Balance Sheet Structure

Solutions for End-of-Chapter Questions and Problems: Chapter Seven

1. A financial institution has the following balance sheet structure:

         Assets                                                                 Liabilities and Equity

         Cash                                      $2,000                  Certificate of Deposit                  $10,000

         Bond                                   $10,000                  Equity                                            $2,000

         Total Assets                        $12,000                  Total Liabilities and Equity         $12,000

         The bond has a ten-year maturity and a fixed-rate coupon of 10 percent.  The certificate of deposit has a one-year maturity and a 6 percent fixed rate of interest.  The FI expects no additional asset growth.

1. What will be the net interest income (NII) at the end of the first year?  Note: Net interest income equals interest income minus interest expense.

               Interest income                                 $1,000            $10,000 x 0.10

               Interest expense                                     600            $10,000 x 0.06

               Net interest income (NII)                  $400

1. If at the end of year 1, market interest rates have increased 100 basis points (1 percent), what will be the net interest income for the second year?  Is the change in NII caused by reinvestment risk or refinancing risk?

               Interest income                                 $1,000            $10,000 x 0.10

               Interest expense                                     700            $10,000 x 0.07

               Net interest income (NII)                  $300

         The decrease in net interest income is caused by the increase in financing cost without a corresponding increase in the earnings rate.  Thus, the change in NII is caused by refinancing risk.  The increase in market interest rates does not affect the interest income because the bond has a fixed-rate coupon for ten years.  Note: this answer makes no assumption about reinvesting the first year’s interest income at the new higher rate.

1. Assuming that market interest rates increase 1 percent, the bond will have a value of $9,446 at the end of year 1.  What will be the market value of the equity for the bank?  (Remember after one year, there are 9 years left; find price of bond with PMT = 1000, N = 9, FV = 10,000, R (interest rate) = 11%; find PV = $9,446.30;  we are looking at a “Eurobond” since coupon paid annually.)  (If the bond were semi-annual coupon paying, the bond price would be $9447.70.)  (Note: the market value of the bond falls when interest rates rise.)  Assume that all of the NII in part (a) is used to cover operating expenses or is distributed as dividends because the bank expects no additional asset growth.

               Cash                                      $2,000               Certificate of deposit          $10,000

               Bond                                     $9,446               Equity                                  $ 1,446

               Total assets                         $11,446               Total liabilities and equity  $11,446

Note: market value of equity falls to $1,446 due to lower market value of the bond

How do we know that bond price will be $9,446? If the coupon rate is 10%, yield to maturity = 11%, then using our financial calculator, N = 18 (only 9 years left), PMT = 50, I = 5.5%, FV = 10,000. Compute PV; find PV = -9437.70

1. If market interest rates had decreased 100 basis points by the end of year 1, would the market value of equity be higher or lower than $1,000?  Why?

         The market value of the equity would be higher ($2,600) because the value of the bond would be higher ($10,600) and the value of the CD would remain unchanged.

(Note: if you rounded to the nearest cent, instead of to the nearest dollar, the new market value of equity would be $599.52; that answer also is considered correct.)

1. What factors have caused the change in operating performance and market value for this firm?

(By operating performance I mean what caused the change in net interest income, look at parts a. and b.; by market value, I mean what caused the change in market value in parts c. and d.)

For descriptions of refinancing and reinvestment risk, look at practice discussion problems 2 and 3.

       The operating performance has been affected by the changes in the market interest rates that have caused the corresponding changes in interest income, interest expense, and net interest income.  These specific changes have occurred because of the unique maturities of the fixed-rate assets and fixed-rate liabilities.  Similarly, the economic market value of the firm has changed because of the effect of the changing rates on the market value of the bond.

Question #2 was not assigned; it is just being shown here to contrast with #3.

2. Two ten-year bonds are being considered for an investment that may have to be liquidated before the maturity of the bonds. The first bond is a ten-year premium bond with a coupon rate higher than its required rate of return, and the second bond is a zero-coupon bond that pays only a lump-sum payment after ten years with no interest over its life.  Which bond would have more interest rate risk?  That is, which bond’s price would change by a larger amount for a given change in interest rates?  Explain your answer.

The zero-coupon bond would have more interest rate risk.  Because the entire cash flow is not received until the bond matures, the entire cash flow is exposed to interest rate changes over the entire life of the bond.  The cash flows of the coupon-paying bond are returned with periodic regularity, thus allowing less exposure to interest rate changes.  In effect, some of the cash flows may be received before interest rates change.

3. Consider again the two bonds in problem (2). If the investment goal is to leave the assets untouched until maturity, such as for a child’s education or for one’s retirement, which of the two bonds has more interest rate risk?  What is the source of this risk?

In this situation the coupon-paying bond has more interest rate risk.  The zero-coupon bond will generate exactly the expected return at the time of purchase because no interim cash flows will be realized.  Thus the zero has no reinvestment risk.  The coupon-paying bond faces reinvestment risk each time a coupon payment is received.  The results of reinvestment will be beneficial if interest rates rise, but decreases in interest rate will cause the realized return to be less than the expected return.

Below are answers to some text book problems that were not assigned:

27. Six months ago, Qualitybank, LTD., issued a $100 million, one-year maturity CD denominated in German deutsche marks (Euromark CD). On the same date, $60 million was invested in a DM-denominated loan and $40 million was invested in a U.S. Treasury bill.  The exchange rate six months ago was DM1.7382/$.  Assume no repayment of principal, and an exchange rate today of DM1.3905/$. ($/DM was $.57 & now $.72). (Ignore interest)

1. What is the current value of the Euromark CD principal (in DM and dollars)?

         Today's principal value on the Euromark CD is DM173.82 and $125m (173.82/1.3905).

