Ch 4 -Hwk

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School
California State University, Fullerton **We aren't endorsed by this school
Course
FIN 320
Subject
Finance
Date
Oct 21, 2023
Pages
5
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Student: Everardo Navarro Instructor: Erdem Ucar Date: 10/21/23 Course: FIN320_54 Fall_2023 Assignment: Chapter 4 Homework 1. You plan to deposit $300 in a bank account now and $200 at the end of the year. If the account earns 5% interest per year, what will be the balance in the account right after you make the second deposit? Review Only Click the icon to see the Worked Solution (Formula Solution). The balance in the account right after you make the second deposit will be $ 515.00 . (Round to the nearest dollar.) You have a loan outstanding. It requires making three annual payments of $8,000 each at the end of the next three years. Your bank has offered to allow you to skip making the next two payments in lieu of making one large payment at the end of the loan's term in three years. If the interest rate on the loan is 4%, what final payment will the bank require you to make so that it is indifferent to the two forms of payment? Review Only ! Click the icon to see the Worked Solution (Formula Solution). 2 Click the icon to see the Worked Solution (Financial Calculator and Spreadsheet Solution). The final payment the bank will require you to make is $ 0.00' . (Round to the nearest cent.) 1: Review Worked Solution (Formula Solution) First, compute the present value of the cash flows using the following formula: Cq C, Cn d——t———+ s+ (+0 (1407 (1+n" where PV is the present value, C,, is the cash flow at date n, ris the interest rate, and N is the date of the last cash flow in a stream of cash flows. Therefore, $8,000 $8,000 $8,000 V = + St —————= 1+0.04 (1+0.04) (1+0.04)"" The present value of the cash flows is $0.00. Then, find the future value of the present value amount using the following formula: FV,=PVvx(1+n)" where FV,, is the future value on date n. Therefore, FV'=$0.00x (1 +0.04)""¢ = $0.00 The final payment the bank will require you to make is $0.00. 2: Review Worked Solution (Financial Calculator and Spreadsheet Solution) First, compute the present value of the cash flows using a financial calculator or Excel: N Y PV PMT FV Given: nine 4 -8,000 0 Solve for: 0.00 Excel Formula: = PV(RATE,NPER,PMT,FV) = PV(0.04,nine, 8000,0) The present value of the cash flows is $0.00. Then, once you know the present value of the cash flows, compute the future value (of this present value) as follows: N iy PV PMT FV Given: nine 4 0.00 0 Solve for: -0.00 Excel Formula: = FV(RATE,NPER,PMT,PV) = FV(0.04,nine,0,0.00) The final payment the bank will require you to make is $0.00. YOU ANSWERED: nothing
3. What is the present value of $5,000 paid at the end of each of the next 87 years if the interest rate is 5% per year? Review Only Click the icon to see the Worked Solution (Formula Solution). Click the icon to see the Worked Solution (Financial Calculator and Spreadsheet Solution). The present value is 98566.06 . (Round to the nearest cent.) 4. Assume that your parents wanted to have $120,000 saved for college by your 18th birthday and they started saving on your first birthday. They saved the same amount each year on your birthday and earned 8.5% per year on their investments. a. How much would they have to save each year to reach their goal? b. If they think you will take five years instead of four to graduate and decide to have $160,000 saved just in case, how much would they have to save each year to reach their new goal? Review Only Click the icon to see the Worked Solution (Formula Solution). Click the icon to see the Worked Solution (Financial Calculator and Spreadsheet Solution). a. How much would they have to save each year to reach their goal? To reach the goal of $120,000, the amount they have to save eachyearis$ 3051.65 . (Round to the nearest cent.) b. If they think you will take five years instead of four to graduate and decide to have $160,000 saved just in case, how much would they have to save each year to reach their new goal? To reach the goal of $160,000, the amount they have to save each yearis $ 4068.87 . (Round to the nearest cent.) 