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 $9.8 million today and $4.8 million in one year. The government will pay you $21.5 million in one year upon the building's completion. Suppose the interest rate is 10.8%.

a. What is the NPV of this opportunity?

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

Answer 1

Part (a) NPV :
NPV means Net Present Value
NPV = PV of Cash Inflows - PV of Cash Outflows
If NPV > 0 , Project can be accepted
NPV = 0 , Indifference point. Project can be accepted/ Rejected.
NPV < 0 , Project will be rejected.

Present value factor = 1 / (1+r)^n

r - interest rate = 10.8 %

n- no. of the year of cash flows

Year of cash flows	Cash Flows	PVF @10.8 %	Disc Cash Flows
0	$    -9,800,000.00	1.0000	$    -9,800,000.00
1	$    -4,800,000.00	0.9025	$    -4,332,129.96
1	$   21,500,000.00	0.9025	$   19,404,332.13
NPV			$     5,272,202.17

NPV of this​ opportunity = $ 5.2722 million

Part (b)

Government will pay $ 21.5 million after one year

the present value of the $ 21.5 million at 10.8 % = $ 19.4043 million

Borrow $ 19.4043 million today at 10.8 % interest rate

out of this , $ 9.8 million will be invested today and $ 4.8 million required after one year

present value of $ 4.8 million at 10.8 % = $ 4.3321 million

Cash Today = $ 19.4043 million - $ 9.8 million - $ 4.3321 million =  $ 5.2722 million