1. What is the current value of the German loan principal (in DM and dollars)?

         Today's principal value on the loan is DM104.292 ($60MM x 1.7382) and $75 (104.292/1.3905).

1. What is the current value of the U.S. Treasury bill (in dollars and DM)?

         Today's principal value on the U.S. Treasury bill is $40m and DM55.62 (40 x 1.3905),        although for a U.S. bank this does not change in value.

1. What is Qualitybank’s profit/loss from this transaction (in dollars and DM)?

         Qualitybank's loss is $10m or DM13.908.

Solution matrix for problem 27:

At Issue Date:

Dollar Transaction Values (in millions)          D-Marks Transaction Values (in millions)

German                 Euromark                          German                             Euromark                   

Loan          $60      CD                 $100            Loan           DM104.292   CD             DM173.82

U.S T-bill  $40                                                U.S. T-bill    DM69.528

                $100                            $100                                  DM173.82                      DM173.82

Today:

Dollar Transaction Values (in millions)          DM Transaction Values (in millions)

German                 Euromark                          German                             Euromark

Loan          $75      CD                 $125            Loan           DM104.292   CD             DM173.82

U.S. T-bill $40                                                U.S. T-bill    DM55.620

                $115                            $125                                DM159.912                      DM173.82

28. Suppose you purchase a 10-year, AAA-rated Swiss bond for par that is paying an annual coupon of 8 percent. The bond has a face value of 1,000 Swiss francs (SF).  The spot rate at the time of purchase is SF1.50/$.  At the end of the year, the bond is downgraded to AA and the yield increases to 10 percent.  In addition, the SF appreciates to SF1.35/$.
29. What is the loss or gain to a Swiss investor who holds this bond for a year?  What portion of this loss or gain is due to foreign exchange risk?  What portion is due to interest rate risk?

         Beginning of the Year

         End of the Year

         The loss to the Swiss investor (SF884.82 + SF80 - SF1,000)/$1,000 = -3.52 percent.  The entire amount of the loss is due to interest rate risk.

1. What is the loss or gain to a U.S. investor who holds this bond for a year?  What portion of this loss or gain is due to foreign exchange risk?  What portion is due to interest rate risk?

         Price at beginning of year           = SF1,000/SF1.50     = $666.67

         Price at end of year                     = SF884.82/SF1.35   = $655.42

         Interest received at end of year   = SF80/SF1.35          = $59.26

         Gain to U.S. investor = ($655.42 + $59.26 - $666.67)/$666.67 = +7.20%.

         The U.S. investor had an equivalent loss of 3.52 percent from interest rate risk, but he had a gain of 10.72 percent (7.20 - (-3.52)) from foreign exchange risk.  If the Swiss franc had depreciated, the loss to the U.S. investor would have been larger than 3.52 percent.

30. Characterize the risk exposure(s) of the following FI transactions by choosing one or more of the risk types listed below:

1. Interest rate risk                   d.   Technology risk
2. Credit risk                            e.   Foreign exchange rate risk
3. Off-balance-sheet risk          f.    Country or sovereign risk

         (1)     A bank finances a $10 million, six-year fixed-rate commercial loan by selling one-year certificates of deposit. a, b

         (2)     An insurance company invests its policy premiums in a long-term municipal bond portfolio.                                 a, b

         (3)     A French bank sells two-year fixed-rate notes to finance a two-year fixed-rate loan to a British entrepreneur.                     b, e, f

         (4)     A Japanese bank acquires an Austrian bank to facilitate clearing operations.    

                                                                        a, b, c, d, e, f

         (5)     A mutual fund completely hedges its interest rate risk exposure using forward contingent contracts.               b, c

         (6)     A bond dealer uses his own equity to buy Mexican debt on the less-developed country (LDC) bond market.                  a, b, e, f

         (7)     A securities firm sells a package of mortgage loans as mortgage backed securities.

                                                                        A, b, c

32. What is liquidity risk? What routine operating factors allow FIs to deal with this risk in times of normal economic activity?  What market reality can create severe financial difficulty for an FI in times of extreme liquidity crises?

Liquidity risk is the uncertainty that an FI may need to obtain large amounts of cash to meet the withdrawals of depositors or other liability claimants. In times of normal economic activity, depository FIs meet cash withdrawals by accepting new deposits and borrowing funds in the short-term money markets.  However, in times of harsh liquidity crises, the FI may need to sell assets at significant losses in order to generate cash quickly.

33. Why can insolvency risk be classified as a consequence or outcome of any or all of the other types of risks?

Insolvency risk involves the shortfall of capital in times when the operating performance of the institution generates accounting losses.  These losses may be the result of one or more of interest rate, market, credit, liquidity, sovereign, foreign exchange, technological, and off-balance-sheet risks.

34. Discuss the interrelationships among the different sources of bank risk exposure. Why would the construction of a bank risk-management model to measure and manage only one type of risk be incomplete?

Measuring each source of bank risk exposure individually creates the false impression that they are independent of each other.  For example, the interest rate risk exposure of a bank could be reduced by requiring bank customers to take on more interest rate risk exposure through the use of floating rate products.  However, this reduction in bank risk may be obtained only at the possible expense of increased credit risk.  That is, customers experiencing losses resulting from unanticipated interest rate changes may be forced into insolvency, thereby increasing bank default risk. Similarly, off-balance sheet risk encompasses several risks since off-balance sheet contingent contracts typically have credit risk and interest rate risk as well as currency risk.  Moreover, the failure of collection and payment systems may lead corporate customers into bankruptcy.  Thus, technology risk may influence the credit risk of FIs.

As a result of these interdependencies, FIs have focused on developing sophisticated models that attempt to measure all of the risks faced by the FI at any point in time.