Chapter 17 - Selected Quantitative Problems & Solutions Quantitative Problems Question 1 (Useful) The balance sheet of TriBank starts with an allowance for loan losses of $1.33 million. During the year, TriBank charges off worthless loans of $0.84 million, recovers $0.22 million on loans previously charged off, and charges current income for $1.48 million provisions for loan losses. Calculate the end of year allowance for loan losses. Solution: 1.33 M 0.84 M 0.22 M 1.48 M $2.19 M     Question 2 (Useful) X-Bank reported an ROE of 15% and an ROA of 1%. How well capitalized in this bank? Solution: ROE ROA  EM 0.15 0.01  EM 15 assets/equity   EM So equity/assets 6.66%. This is a well-capitalized bank.  Question 3 In mid-1978, Wiggley S&L issued a standard 30-year fixed rate mortgage at 7.8% for $150,000. 36 months later, mortgage rates jumped to 13%. If the S&L sells the mortgage, how much of a loss is expected? Solution: When issued, the required payment is:  $150,000,  7.8/12,  360,  0 PV I N FV Compute PMT. $1,079.81 PMT  After 36 months, the mortgage balance is: $1,079.81, 7.8/12, 324, 0 PMT  I  N  FV  Compute  $145,764.43 PV. PV However, at current rates, the remaining cash flows are worth: $1,079.81, 13/12, 324, 0 PMT  I  N  FV  Compute  $96,637.64 PV. PV Wiggley S&L expects to take a loss of $49,126 if it sells the mortgage. Question 4 Refer to the previous question. In 1981 Congress allowed S&Ls to sell mortgages at a loss and to amortize the loss over the remaining life of the mortgage. If this were used for the previous question, how would the transaction have been recorded? What would be the annual adjustment? When would that end? The sale would be recorded as: Solution:
Chapter 17 - Selected Quantitative Problems & Solutions Quantitative Problems Question 1 (Useful) The balance sheet of TriBank starts with an allowance for loan losses of $1.33 million. During the year, TriBank charges off worthless loans of $0.84 million, recovers $0.22 million on loans previously charged off, and charges current income for $1.48 million provisions for loan losses. Calculate the end of year allowance for loan losses. Solution: 1.33 M  0.84 M  0.22 M  1.48 M  $2.19 M Question 2 (Useful) X-Bank reported an ROE of 15% and an ROA of 1%. How well capitalized in this bank? Solution: ROE  ROA EM 0.15  0.01 EM EM  15  assets/equity So equity/assets  6.66%. This is a well-capitalized bank. Question 3 In mid-1978, Wiggley S&L issued a standard 30-year fixed rate mortgage at 7.8% for $150,000. 36 months later, mortgage rates jumped to 13%. If the S&L sells the mortgage, how much of a loss is expected? Solution: When issued, the required payment is: PV  $150,000, I  7.8/12, N  360, FV  0 Compute PMT. PMT  $1,079.81 After 36 months, the mortgage balance is: PMT  $1,079.81, I  7.8/12, N  324, FV  0 Compute PV. PV  $145,764.43 However, at current rates, the remaining cash flows are worth: PMT  $1,079.81, I  13/12, N  324, FV  0 Compute PV. PV  $96,637.64 Wiggley S&L expects to take a loss of $49,126 if it sells the mortgage. Question 4 Refer to the previous question. In 1981 Congress allowed S&Ls to sell mortgages at a loss and to amortize the loss over the remaining life of the mortgage. If this were used for the previous question, how would the transaction have been recorded? What would be the annual adjustment? When would that end? Solution: The sale would be recorded as: