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Practice Problems Solutions for Assignment - Real Estate Finance | RE 611, Assignments of Real Estate Management

Wichita State University (WSU)Real Estate Management
Prof. Stanley D. Longhofer

Material Type: Assignment; Professor: Longhofer; Class: Real Estate Finance; Subject: Real Estate; University: Wichita State University; Term: Unknown 1989;

Typology: Assignments

Pre 2010

Uploaded on 08/19/2009

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RE 611 / Fin 611 โ€“ Real Estate Finance
Effective Borrowing Costs and the APR / Charging Fees to Achieve Yield
Practice Problems โˆ’ Solutions
Dr. Stanley D. Longhofer
Effective Borrowing Costs and the APR
1) Highpoint Mortgage has offered you a $95,000, 30-year, fixed-rate mortgage at 6.00
percent interest with 1.5 points. In addition, Highpoint will charge $750 in
processing fees to originate the loan.
a) What is the required monthly payment on this mortgage?
P/Y = 12, N = 360, I = 6.00, PV = 95,000, FV = 0 โ‡’ PMT = โˆ’ $569.57.
b) Assuming that you hold this loan until maturity, what is the effective borrowing
cost (EBC) on this mortgage?
Total up-front costs on this loan are 95,000 ร— 0.015 + 750 = $2,175. Thus, the
actual cash received at origination will be only 95,000 โˆ’ 2,175 = $92,825.
With the above information entered in your financial calculator, enter
PV = 92,825 and solve for I = 6.22%.
c) What is the EBC if you are only going to hold this loan for five years? Explain
the difference between your answer here and your answer in part (a).
Make sure you reenter the information from part (a): P/Y = 12, N = 360, I =
6.00, PV = 95,000, FV = 0 โ‡’ PMT = โˆ’ $569.57.
Then enter the new holding period and solve for the balance due at the end of
5 years: N = 5 ร— 12 = 60 โ‡’ FV = โˆ’ $88,401.64.
Then reenter PV = 92,825 and solve for I = 6.55%.
Your effective borrowing cost is higher in this case because you have less
time over which to spread the up-front fees associated with the loan.
d) What is the annual percentage rate (APR) on this mortgage assuming you hold the
loan until maturity?
APR = EBC = 6.22%.
e) What is the APR on this mortgage if the expected holding period is only four
years?
The APR is unaffected by the expected holding period, so APR = 6.22%.
2) Patriot Mortgage has offered Mr. Brady a $165,000, 15-year, fixed-rate mortgage at
6.00 percent interest with 0.75 points. In addition, Patriot will charge $1,500 in
processing fees to originate the loan.
a) What is the required monthly payment on this mortgage?
P/Y = 12, N = 180, I = 6.00, PV = 165,000, FV = 0 โ‡’ PMT = โˆ’ $1,392.36.
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RE 611 / Fin 611 โ€“ Real Estate Finance

Effective Borrowing Costs and the APR / Charging Fees to Achieve Yield Practice Problems โˆ’ Solutions

Dr. Stanley D. Longhofer

Effective Borrowing Costs and the APR

  1. Highpoint Mortgage has offered you a $95,000, 30-year, fixed-rate mortgage at 6. percent interest with 1.5 points. In addition, Highpoint will charge $750 in processing fees to originate the loan. a) What is the required monthly payment on this mortgage? P/Y = 12, N = 360, I = 6.00, PV = 95,000, FV = 0 โ‡’ PMT = โˆ’ $569.57. b) Assuming that you hold this loan until maturity, what is the effective borrowing cost (EBC) on this mortgage? Total up-front costs on this loan are 95,000 ร— 0.015 + 750 = $2,175. Thus, the actual cash received at origination will be only 95,000 โˆ’ 2,175 = $92,825. With the above information entered in your financial calculator, enter PV = 92,825 and solve for I = 6.22%. c) What is the EBC if you are only going to hold this loan for five years? Explain the difference between your answer here and your answer in part (a). Make sure you reenter the information from part (a): P/Y = 12, N = 360, I = 6.00, PV = 95,000, FV = 0 โ‡’ PMT = โˆ’ $569.57. Then enter the new holding period and solve for the balance due at the end of 5 years: N = 5 ร— 12 = 60 โ‡’ FV = โˆ’ $88,401.64. Then reenter PV = 92,825 and solve for I = 6.55%. Your effective borrowing cost is higher in this case because you have less time over which to spread the up-front fees associated with the loan. d) What is the annual percentage rate (APR) on this mortgage assuming you hold the loan until maturity? APR = EBC = 6.22%. e) What is the APR on this mortgage if the expected holding period is only four years? The APR is unaffected by the expected holding period, so APR = 6.22%.

