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Questions for Slide Deck 2: Learn Your Calculator 7. A lender offers you a $100,000 30-year, fully amortizing, fixed rate mortgage with monthly payments at an annual interest rate of 6%. What is the monthly payment? After making 3 years of payments of the mortgage above, what is the mortgage balance? Make sure P/Y = 12 N = 30*12 = 360 I/YR = 6 PV = -$100,000 FV = 0 PMT = 599.5505 Then set N = 36 and compute FV = 96,084.0701 (or set N = 324 and compute PV = -96,084.0701) 8. A borrower has offered to pay you a constant $2,500 per month at the end of each month for 20 years. You discount these cash flows at a mortgage rate of 6%. What is this worth to you? Make sure P/Y = 12 N = 20*12 = 240 I/YR = 6 PMT = 2,500 FV = 0 PV = -348,951.9292 9. A borrower has offered to pay you (the lender) a constant $1,000 per month at the end of each month for the next 30 years. You discount these cash flows at the nominal mortgage equivalent rate of 5%. What is this worth to you? Make sure P/Y = 12 N = 360 I/YR = 5 PMT = 1,000 FV = 0 PV = -186,281.617 10. Your bank is thinking of selling the loan issued in the previous question to secondary markets. At the time of the sale, there is a 50% chance the contractual cash flows will be discounted at a 6 percent rate and a 50% chance the cash flows will be discounted at a 4 percent rate. What is the expected value of the loan to be sold to secondary markets? Set N = 360, PMT = 1,000, FV = 0 PV at 6%: Set I/YR = 6, PV = -166,791.6144 PV at 4%: Set I/YR = 4, PV = -209,461.2405 Expected value = 0.5*166,791.6144 + 0.5*209,461.2405 = 188,126.4274 11. A borrower approaches a lender and offers to pay $1,000 each year for 5 years (end of year) for a loan issued today. Assume the lender discount cash flows using an annual interest rate of 5%. What size loan can the lender offer? Set P/YR = 1 N = 5, I/YR = 5, PMT = 1,000, FV = 0, PV = -4,329.4767 12. The borrower comes back to the lender and asks if he can borrow more money today if he offers $1,000 at the end of the first year and then “steps up” subsequent payments over time at the rate of 3 percent per year for rest of the life the loan. The lender continues to discount the loan at an annual interest rate of 5%. What size loan can the lender offer? (compute with calculator) Set P/YR = 1 CF0 = 0 CF1 = 1,000 CF2 = 1,030 CF3 = 1,060.90 CF4 = 1,092.727 CF5 = 1,125.5088 Set I/YR = 5, compute NPV = 4,583.9214 13. The lender comes back to the borrower and offers the following deal: Pay me $900 at the end of the 1st year, and then step up payments each year at 15% per year. Your discount rate will be 6.2 percent. How much money does the lender offer to the borrower? Set P/YR = 1 CF0 = 0 CF1 = 900 CF2 = 1,035 CF3 = 1,190.25 CF4 = 1,368.7875 CF5 = 1,574.1056 Set I/YR = 6.2, compute NPV = 5,000 14. You own a property that pays $1,500 in net rent at the end of years 1 and 2. You expect to sell the property at a cap rate of 5% at the end of year 2. Assume you discount net rents at a 3% rate and you discount the proceeds from the sale of the building at a 5.16% annual rate. How much do you expect to sell the property for? What is the building worth to you today? The rent payments are worth $1,500/(1.03) + $1,500/(1.03)2 = $1,456.311 + $1,413.894 = $2,870.205 The sale price of the building is $1,500/0.05 = $30,000 which is worth $30,000/(1.0516)2 = $27,128.145 The total amount you would pay is $29,998.35 15. Suppose you purchase the building for the answer the previous question and then experienced the cash flows as expected including the sale price. What was the IRR of the building’s cash flows? (Hint: use cash flow buttons on your calculator) Make sure P/YR = 1. Then