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E120 Fall 2022 Homework 4 Due: Thursday, September 29, 2022 11:59PM • Please show your work for the following problems and submit on Gradescope. • You can either print this document out and scan it, upload your written work on blank paper, use a tablet, or type up your work. Problem 1 You Have Been Offered A Unique Investment Opportunity. If You Invest $ 10,000 Today, You Will Receive $ 1,000 One Year From Now, $ 1,500 Two Years From Now, And $ 12,000 Ten Years From Now. (a) What is the NPV of the opportunity if the interest rate is 6% per year? Should you take the investment? NPV = − 10000 + 1000 1 . 06 + 1500 1 . 06 2 + 12000 1 . 06 3 = 2353 . 82 Yes, take the deal (b) What is the NPV of the opportunity if the interest rate is 2% per year? Should you take the deal then? − 10000 + 1000 1 . 02 + 1500 1 . 02 2 + 12000 1 . 02 3 = 3730 . 01, still yes. 1

Problem 2 When you purchased your house, you took out a 35-year annual payment mortgage with an interest rate of 10% per year. The annual payment on the mortgage is $ 12,500. You have just made a payment and have now decided to pay the mortgage off by repaying the outstanding balance. What is the payoff amount if: (a) You have lived in the house for 15 years? (So there are 15 years left of the mortgage) 12500 0 . 10 (1 − 1 (1 . 10) 15 ) = 95075 . 99 (b) You have lived in the house for 19 years? (So there are 11 years left on the mortgage) 12500 0 . 10 (1 − 1 (1 . 10) 11 ) = 81188 . 26 (c) You have lived in the house for 15 years and you decide to pay off the mortgage immediately before the 15th payment is due? 95075 . 99 + 12500 = 107575 . 99 Problem 3 You work for a pharmaceutical company that has developed a new drug. The patent on the drug will last 20 years. You expect that the drug’s profits will be $ 1.5 million in its first year and this amount will grow at a rate of 5% per year for the next 19 years. Once the patent expires, other pharmaceutical companies will be able to produce the same drug and competition will likely drive profits to zero. What is the present value of the new drug if the interest rate is 8% per year? 1 . 5 . 08 − . 05 (1 − ( 1 . 05 1 . 08 ) 19 ) = 20 . 72 million 2

Problem 4 Suppose you currently have $ 10,000 in your savings account, and your bank pays interest at a rate of 0.1% per month. If you make no further deposits or withdrawals, how much will you have in the account in 17 years? 10000 ∗ 1 . 01 17 ∗ 12 = 76130 . 77 Problem 5 You have decided to buy a perpetuity. The bond makes one payment at the end of every year forever and has an interest rate of 5%. If the bond initially costs $ 3000, what is the payment every year? 3000 = c 0 . 05 c = 150 Problem 6 You are thinking of purchasing a house. The house costs $ 450,000. You have $ 60,000 in cash that you can use as a down payment on the house, but you need to borrow the rest of the purchase price. The bank is offering a 30-year mortgage that requires annual payments and has an interest rate of 5% per year. What will be your annual payment if you sign this mortgage? 450000 − 60000 = c 1 . 05 ∗ (1 − 1 (1 . 05) 30 ) c = 25370 . 10 Problem 7 You have an investment opportunity that requires an initial investment of $ 13,500 today and will pay $ 17,000 in one year. What is the IRR (Internal rate of return) of this opportunity? 17000 13500 − 1 = 0 . 2592 25.92% 3

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Problem 8 You are considering purchasing a warehouse. The cost to purchase the warehouse is $ 500,000. Renting the equivalent space costs $ 20,000 per year. If the annual interest rate is 5.5%, at what rate must rental costs increase each year to make the cost of renting comparable to purchasing? Assume that the rent will be paid at the end of each year. Hint: what is the growth rate? 500000 = 20000 . 055 − x x = . 015 1.5% 4

Optional Bonus Problem 9 - Create and Solve Directions: For this problem, choose a topic covered during for this problem set “period”, design a question, and then solve it. The question and solution must be written by you and be uniquely yours. However, you may use the textbook, the class material, the internet, or any other resource you want for inspiration. Make sure you cite your inspirational sources or declare that there are none. Required Components: • Inspiration statement • Question • Statement 5