Busfin 3220 Practice
Chapter 5 Problems
1. After deciding to buy a new car, you can either lease the car or purchase it on a three-year loan. The car you wish to buy costs $32,000. The dealer has a special leasing arrangement where you pay $99 today and $450 per month for the next three years. If you purchase the car, you will pay it off in monthly payments over the next three years at a 7% APR. You believe you will be able to sell the car for $23,000 in three years. Should you buy or lease the car? 2. You have just arranged for a $750,000 mortgage to finance the purchase of a large tract of land. The mortgage has an 8.1% APR, and it calls for monthly payments over the next 30 years. However, the loan has an eight-year balloon payment, meaning that the loan must be paid off then. How big will the balloon payment be? 3. You have just purchased a new warehouse. To finance the purchase, you’ve arranged for a 30-year mortgage loan for 80% of the $2,900,000 purchase price. The monthly payment on this loan will be $15,000. What is the APR on this loan? The EAR?
Answers
1. To answer this question, we should find the PV of both options, and compare them. Since we are purchasing the car, the lowest PV is the best option. The PV of the leasing is simply the PV of the lease payments, plus the $99. The interest rate we would use for the leasing option is the same as the interest rate of the loan. The PV of leasing is: Enter | 36 | 7/12=.5833 | | -$450 | 0 | | | N | | | I/Y | | | PV | | | PMT | | | FV | | Solve for | | | $14,573.91 | | | PV = $99 + $450{1 – [1 / (1 + .07/12)12(3)]} / (.07/12) = $14,672.91 The PV of purchasing the car is the current price of the car minus the PV of the resale price. The PV of the resale price is: Enter | 36 | .5833 | | 0 | -23000 | | | N | | | I/Y | | | PV | | | PMT | | | FV | | Solve for | | | $18,654.82 | | |
PV = $23,000 / [1 + (.07/12)]12(3) = $18,654.82
1. After deciding to buy a new car, you can either lease the car or purchase it on a three-year loan. The car you wish to buy costs $32,000. The dealer has a special leasing arrangement where you pay $99 today and $450 per month for the next three years. If you purchase the car, you will pay it off in monthly payments over the next three years at a 7% APR. You believe you will be able to sell the car for $23,000 in three years. Should you buy or lease the car? 2. You have just arranged for a $750,000 mortgage to finance the purchase of a large tract of land. The mortgage has an 8.1% APR, and it calls for monthly payments over the next 30 years. However, the loan has an eight-year balloon payment, meaning that the loan must be paid off then. How big will the balloon payment be? 3. You have just purchased a new warehouse. To finance the purchase, you’ve arranged for a 30-year mortgage loan for 80% of the $2,900,000 purchase price. The monthly payment on this loan will be $15,000. What is the APR on this loan? The EAR?
Answers
1. To answer this question, we should find the PV of both options, and compare them. Since we are purchasing the car, the lowest PV is the best option. The PV of the leasing is simply the PV of the lease payments, plus the $99. The interest rate we would use for the leasing option is the same as the interest rate of the loan. The PV of leasing is: Enter | 36 | 7/12=.5833 | | -$450 | 0 | | | N | | | I/Y | | | PV | | | PMT | | | FV | | Solve for | | | $14,573.91 | | | PV = $99 + $450{1 – [1 / (1 + .07/12)12(3)]} / (.07/12) = $14,672.91 The PV of purchasing the car is the current price of the car minus the PV of the resale price. The PV of the resale price is: Enter | 36 | .5833 | | 0 | -23000 | | | N | | | I/Y | | | PV | | | PMT | | | FV | | Solve for | | | $18,654.82 | | |
PV = $23,000 / [1 + (.07/12)]12(3) = $18,654.82