Consider the project with the following expected cash flows: Year Cash flow 0 -

Question

Consider the project with the following expected cash flows:
Year Cash flow
0 - $400,000
1 $100,000
2 $120,000
3 $850,000
• If the discount rate is 0%, what is the project's net present value?
• If the discount rate is 2%, what is the project's net present value?
• If the discount rate is 6%, what is the project's net present value?
• If the discount rate is 11%, what is the project's net present value?
• What is this project's modified internal rate of return?
Now draw (for yourself) a chart where the discount rate is on the horizontal axis (the "x" axis) and the net present value on the vertical axis (the Y axis). Plot the net present value of the project as a function of the discount rate by dots for the four discount rates. Connect the four points using a free hand 'smooth' curve. The curve intersects the horizontal line at a particular discount rate. What is this discount rate at which the graph intersects the horizontal axis?

Explanation / Answer

NPV = -400,000 + 100,000/(1+d) + 120,000(1+d)2 + 850,000/(1+d)3

where d = discount rate

d NPV

0% 680,000

2% 614,353

6% 514,816

11% 408,997

MIRR = ( FV of positive cash flow @ cost of capital / Initial investment )1/n-1

Assume using cost of capital of 11%

MIRR = { ( 100,000*1.112+120,000*1.1+850,000 ) / 400,000 } 1/3-1= 40.32%

The curve intersects the horizontal line at a particular discount rate.

What is this discount rate at which the graph intersects the horizontal axis?

--> This is IRR which is approximately 45.7% from the curve.

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