Question

1. How many points must a lender charge for a 5 percent, 30-year note to achieve a yield of 6%? (Though the loan amount does not matter, assume a $100,000 loan for computations)  

A. Assume the borrower holds the note for the entire term

B. Assume the borrower holds the note for 5-years How does the prepayment assumption affect the lender’s yield?

2. You are offered a bullet loan of 250,000 at 6% for 36 months with 2 points. What is your expected financing cost expressed as an EAR assuming you make monthly interest only payments and repay the loan at month 36?

If you choose to make payments of $2000 per month, and then repay the balance at month 36, what will your expected financing costs (expressed as EAR) be?

Why are these different?

Answer 1

The lender charges points, i.e fees at the beginning of the loan . The borrower then has to pay a lower interest , so lower monthly payments.

Note that 1 point corresponds to 1% of the loan value

This problem requires the use of a financial calculator, I have used a BA 2 plus Texas Instruments calculator(financial calculator)

1) The borrower holds the note for the entre term,

Cpt PMT( Input N=360, I/YR=5, PV=-100000) = $536.82

Cpt PV(Input N=360, I/YR=6, PMT=536.82) = $ 89,537.35

This PV will be deducted from the note amount to find the mortgage/discount points.

So, $100,000- $89,537.35= $10,462.65

As points are calculated as a % of loan amount, it comes to 10.5%()

Early prepayment(5 yr)

Cpt PV(Input N=60, I/YR=6, PMT=536.82, FV=89537.35) = $ 95,846.72

This PV will be be deducted from the note amount to find the mortgage/discount points.

So, $100,000 -$95,846.72 = $ 4153.28

As points are calculated as a % of loan amount, it comes to 4.125%

The shorter the term of prepayment, the higher will be the yield to the lender, so as is observed the points charged by a lender is not as high as before as the lender is compensated with a higher yield.

2)Bullet loan- The payment is due at the end of the loan

Mentioned, 2 points which corresponds to 2% of the loan amount so 2% of 250,000= $5000

Cpt PMT(Input N=36, I/YR=6, PV=-250000, FV=250000)=$1250 , this is the EMI

CptI/YR(Input N=36, PMT=1250, PV=-245000 as 2 points given as fees to the lender, FV=250000)= 6.75

EFF(expected financing costs)=6.75+0.2%(points) = 6.95%

If I choose to pay $2000 a month then,

Cpt FV( Input I/YR=6, PV=-250000, PMT=2000) = $220,497.92

Cpt I/YR(Input N=36, PMT=2000, PV=-245000, FV=220497.92)= 6.78 as 5000 deducted as pointsl

Similarly,effective financing costs is 6.78%+0.2%=6.98% approximately 7%