# What are they doing under your mattress? – Randy Dong

“What are they doing under your mattress?”

“They work like cushions, you know. Support my back.”

“Jeez, you aren’t too smart, are you?”

Lock the concept of opportunity cost in your head, then you become a gamer in the Finance world at a whole new level. Opportunity cost has the simplest idea: if money isn’t helping you gaining the most wealth it can, it’s losing value.

“But my hundred-dollar bill is still gonna say a hundred tomorrow.” You might argue.

True. However, in a world of finite resources, your share of the “world” would be decreasing if others are using their bills to generate more bills and yours aren’t. So, you better pull them out of your mattress.

“You’re right. But there are so many options. I can buy bonds. I can put them into banks. I can purchase stocks. I might even start a business with what I have now.”

Good! You are thinking on the right direction. So you have all these options right now and you have at least a vague idea of what the costs and returns should be like. Only problem is: the costs and returns are spent and received at different times. How do we know which has the most value?

“Wait a minute. What do you mean by that? I know 200 is always more than 100.”

200 dollars today is always more than 100 dollars today. However, 200 dollars in ten years time may not worth as much as 100 dollars today, because maybe if you purchase the right bonds with the 100 dollars, after ten years, you may receive more than 200.

We need a way to compare how much the amount of money is worth in different years. The way to do it is a system called time value of money. With this system, we can translate what the dollar bills are worth in any year to what they are worth in any other year. The formula goes like this:

FV should be the year you want to compare the value of money at. PV doesn’t have to be the present year. It can be any year, but people are more accustomed to use present year value. Interest here isn’t just bank interest, bond coupon rate, or stock price. It is the highest possible value of return rate you can get through any means of business or financial activities. It doesn’t have to be an annual interest that you are most familiar with. It could be paid in any span of time. This is also the reason that N represents “period” here, a very unspecific term. It is related to the features of the particular interest rate. Note that the value of N could be negative. If you want to know how much your hundred dollar bill was worth back in 2008, simply put in -6 as N.

Let’s say Shike coffee starts to issue a bond today, looking to expand its business to George school. It has a face value of 100 dollars, a coupon rate at 8 percent, and it matures in 5 years. You want to know if you should buy the bond with the only 100 dollars you have free at hand. The only other means to make use of the money for you is putting it in a bank with an interest rate of 5 percent. We want to know the present value of the returns from the bond.

FV = 100×8%x(1+5%)^-1 +100×8%x(1+5%)^-2 + 100×8%x(1+5%)^-3 + 100×8%x(1+5%)^-4 + 100×8%x(1+5%)^-5 + 100x(1+5%)^-5 = 112.988 dollars

So what does this number mean? Why is it important?

Well, obviously it is easy to calculate how much you would own after five years. It is just the sum of the coupons and the return of the face value: 140 dollars. The 112.998 dollars represents the amount of money needed to put in the bank to have a return of 140 dollars in 5 years. (Wanna know the logic behind the calculation? Comment on the blog. But I think it’s a really nice problem for yourself to figure out.) And now you only have 100 dollars. So it is impossible to get a return of 140 dollars from the bank in 5 years, which tells you it is more prolific to purchase the Shike Coffee bond.

“Cool. That make sense. But we can simply calculate what the bank’s return in 5 years would be and compare that number to the bond’s return. Right?”

Absolutely. However, we always try to calculate the present value of returns because usually we face more than two financial opportunities and they all have different spans and periods. Therefore, we need a standard time to compare them: right now. In situations where you have multiple financial options, simply take the option you think will earn you the most return as the standard. It’s interest rate will be the i for your calculations. If the calculations show that all the other financial options has a lower present value, then your standard option is the most prolific one. If other options have higher present values, then the highest present value claims the most prolific.

“Simple right?”

“Yes! And according to my calculations, the best thing I should do is buying lottery!”

“Ayy… You are helpless aren’t you…”