HW3_S2023 (1)



Carnegie Mellon University *

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Feb 20, 2024





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H OMEWORK A SSIGNMENT #3 1) Tim is graduating and moving from Pittsburgh, so he agrees to sell his car to his friend Francis. Tim accumulated a lot of credit card debt as a student, and he intends to use the money from selling his car to pay down his credit card debt, which has an 8% APR (interest rate). Francis has a part-time campus job that he has used to pay for his meal plan, but he can use these earnings to pay for the car and then increase his student loan amount to pay for his meal plan. His student loan has a 6.5% APR (interest rate). Tim and Francis are considering whether Francis will pay for the car entirely up front with a single payment of $3000 now or in two installments of $1500 now and another $1700 one year from now. What is the NPV of each payment plan for each of them? [20 points] Which payment plan do you expect they will agree on? [5 points] 2) The Righton Corporation is taking out a loan of $38,000 at 7.8% interest (see table below). This interest rate is locked in for the life of the loan. They recognize that if/when they want to take out another loan in the future, the interest rate may change, but they have no reason to expect it to be higher or lower, and they are confident that the bank would extend them another loan on similar terms. They are considering three different possible repayment plans for the current loan. Under Plan 1, they must pay yearly interest of $2,964 and the entire principal at the end. Plan 2 is an annuity-type plan where they pay equal payments of $5612.14 every year. With Plan 3, they pay a balloon payment of principal plus all accumulated interest in year 10. Year Plan1 Plan2 Plan3 0 38,000 38,000 38,000 1 -2,964 -5612.14 0 2 -2,964 -5612.14 0 3 -2,964 -5612.14 0 4 -2,964 -5612.14 0 5 -2,964 -5612.14 0 6 -2,964 -5612.14 0 7 -2,964 -5612.14 0 8 -2,964 -5612.14 0 9 -2,964 -5612.14 0 10 -40,964 -5612.14 -80,533 payment sum: -67,640 -56,121.4 -80,533 NPV: ? ? ? a) Show how the bank calculates the balloon payment of $80,533. [5 points] 1
b) What are the NPVs of the payment streams for the three plans? Can you use NPV to recommend one plan over the others? Why should one plan be preferred over another? [10 points] c) Suppose that the company agreed on paying the 7.8% rate and signed a contract locking in that rate, and then the very next day the market interest rate dropped to 5.5%. Under which plan would the Righton Corporation be happiest? Under which plan would the bank be happiest? Why? How large would the gain or loss in NPV be for each plan? [20 points] 3) The government is proposing a new program to encourage college students to go into government jobs (teaching and service). The program will help cover the cost of college if you work in the government. With the new program, you would only need to pay back college loans for 10 years, regardless of what you owed. Unfortunately, government salaries are generally lower than those in private industry and pay does not grow as fast. Base salary government job: $70,000/yr starting after graduation Base salary private industry job: $90,000/yr starting after graduation Inflation: 6% annually Government salary growth: 2% over inflation annually Private salary growth: 3% over inflation annually Living expenses: $35,000/yr starting after graduation (inflate after that) Loan interest rate: 4% annually Annual loan payments: 25% of (salary minus cost of living) Years before loan forgiveness, government job: 10 Years before loan forgiveness, private job: 15 Cost of college $59,000 per year for each of four years (no inflation) Discount rate: 9% Assume that you are a freshman entering college and that once you start in government or industry, you stay there for 35 years. Should you consider the new government program? [40 points] 2
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