5. Arich relative has bequeathed you a growing perpetuity. The first payment will occur in a year and will be $2,000. Each year after that, you will receive a payment on the anniversary of the last payment that is 7% larger than the last payment. This pattern of payments will go on forever. Assume that the interest rate is 13% per year. a. What is today's value of the bequest? b. What is the value of the bequest immediately after the first payment is made? Review Only Click the icon to see the Worked Solution (Formula Solution). a. What is today's value of the bequest? Today's value of the bequestis $ 33333.33 . (Round to the nearest dollar.) b. What is the value of the bequest immediately after the first payment is made? The value of the bequest immediately after the first paymentis made is $ 35666.66 . (Round to the nearest dollar.) 6. You work for a pharmaceutical company that has developed a new drug. The patent on the drug will last 18 years. You expect that the drug's profits will be $4 million in its first year and that this amount will grow at a rate of 5% per year for the next 18 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? Review Only 3 Click the icon to see the Worked Solution (Formula Solution). The present value of the new drug is $ 53.033" million. (Round to three decimal places.) 3: Review Worked Solution (Formula Solution) Here is the timeline of the cash flows for the new drug: Years 0 1 2 3 18 | | | | Cash Flows $4M $4M(1.05) $4M(1.05)2 $4M(1.05)17 To determine the present value of a growing annuity, use the following formula: c 1+g\N PV=——x|1- r-g 1+r where PV is the present value, C is the cash flow, r is the interest rate, g is the growth rate, and N is the date of the last cash flow in a stream of cash flows. Therefore, $4 million 1+0.05 = x|1- | 0.08 -0.05 1+0.08 18 ] ] =$53.033 million The present value of the new drug is $53.033 million. YOU ANSWERED: 50.773
7. You have an investment account that started with $3,000 10 years ago and which now has grown to $11,000. a. What annual rate of return have you earned (you have made no additional contributions to the account)? b. If the savings bond earns 13% per year from now on, what will the account's value be 10 years from now? Review Only 4 Click the icon to see the Worked Solution (Formula Solution). 5 Click the icon to see the Worked Solution (Financial Calculator and Spreadshest Solution). a. What annual rate of return have you earned (you have made no additional contributions to the account)? Your annual rate of return is 13.87 %. (Round to two decimal places.) b. If the savings bond earns 13% per year from now on, what will the account's value be 10 years from now? The account's value in ten years willbe $ 37340.24 . (Round to the nearest cent.) 4: Review Worked Solution (Formula Solution) a. To determine the rate of return, use the following formula: FV=pPVx(1+n)" where PV is the amount you invest today, FV is the future value you will receive in n, number of years, and solve for r, the annual rate. 1 FvY" ; =\ pv Therefore, 1 _ [$11,ooo 10 -4 = = o $3,000 ] 1=0.1387=13.87% b. To calculate the amount in your account ten years later, use the following formula: FV=PVx(1+n)" Therefore, FV=$11,000x(1+ 0.13)10 =$37,340.24 5: Review Worked Solution (Financial Calculator and Spreadsheet Solution) The annual rate of return you have eamed is computed as follows: N Y PV PMT FV Given: 10 - 3,000 0 11,000 Solve for: 0.1387 Excel Formula: = RATE(NPER,PMT,PV,FV,0,GUESS)=RATE(10,0, - 3000,11000,0,0.1)= 0.1387 b. If the savings bond earns 13% per year from now on, the account's value 10 years from now is computed as: N Y PV PMT FV Given: 10 13 -11,000 0 Solve for: 37,340.24 Excel Formula: =FV(RATE,NPER,PMT,PV)=FV(0.13,10,0,-11000)= 37,340.24 8. You are thinking of purchasing a house. The house costs $400,000. You have $57,000 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 9% per year. What will be your annual payment if you sign this mortgage? Review Only Click the icon to see the Worked Solution (Formula Solution). Click the icon to see the Worked Solution (Financial Calculator and Spreadsheet Solution). The annual payment is $ 33386 . (Round to the nearest dollar.)
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