

First let us find out the present values of cash outflows and cash inflows:

Cash flows Discount Factor @ 10% Cash flows Discounted at 10 % Year (850,000) (850,000.00) 1 (850,000.00 Present Value Total Cash Outflows Cash flows Discount Factor @ 10% Cash flows Discounted at 10 % Year 1 350,000 0.90909 318,181.82 350,000 2 0.82645 289,256.20 250,000 0.75131 3 187,828.70 4 200,000 0.68301 136,602.69 5 200,000 0.62092 124,184.26 Present Value of Total Cash inflows 1,056,053.67

Now that we have present value of cash outflows and inflows, let us find the (a) Profitability Index (PI)

$Profitability~Index= \frac{Present~Value~of~Total~Cash~inflows}{Present~Value~Total~Cash~outflows}$

$= \frac{1,056,053.67}{850,000}$

b) Net Present Value (NPV):

Present Value of Total Cash inflows Net Present Value Present Value of Total Cash outflows

c) Internal Rate of Return (IRR):

We can use trial and error method here, we have to select 2 discount rates where, when discounted one should show greater than cash outflow and other should show less than cash inflow. We cannot use 10% here because it is too far from 850,000 which can give you errors.

Here we have taken 20% and 22%

Cash flows Cash flows Discount Factor Cash flows Discount Factor @ 20% Discounted at 20% Discounted at 22% Year @ 22% 0.83333 286,885.25 350,000 291,666.67 0.81967 2 350,000 0.69444 243,055.56 0.67186 235,151.84 250,000 0.57870 144,675.93 0.55071 137,676.72 4 200,000 0.48225 96,450.62 0.45140 90,279.82 0.37000 0.40188 5 200,000 80,375.51 73,999.85 Present Value of Total Cash inflows 856,224.28 823,993.48

$IRR=20 + \left [ \frac{856224.28-850000}{856224.28-823993.48} \right ]*(22-20)$

Answer Meaning It is used for ranking the projects. When profitability index is above 1, it signals to accept the project. In our problem Pl is 1.24, it means for every one dollar you invest in the project you will get $0.24 a) Profitability Index 1.24 In our problem we have used 10% discount rate to discount the cash flows. This 10% may mean opportunity cost, risk free return, or expected return. Suppose 206053.67 that 10% is our expected return then an NPV above "O" means it gives over and above the expected return. In our case the project must be accepted because it gives $206,503.67 above the expected return. b) NPV It is the rate at which NPV becomes zero. That means if we discount the cash inflows with IRR i.e 20.39 % then NPV will become zero. It is the actual rate of return given by the project c) IRR 20.39%