The Answer
Well obviously it should be less. This is why it's called a "discount rate." It tells us how much cheaper a future payment is in value. Let's work backwards to find out why.

Suppose you were given β 909,091 right now. You could use that to buy more buildings. And we know that buildings give us a Return on Investment of 10%. In 24 hours we would earn 10% of that amount, or β90,909.

909,091 + 90,909 = 1,000,000

So that's the answer. The amount we could get today, plus one day's return, equals the amount we could get tomorrow.

And to get that, I just divided interest instead of multiplying it.

100% (basic amount) + 10% (ROI) = 110% = 1.1

β1,000,000 / 1.1 = β909,091

And it's just that simple. Now we know not just that money is less tomorrow, but

*how much less* it is worth. 1 million tomorrow is worth 909k today.

Even Further in the Future
Based on that, how much is a million βucks worth in 2 days?

β1,000,000 / 1.1 / 1.1 = β826,446

And so on for as far in the future as you like. If you were getting paid

*every* day, you could just take the earnings each day in the future, use the

**discount rate** to find out what it's worth today, and add them up. This is called a

**"Discounted Cash Flow"**
Example: β1 million a day for 5 days (starting today) is worth how much right now? (Hint, not 5 million)

**Code:**

Day # Payment then Value Today

------+--------------+------------

Day 0: 1,000,000 909,091

Day 1: 1,000,000 826,446

Day 2: 1,000,000 751,315

Day 3: 1,000,000 683,013

Day 4: 1,000,000 620,921

----------

Total Value Today 3,790,786

That sum is often known as

**Present Value**, which means simply "what it's all worth right now."

Back to Raw MaterialsAs you might have guessed, we can do exactly this with our Timber Land. Because it's 120 days, I'm going to do it in an Excel spreadsheet rather than fill up this page with numbers. But it is done exactly in the style of that last example, with the number we found earlier of β25,000 per day.

**Code:**

Day # Payment then Value Today

------+--------------+------------

Day 1: 25,000 22,727.27

Day 2: 25,000 20,661.15

...

Day 120: 25,000 0.27

That's no typo. Receiving that money 4 months out is so unimportant today it's worth pennies. That's why interest is so powerful.

The sum, or Present Value, of all 120 days is β249,997 (If anyone is curious by the way, had we gone on earning forever it would have added up to a perfect β250,000.)

**But then I have to buy a new one!**True. But if money

*in* has to get discounted, then money

*out* can get discounted too.

Day 120: -210,000

Discounted: -210,000 / (1.1 ^ 120)

Value today = β2.27

That's right, 2 bucks. You spend just 2 bucks now, and earn 10% a day, by the time your Raw Materials Site runs out you will have all you need for a new one. And you're spending a lot more than β2.27 now, so that replacement will be like nothing.

Value of the DealTo be complete in our analysis, we should consider what we pay now and subtract that from the sum.

Cost to buy = β210,000

Present Value of Earnings = β249,997

Value of the Deal = β249,997 - 210,000 = β39,997

If that doesn't seem like a lot, remember that you have

*already earned a full return on your money*. That's not β40k on your investment. That's 40k in your pocket right now because you were smart enough to make this deal. You make millions on your investment, and discounting factored it out.

Even if the value of a deal is zero, it's still a good place for your money because you earn the full ROI. Only a negative number is a bad thing. (For example, investing β300k for a Present Value of β250k would not be smart.)

**And if we expand?**To calculate it expanded is the same thing. Now the cost is twice as much, the earnings per day are twice as much, and the time is half (60 days). This time I will include the investment:

**Code:**

Day # Payment then Value Today

------+--------------+------------

Day 0: -210,000 -210,000.00 (Initial purchase)

Day 0: -160,000 -160,000.00 (Full Expansion)

Day 1: 50,000 45,454.55

Day 2: 50,000 41,322.31

...

Day 60: 50,000 164.21

-----------------------------------

Value of the Deal = 128,357.90

Not only is it still positive, it's bigger! Even though your investment seems to "run out" faster, getting that money faster is worth

*more* than what you spend.

And expanding twice gives Value = β128,357.90 even though you run out in 40 days.

Conclusion
We get spoiled with the idea that you buy a building once and it lasts forever. And it may seem surprising that profit is good on something that runs out. But you also know that your company 4 months from now will be huge compared to its size today. Even one month out you're big enough not to worry about it. And that's basically why a replacement cost in the future should not talk you out of a good deal today.

Not only can buying a Raw Materials land be profitable, but expanding it is

*even better*.