  2. Patriot Mortgage has offered Mr. Brady a $165,000, 15-year, fixed-rate mortgage at 6.00 percent interest with 0.75 points. In addition, Patriot will charge $1,500 in processing fees to originate the loan. a) What is the required monthly payment on this mortgage? P/Y = 12, N = 180, I = 6.00, PV = 165,000, FV = 0 โ‡’ PMT = โˆ’ $1,392.36.

b) Assuming that Mr. Brady holds this loan until maturity, what is the EBC on this mortgage? Total up-front costs on this loan are 165,000 ร— 0.0075 + 1,500 = $2,737.50. Thus, the actual cash received at origination will be only 165,000 โˆ’ 2,737. = $162,262.50. With the above information entered in your financial calculator, enter PV = 162,262.50 and solve for I = 6.26%. c) What is the EBC if Mr. Brady is only going to hold this loan for five years? With the information from part (a) entered in your calculator, solve for the balance due at the end of four years: P/Y = 12, N = 180, I = 6.00, PV = 165,000, FV = 0 โ‡’ PMT = โˆ’ $1,392.36. N = 5 ร— 12 = 60 โ‡’ FV = โˆ’ $125,415.01. Then reenter PV = 162,26.50 and solve for I = 6.43%. d) What is the APR on this mortgage assuming Mr. Brady holds the loan until maturity? APR = EBC = 6.26%. e) What is the APR on this mortgage if the expected holding period is only four years? The APR is unaffected by the expected holding period, so APR = 6.26%. f) Now suppose that this mortgage also entails a three percent prepayment penalty on all principal paid early. What is the new EBC on this mortgage, once again assuming a five-year holding period? With a three percent prepayment penalty, Mr. Brady will have to pay a total of 125,415.01 ร— 1.03 = $129,177.46 at the end of five years to pay off the loan. With the same information from part (c) entered in your calculator, input FV = โˆ’ 129,177.46 and solve for I = 6.87%. g) What is the APR on this mortgage when a prepayment penalty applies? The APR is unaffected by the prepayment penalty because it is calculated assuming the loan is held until maturity (in which case no prepayment penalties will be paid by the borrower).

  1. ACME Mortgage has offered W. E. Coyote a $150,000, 15-year, fixed-rate mortgage at 6.25 percent interest with 1.5 points. In addition, ACME will charge $500 in processing fees to originate the loan. a) What is the required monthly payment on this mortgage? P/Y = 12, N = 180, I = 6.25, PV = 150,000, FV = 0 โ‡’ PMT = โˆ’ $1,286.13. b) Assuming the borrow holds this loan until maturity, what is the EBC on this mortgage?

The easiest way to solve this is to assume a loan amount; I chose $100,000: P/Y = 12, N = 30 ร— 12 = 360, I = 5, PV = 100,000, FV = 0 โ‡’ PMT = โˆ’ 536.82. Then enter N = 7 ร— 12 = 84 and solve for FV = โˆ’ 87,945.02. Next enter I = 5.50 and solve for PV = 97,251.90. Thus, on a $100,000 mortgage, the lender needs to receive back $100,000.00 โˆ’ $97,251.90 = $2,748.10 in fees. In terms of points this is 2,748.10 รท 100,000.00 = 2.75 points. Note: The size of the loan doesnโ€™t matter because both the interest rate and the points are expressed as a percentage of the outstanding principal balance. Thus, 2.75 points will ensure a lender earns a 5.50 percent yield on a 5.00 percent 30- year mortgage held for 7 years, regardless of the loan size.

  1. How many points must a lender charge to earn a 7.5 percent yield on a $110,000, 30- year, fixed-rate mortgage, with 7.0 percent interest and monthly payments? Assume that the expected holding period for the loan will be seven years, and round your answer to the nearest 1/8th^ point. Begin by calculating the monthly payment on this mortgage: P/Y = 12, N = 360, I = 7.0, PV = 110,000, FV = 0 โ‡’ PMT = โˆ’ $731.83. Next, calculate the balance that will be repaid at the end of seven years: N = 7 ร— 12 = 84 โ‡’ FV = โˆ’ $100,262.16. Then calculate the present value that will allow the lender to earn its required yield: I = 7.5 โ‡’ $107,120.44. Thus, the lender must receive 110,000.00 โˆ’ 107,120.44 = $2,879.56 in up-front fees in order to earn a 7.50 percent yield. Since each point is $1,100, this translates into 2.62 points. Rounded to the nearest 1/8 point, this is 2 5/8 points (2.625). You can check your work by calculating the EBC on this loan assuming 2. points will be charged: PV = 110,000 ร— (1 โˆ’ 0.02625) = 107,112. โ‡’ I = 7.50%.

  2. How many points must a lender charge to earn a 6.50 percent yield on a $140,000, 30-year, fixed-rate mortgage, with 6.00 percent interest and monthly payments? Assume that the expected holding period for the loan will be six years, and round your answer to the nearest 1/8th^ point. Begin by calculating the monthly payment on this mortgage: P/Y = 12, N = 360, I = 6.00, PV = 140,000, FV = 0 โ‡’ PMT = โˆ’ $839.37. Next, calculate the balance that will be repaid at the end of six years: N = 6 ร— 12 = 72 โ‡’ FV = โˆ’ $127,957.13. Then calculate the present value that will allow the lender to earn its required yield: I = 6.50 โ‡’ $136,658.51. Thus, the lender must receive 140,000.00 โˆ’ 136,658.51 = $3,341.49 in up-front fees in order to earn a 6.50 percent yield. Since each point is $1,400, this

translates into 2.39 points. Rounded to the nearest 1/8 point, this is 2 3/8 points (2.375).

You can check your work by calculating the EBC on this loan assuming 2. points will be charged: PV = 140,000 ร— (1 โˆ’ 0.02375) = 136,675 โ‡’ I = 6.50%.