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# Calculating NPV & IRR of cash flows associated with Project

1.Consider a project with the expected cash flows:

Year Cash flow
0 - \$615,000
1 + 141,000
2 + 300,000
3 + \$300,000

What is this project's internal rate of return?
If the discount rate is 0%, what is this project's net present value?
If the discount rate is 4%, what is this project's net present value?
If the discount rate is 8%, what is this project's net present value?
If the discount rate is 12%, what is this project's net present value?

2. If you drew a chart with the discount rate (X axis)and the net present value (y axis, and you plotted the net present value of the project as a function of the discount rate by dots for the four discount rates, what is this discount rate at which the graph intersects the horizontal axis?
What would this graph mean to me?

3. A project requiring a \$3.2 million investment has a profitability index of 0.97. What is its net present value? (Remember: Profitability Index is defined as Present Value of the proceeds divided by the initial investment)

Which method do you think is the better one for making capital budgeting decisions - IRR or NPV? what would the determing factors be?

#### Solution Preview

Please see the attached file for complete solution. Graph and tables may not print here.

Solution :
Present Value = Future Value*(1+r)^-n
r is rate of discount (like 0.06 for 6%)
n is number of period
By applying this formula we can get present value of any cash flow at r rate of interest and n period.

We will calculate Present Value of Each Cash flow for different Rates of discount with the help of above formula
Net present Value is sum of present Values of all cash flows at a particular discount rate.

Present Values at Discount Rate
Cash Flow 0% 4% 8% 12%
0 -615,000 -615000 -615000 -615000 -615000
1 141,000 141000 135577 130556 125893
2 300,000 300000 277367 257202 239158
3 300,000 300000 266699 238150 213534
Net Present Value 126000 64643 10907 -36415

From above table we get
If the discount rate is 0%, project's net present value is \$126,000
If the discount rate is 4%, project's net present value is \$64,643
If the discount rate is 8%, project's net present value is \$10907
If the discount rate is 12%, ...

#### Solution Summary

Solution describes the steps in calculating NPV of cash flows associated with a given project at variuos discout rates. Concept of IRR is explained with the help of graph. At last it which method of project evaluation is better.

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