Net Present Value-HELP

[Tallulah]

Here is the question that I am being asked..verbatum:

You run a construction firm. You have just won a contract to build a government office building. Building it will require an investment of $ 10 million today and $5 million in one year. The government will pay you $20 million in one year upon the building's completion (building is completed in one year). Suppose the cash flows and their times of paymant are certain; and the risk free interest rate is 10%. 1)Determine the PW of the investment.2) How could the firm turn this PW into cash today?

I figure that I have to use Net Present Value, but I dont understand how to use it. Here is my table:

A B
Year Cash Flow
0 ($10,000,000)
1 ($5,000,000) + $20,000,000

NPV = (10%,B2:B3) = $3,305,785.12


To answer the second question, I figure the firm could invest their money (approx. $13.3M) into anther high-interest bearing account (say 10%) before the start of the project that will pay out the interest at the time they need to upfront the first payment. This way the company will always have a small surplus of cash at the time of the payouts.

Year Interest Earned Total Cash amount Payment Total after payment
-1 - - - $13,300,000.00
0 $1,330,000.00 $14,630,000.00 ($10,000,000.00) $4,630,000.00
1 $463,000.00 $5,093,000.00 ($5,000,000.00) $93,000.00

 

[tkhunny]

Please check you usage of the NPV() function. It may not be doing what youthink it is doing.

\(\displaystyle 10000000 + \frac{15000000}{1.1} = 3636364 \ne 3305785\)

As you have used it, the 10 MM is discounted one year and the 15 MM TWO years!

 

[Denis]

Hmmm...can your problem not be as simple as:
Invest 10 million today; get back 15 million in 1 year.
??

 

[Tallulah]

Dennis:

I dont know. The professor will not provide any clairification except that the $10m payment is at year 0, $5mil payment and the $20mil are simultaneous at year 1. I am not sure whether I shoudl calculate the PW of the $5mil separatly or as $15mil. I am very confused. Plus, I am nto clear on how to turn the PW into cash at year 0 if the firm does not have any cash on hand without taking out a loan. Is there a way to do this?

 

[Denis]

Don't think any of use are "sure" either! Can't you get that "professor" fired? :shock:

All I can offer is this:
- assume the company needs to borrow the 10 million; so cost (10%) is 1 million
- so a year later, company nets 20-10-5-1 = 4 million

How is cash obtained now? By borrowing, I guess: offer the 4 million as guarantee...

 

[JeffM]

Here is the question that I am being asked..verbatum:

You run a construction firm. You have just won a contract to build a government office building. Building it will require an investment of $ 10 million today and $5 million in one year. The government will pay you $20 million in one year upon the building's completion (building is completed in one year). Suppose the cash flows and their times of paymant are certain; and the risk free interest rate is 10%. 1)Determine the PW of the investment.2) How could the firm turn this PW into cash today?

I figure that I have to use Net Present Value, but I dont understand how to use it. The basic idea of present value calculations is to get all cash flows discounted to their respective present values so they are equivalent and so can be added up. It is a way of turning apples, oranges, and pears all into apples. CONCEPTUALLY that is all there is to it.
Here is my table:

A B
Year Cash Flow
0 ($10,000,000)
1 ($5,000,000) + $20,000,000

NPV = (10%,B2:B3) = $3,305,785.12 This formula is wrong for THIS PROBLEM. It is calculating the value of 10 million disbursed in 1 year and 15 million received in 2 years. But you want the value of 10 million disbursed immediately and 15 million received in 1 year. You have to be careful with Excel formulas because they may not reflect what you want to do.
The general cash flow formula is P = C/(1 + i)[sup:3r67ymjm]n[/sup:3r67ymjm], where
P[sub:3r67ymjm]n[/sub:3r67ymjm] = present value of the cash flow received or disbursed at the end of period n,
C[sub:3r67ymjm]n[/sub:3r67ymjm] = the cash flow received or disbursed at the end of period n, and
i[sub:3r67ymjm]n[/sub:3r67ymjm] = the relevant interest rate for period n expressed as a decimal eg 10% = 0.1.
Note that n= 0 for things that happen immediately because there is NO number of periods to wait.
So, as tkhunny explained above, P[sub:3r67ymjm]0[/sub:3r67ymjm] = C[sub:3r67ymjm]0[/sub:3r67ymjm]/(1 + i[sub:3r67ymjm]n[/sub:3r67ymjm])[sup:3r67ymjm]0[/sup:3r67ymjm] = -10,000,000.00 / 1.1[sup:3r67ymjm]0[/sup:3r67ymjm] = -10,000,000.00, and
P[sub:3r67ymjm]1[/sub:3r67ymjm] = C[sub:3r67ymjm]2[/sub:3r67ymjm]/(1.1)[sup:3r67ymjm]1[/sup:3r67ymjm] = 15,000,000.00/1.1 = 13,636,363.64. Thus P[sub:3r67ymjm]0[/sub:3r67ymjm] + P[sub:3r67ymjm]1[/sub:3r67ymjm] = 3,636,363.64 as tkhunny said.

To answer the second question, I figure the firm could invest their money (approx. $13.3M) into anther high-interest bearing account (say 10%) before the start of the project that will pay out the interest at the time they need to upfront the first payment. This is wrong. First, to perform this project from its own cash, the company needs to spend 10,000,000 right now and another 5,000,000 in one year. So what is the present value of the money it needs; it is quite a bit more than 13.3. But you are right that they do not need 15 million. They need to put enough in a risk free investment to generate 5 million in 1 year plus 10 million now.

This way the company will always have a small surplus of cash at the time of the payouts. Well, your approach does not really give them any spare cash and probably the problem does not expect you to arrange for that, but that is good practical thinking. I suspect that what the problem wants as an answer is to sell the rights to the 20 million payment, presumably at a discount of 10%. I suspect that if you work out the present values on such a sale you will find that the firm gets the present value of its profit before it does the work. Needless to say, that is not a very practical scenario, but it seems like a good exercise.

Year Interest Earned Total Cash amount Payment Total after payment
-1 - - - $13,300,000.00
0 $1,330,000.00 $14,630,000.00 ($10,000,000.00) $4,630,000.00
1 $463,000.00 $5,093,000.00 ($5,000,000.00) $93,000.00

 

[Tallulah]

Thanks, Jeff for explaining NPV and going through the problem. I understand now how to approach the the problem.