compute this as CF0 = -$29,998.35 CF1 = $1,500 CF2 = $31,500 Compute IRR/YR = 5.003 16. Assume in the previous 2 questions that you discount the proceeds from the sale of the building at a 5.5% annual rate. Compute (a) how much you would pay for the property and (b) the IRR. The rent payments are worth $2,870.205 … this hasn’t changed The sale price of the building is worth $30,000/(1.055)2 = $26,953.572 The total amount you would pay is $29,823.777 Make sure P/YR = 1. Enter CF0 = -$29,823.777, CF1 = $1,500, CF2 = $31,500 Compute IRR/YR = 5.317 17. You buy a hotel that pays $1,500 in annual year‐end NOI for 5 years and then expect to sell the hotel for at a cap rate of 4% at the end of year 5. You purchased the hotel at a 5% cap rate. What is the IRR? Purchase price 1500/0.05 = $30,000. Sale price is $37,500.00 Enter CF0 = -$30,000, CF1 = $1,500, N1 = 4, CF2 = $39,000 Compute IRR/YR = 9.164 18. You pay $10,467 for a building that generates annual net rent of $1,000 at the end of year 1 $2,000 at the end of years 2, 3, 4, 5, 6 $3,000 at the end of year 7 What is the IRR/YR of the purchase of the building? Make sure P/YR = 1. Then compute this as CF0 = -$10,467 CF1 = $1,000 CF2 = $2,000 N2 = 5 CF3 = 3,000 Compute IRR/YR = 6.9994 19. What is the most you would pay in the previous problem if you only require a 5% return on the building? HINT: clear all, Set I/YR=5 and use NPV to solve when CF0 = 0. Make sure P/YR = 1. Then compute this as CF0 = 0, CF1 = $1,000, CF2 = $2,000 , N2 = 5, CF3 = 3,000, Set I/YR = 5, Compute NPV = 11,331.0472 20. You pay $30,000 for a building that pays net rents of $1,500 in the first year. You expect to sell at the end of the first year. The going out cap rate is heavily dependent on how the Federal Reserve ends its QE program. There is a 70% chance the Federal Reserve “softly” tapers, and your going out cap rate will be 4% implying a sale price of $37,500. And, there is a 30% chance the Federal Reserve ends QE abruptly, implying a going out cap of 6.5% and therefore a sale price of $23,077. a. What is the IRR in the softly taper scenario? b. What is the IRR in the abrupt ending scenario? c. If you were to compute an “expected” sales price of the building, and then compute the IRR based on the expected sales price, what would it be? Softly taper sale price is $1,500/0.04 = $37,500 Abrupt landing sale price is $1,500/0.065 = $23,076.923 Expected sale price = 0.7*$37,500 + 0.3*23,076.923 = $33,173.077 Make sure P/YR = 1 a. CF0 = -$30,000, CF1 = $39,000, IRR/YR = 30.000 b. CF0 = -$30,000, CF1 = $24,576.923, IRR/YR = -18.077 c. CF0 = -$30,000, CF1 = $34,673.077, IRR/YR = 15.577 21. You own a property that pays $3,000 in NOI at the end of years 1 and 2. You expect to sell the property at a cap rate of 6% at the end of year 2. Assume you discount net rents at a 2% annual rate and you discount the proceeds from the sale of the building at a 7% annual rate. a. How much do you expect to sell the property for? b. What is the property worth to you today? Make sure P/YR = 1 Compute value of rents: Clear all. CF0 = 0, CF1 = 3,000, CF2 = 3,000. Set I/YR = 2, compute NPV = $5,824.6828 Compute value of sale (sale price = $3,000/0.06 = $50,000) Clear all. CF0 = 0, CF1 = 0, CF2 = 50,000. Set I/YR = 7, compute NPV = $43,671.9364 Property is worth $5,824.6828 + $43,671.9364 = $49,496.6192 22. You purchase a property on January 1, 2015 that pays a constant $1,500/year in NOI (paid Dec 31 every year). You intend to sell the building on Dec 31, 2017 at an 8% cap rate. What would you have to pay for the building on January 1, 2015 to earn a 7% IRR? Make sure P/YR = 1 CF0 = 0 CF1 = 1,500 CF2 = 1,500 + 1,500/0.08 = 1,500 + 18,750 = 20,250 Set I/YR = 7, compute NPV = 19,089.0034