I have a question about callable bonds. I have read that when interest rates decrease, companies that issue these types of bonds will redeem them. But why would the issuer do that? Shouldn't they wait for the inflation that results from low interest rates to take affect and make the market value of the bond be worth less real money?
A bond is like a loan. The issuer receives money up front in exchange for a fixed set of payments. Let's think about how the issuer views the situation where the rates on similar bonds fall.
If prevailing rates suddenly become low, then the issuer can now take out a new "loan" with lower rates by issuing a new bond with lower coupons. So repurchasing (calling) the bond and issuing a new bond at a lower rate would be analogous to a homeowner refinancing their home when mortgage rates have fallen. Potentially a smart move.
Another way to think about this is that the payments from bonds are discounted using the yields on payments coming at that time. If prevailing interest rates fall, then those payments are being discounted less. In other words, the value of the payments becomes higher. Bonds become more valuable when prevailing interest rates fall. If a company has the option to call their bond, they can essentially buy their own bond for less than its market price. Smart move. At the end of the day, this is the computation that is done. If the bond is worth more than the amount you would have to pay to buy it and you don't think the situation will get even better in the future, then the you, the issuer, (or anyone with that call option) should buy it.
Your question about inflation has a few misconceptions in it. For one thing, if rates are lowered it is not automatically the case that inflation will result. Sometimes this happens, other times it does not. Macroeconomics theory is complex and unreliable, much more so than bond pricing theory. If there is inflation (other things equal), it will benefit borrowers because they pay back their obligations with money that is less valuable. Inflation expectations are built into discount rates and bond yields. Specifically, if inflation is expected, interest rates must rise and bonds will become less valuable. In this case calling your bond for a fixed price would be bad. But the situation you describe in which interest rates cause inflation expectations is nothing like an "all else equal" situation.
Essentially the reduction in interest rates has a first order effect of raising bond prices, which makes calling smart. Increased inflation expectation due to a drop in rate has at best a second order effect that reduces the amount by which bond prices rise. But they still rise, which is what determines whether it's good to call a bond or not.