When project probability is 14.98%, completing a project cost $5 million for 30

Question

When project probability is 14.98%, completing a project cost $5 million for 30 months worth doing it? Defend. When project probability is 14.98%, completing a project cost $5 million for 30 months worth doing it? Defend. When project probability is 14.98%, completing a project cost $5 million for 30 months worth doing it? Defend. When project probability is 14.98%, completing a project cost $5 million for 30 months worth doing it? Defend. When project probability is 14.98%, completing a project cost $5 million for 30 months worth doing it? Defend.

Explanation / Answer

The cost of the project is $5 million. The given profitability percentage is 14.98%. So, at the end of the project, the profit earned will be $5 x 14.98% = $0.749 million. However, this profit will be realized after 30 months. We can assume another 6 months for the processing of payment. The total payment will be cost plus return i.e. $5.749 million. So, a three years period will be required to realize this profit. We are not given the information regarding the opportunity cost of capital. We can assume it to be 10% as per the present situation in the US market. The present value of the payment received is calculated as:

PV = 5.749 / (1+0.1)^3 = $4.319 million

So, the Net Present Value (NPV) is $4.319 - $5 = - $0.68 million.

Note that the NPV being negative at a 10% opportunity cost of capital, the project is not worthy to consider. The sensitivity of opportunity cost of capital on the NPV is shown in the following table.

The table shows that it is nearly impossible to attain a positive NPV for this project as below 5% opportunity cost of capital is near to absurdity.

Cot of capital NPV ($ million) 5% -0.0338 6% -0.1730 7% -0.3071 8% -0.4363 9% -0.5607 10% -0.6807 11% -0.7964 12% -0.9080 13% -1.0157 14% -1.1196 15% -1.2199

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