How does a prepayment reduce yield for a bank ?

Hi,

One of the rationales behind the imposition of prepayment penalties by banks is that they reduce the yield for the loan disbursed .i tried to analyse it ,but could not figure out how :

To start with ,assuming a loan of an amount $100 disbursed today @10% per compounding period ,for a total of 10 periods .The periodic payment will be $16.27 ,starting from the beginning of period 1 .The IRR is,obviously ,10% .

Suppose the loan is prepayed .The customer pays out the last period’s payment alongwith the second last one ,so that the cash flows look like this :

Time Period Cash Flows


0 -$100

1 $16.27

2 $16.27

3 $16.27

4 $16.27

5 $16.27

6 $16.27

7 $16.27

8 $16.27

9 $32.55

10 $0

The IRR of the above cash flow being 10.15% ,how does it reduce the yield for the bank ? Where am I wrong here ?

Any help will be appreciated .

You have to make an amortization table for this. Prepayment risk takes into effect that the customer will pay the loan off sooner and the bank may have to lend at a lower interest rate (ie income to them).

The example above doesn’t take into effect a amortization table aspect. You’ll see this in your quant studies/TVM for L1.

^Word. If you pay off the loan at time 9, then you won’t make two payments of $16.27. You’ll make one payment of 16.27, and another payment of something less than that.

Think of a more extreme example–if you took out a $100 loan from a bank today, then went back to the back tomorrow and said, “I want to pay off the loan”, how much would you pay? Would you pay $100 (plus one day’s worth of interest), or would you pay $162.70?

Obviously, you’d only owe the $100. Therefore, the bank gets nothing. Their yield on the loan has been reduced to zero.

It’s not a hard fast rule that a prepayment lowers the yield on a loan. Strictly speaking, the yeild should be what you expected for the life of the loan to date, with the only variations coming from the effect of any reinvested coupons, which is usually fairly small. If interest rates have risen in the interim, a bank might actually appreciate getting their money back and being able to lend it out again at higher interest rates.

However, prepayments are much more likely to happen when interest rates fall. So (as a bank) I used to have $100 of principal due and giving me coupons at 5% for the next 10 years, but the darned guy prepaid everything, so 1) I’m not getting those 5% coupons I was hoping to get, and 2) the next guy I lend to is going to be paying me 3% because interest rates have gotten lower since I made that first loan. So where I used to be getting $5 per year from now until the loan end, I’m now getting $3 per year, which is $2 per year less.

My yield on the original loan did not really change, but that loan doesn’t exist anymore and the new loans can’t get that yeild anymore. But as a bank, my revenue from interest has gone down, and I don’t like that, so I would like to charge a prepayment penalty to make up some of the difference.

The idea is that when interest rates rise, people will generally avoid prepaying unless there are reasons forcing them to, because they’d rather keep the lower interest rate. When interest rates fall, however, people will tend to prepay more often in order to refinance and take advantage of lower rates. Thus, for the bank, the probability of having to lend out at a lower interest rate after a prepayment is higher than the probability of being able to lend out at a higher one. So prepayments will *often* (though not always) result in lower returns for banks.

Depends on the rate of the loan vs the rate of the asset the payments will be placed into. If rates have declined, you don’t want prepayments. If rates rise, you would want them.

Prepayments behave inverse with rates, due to incentives to refinance. As rates decrease, prepay increase and vice versa. This introduces convexity in modeling financial assets.

And for bank specific concerns, you’d want to know how much the asset yield is funding relative to the cost of funding. So rates could fall, prepayments could happen, but your margin could increase. It’s rare, but just depends on the beta coefficients on the various asset accounts. You can do historical analysis with the Call Report and get some information on that

If you prepay, the bank doesn’t get all of the future interest.

Presumably, most people prepay when interest rates drop. So the bank was planning on 30 years of interest payments at 5%, but you prepaid, so they have to reinvest at 3%. That’s bad for them.