Question

You run a construction firm. You have just won a contract to build a government office building. It will take one year to construct it requiring an investment of $ 10.23 million today and $ 5.00 million in one year. The government will pay you $ 22.50 million upon the​ building's completion. Suppose the cash flows and their times of payment are​ certain, and the​ risk-free interest rate is 8 %. a. What is the NPV of this​ opportunity? b. How can your firm turn this NPV into cash​ today?

Answer 1

All financials below are in $ mn.

Part (a)

NPV = - C₀ + C₁ / (1 + r) where

C₀ is the investment at t = 0 and is = 10.23,

C₁ is the net cash flow in year 1 = - 5 + 22.5 = 17.5

and r = discount rate = risk free rate = 8%

Hence, NPV = - 10.23 + 17.5 / (1 + 8%) =  5.97 = $ 5.97 mn

Part (b)

Any future cash flow can be converted into cash today by borrowing an amount equal to PV of the future cash flows. FUture inflow is $ 22.5 from the government. PV of 22.5 = 22.5 / 1.08 =  20.83

Hence,

The firm can borrow $ 20.83 mn today, and pay it back with 8% interest using the $ 22.5 mn  it will receive from the government. The firm can use $ 10.23 mn of the $ 20.83 mn to cover its costs today and save (PV of 5 = 5/1.08 =) $ 4.63 mn in the bank to earn 8% interest to cover its cost of $ 5mn next year. This leaves $ 5.97 mn (Same as NPV calculated above) in cash for the firm today.