Prob Set 2.8 6. (7 points) There is a commercial bank whose only assets are a lo

Question

Prob Set 2.8

6. (7 points) There is a commercial bank whose only assets are a loan portfolio of $100 million of30-year fixed-rate mortgages(with monthly payments), and whose only liability is a single, $90 million 1-year certificate of deposit (CD),interest payable annually. The current value of the bank is therefore $10m ($100m in Assets - $90m in Liabilities). The 30-year mortgages have an average annual fixed interest rate of 5.60%, and the CD has an interest rate of 3.20%. Show all work.

Now assume that after one year, instead of rising, interest rates have fallen by 2.0%, and short-term interest rates for 1-year CDs decrease to 1.2%. Repeat parts b and c above and label those answers h and i (assume that TA =$100m).

((Part B + C=

b. Calculate the annual interest expenseon the CD (Liability Amount x Interest Rate), and the Annual Net Interest Income(NII) for the Bank (NII = Annual Interest Income – Annual Interest Expense).  

c. Calculate the Return on Total Assets (ROA) for the bank (NII / TA), assuming that Total Assets (TA) = $100 million (book value))

Assume now that the bank uses PV, market-based accounting to value its loan portfolio, and 30-year mortgage rates have also fallen by 2.0%, to 3.60%.

j. Calculate the new PV of the bank’s mortgage portfolio, assuming 29 years to maturity, a market interest rate of 3.50% for mortgages, and no change in the bank’s monthly mortgage payments from part a above.  

k. Calculate the new value of the bank, assuming the new PV of the loan portfolio from part j, and assuming the liabilities remain at $90 million.

l. The bank is exposed to interest rate risk. Explain why in a full essay. Identify the source of interest rate risk and refer specifically to your numerical answers above.

m. In part k above, you results should have indicated that the value of the bank increased significantly, at least theoretically. In reality, explain in an essay why the value of the bank would not necessarily increase when interest rates decrease. (Think about what typically happens when mortgage interest rates fall.)

Explanation / Answer

Part B -

Annual interest Expense on CD = $ 90 Mn x 3.20% = $ 2.88 Mn

Interest earned on Mortgage Loan portfolio = $ 100 Mn x 5.60% = $ 5.60 Mn

NII = 5.60 - 2.88 = $ 2.72 Mn

C) ROA = NII/TA = 2.72 / 100 = 2.72% per annum

Therefore Return on Total Assets is 2.72% p.a

After falling of Interest rates by 2% -

H) Annual interest Expense on CD = $ 90 Mn x 1.20% = $ 1.08 Mn

It is assumed that Mortgage interest is also fallen by 2%

Interest earned on Mortgage Loan portfolio = $ 100 Mn x 3.60% = $ 3.60 Mn

NII = 3.60 - 1.08= $ 2.52 Mn

I) ROA = NII/TA = 2.52 / 100 = 2.52% per annum

Therefore Return on Total Assets is 2.52% p.a

J) - PV of Mortgage can be caluculated using following formula -

PV = P (1 - (1 +r) ^ -n)r

Since the monhtly pyaments of Mortgage of part a is missing, it would be difficult to calculate the PV, however, it can be calculated using above formula.

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