You have been asked by your parents to advise your younger sister, who is an entering freshman at a centrally-isolated university located in New York State, about buying instead of renting for the next four years. She is thinking of buying a three-bedroom house, renting two of the rooms to friends, and selling the house when she graduates During your sisters first week of college, she found a three-bedroom house selling for $240,000 as well as two friends at freshman orientation who are willing to pay $850 a month each for the two rooms. (Since shell be living in the third bedroom, you may assume she is implicitly paying the same rent for the third bedroom.) In her second week, she found a local bank that, despite her lack of credit history, is willing to extend a 15 year 70% LTV fixed-rate mortgage at 5% for the purchase. In her third week, utilizing all the tools she acquired in her 26 AP classes, she developed a house price forecast model that predicts house prices will grow by 4% per year for the next four years. As the older sibling taking real estate classes, your parents, who will be making the down payment, have asked you to evaluate this transaction.

a. What is the mortgage size and your parents down payment? What is the mortgage payment? (Ignore taxes and insurance in your calculation) Write out the expression you would need to use to solve for the monthly loan payment. What is the mortgages debt yield?

b. Ignoring expenses and maintenance (a common practice in student rental units) create a table which outlines your sisters annual NOI and debt service. Calculate her DCR. What is the reversion value for the house at the end of year 4? What is the mortgage balance at the time of reversion?

c. What is your parents equity IRR for this venture? Write out the after-tax cash flow for each of the four years. How would your answer change if her lender can only offer a 50% LTV mortgage? d. Suppose your parents are willing to buy the house instead of financing it. What is their unleveraged yield?