Question

You run a construction firm. You have just won a contract to build a government office complex. Building it will require an investment of $10.4 million today and $5.3 million in one year. The government will pay you $20.3 million in one year upon the​ building's completion. Suppose the interest rate is 10.2%.

a. What is the NPV of this​ opportunity?

b. How can your firm turn this NPV into cash​ today?

Answer 1

- Cash outflow in year 0(COF0) = $10.4 million

- Cash outflow in year 1(COF1) = $5.3 million

- Cash inflow in year 1(CIF1) = $20.3 million

Calculating the NPV of this opportunity:-

NPV = $18.421 million - [$10.4 million + $4.809 million]

NPV = $3.212 million

b). You Can Convert the NPV into cash today in the following way:-

First, Take a loan from Bank @10.2% Interest rate such that the amount to be paid in year 1 is $20.3 million which is equal to the amount to be receiived from bank.

The amount of loan = $20.3 million/(1+0.102)^1 = $18.421 million

- Now, use $10.4 million from the loan to pay for the Initial Investment

Amount left = $18.421 million - $10.4 million = $8.021 million

- Now, Invest an appropriate amount in bank at Interest rate of 10.2% such that the accumulated value along with interest will able to pay $5.3 million in year end 1

The amount of Investment = $5.3 million/(1+0.102)^1 = $4.809 million

Amount Left after Investmet = $8.021 million - $4.809 million = $3.212 million

Thus, You get NPV today in Cash

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