Hw Chapter4

5. 4. You have found three investment choices for a one- social class sting 10% APR Compounded monthly, 10% APR intensify annually, and 9% APR compounded daily. drift the spike for each investment choice. (Assume that there are 365 days in the year. ) Sol 1+ pinna= (1+r/k)k So, for 10% APR compounded monthly, the EAR is 1+EAR= (1+0. 1/12)12 = 1. 10471 = EAR= 10. 47% For 10% compounded annually, the EAR is 1+EAR= (1+0. 1)=1. 1 * EAR= 10% (remains the same). For 9% compounded daily 1+EAR= (1+0. 09/365)365 = 1. 09416 * EAR= 9. 4% 5-8. You mass earn $50 in am practise on a $ constant of gravitation set for eight months.If the EAR is the same regardless of the length of the investment, how practically gratify leave you earn on a $1000 deposit for a. 6 months. b. 1 year. c. 1 1/2 years. Sol Since we derriere earn $50 interest on a $1000 deposit, lay out of interest is 5% Therefore, EAR = (1. 05)12/8 -1 =7. 593% a) 1000(1. 075936/12 1) = 37. 27 b) 1000(1. 07593? 1) = 75. 93 c ) 1000(1. 075933/2 ? 1) = 116. 03 5-12. Capital One is advertising a 60-month, 5. 99% APR motorbike bring. If you need to borrow $8000 to purchase your dream Harley Davidson, what will your monthly defrayal be? Sol Discount ramble for 12 months is, 5. 99/12 = 0. 499167%C= 8000/1/0. 004991(1-1/(1+0. 004991)60) = $154. 63 5-16. You have just purchased a home and interpreted out a $500,000 owe. The mortgage has a 30-year term with monthly constitutements and an APR of 6%. a. How often will you present in interest, and how much will you liquidate in question, during the first year? b. How much will you dedicate in interest, and how much will you pay in principal, during the 20th year (i. e. , in the center of 19 and 20 years from now)? Sol a. APR of 6%/12 = 0. 5% per month. Payment = 500,000/(1/. 005)(1- 1/1. 005360)= $2997. 75 Total annual payments = 2997. 75 ? 12 = $35,973. Loan Balance after 1 year is 2997. 51/0. 005(1- 1/1. 005348) = $493,860. Therefore, 500,000 493,86 0 = $6140 is principal repaid in first year. Interest paid in 1st year is 35,973 6140 = $29833. b. Loan balance in 19 years (or 360 19? 12 = 132 remaining pmts) is 2997. 751/0. 005(1- 1/1. 005192)= $289,162 Loan Balance in 20 years = 2997. 751/0. 005(1- 1/1. 005120) = $270,018 Therefore, Principal repaid = 289,162 270,018 = $19,144, and Interest repaid =$35,973 19,144 = $16,829. 5-20. Oppenheimer Bank is run intoering a 30-year mortgage with an APR of 5. 25%. With this mortgage your monthly payments would be $2000 per month.In addition, Oppenheimer Bank offers you the pursuance peck Instead of making the monthly payment of $2000 every month, you mint restore half the payment every two weeks (so that you will make 52 ? 2 = 26 payments per year). With this plan, how long will it take to pay off the mortgage of $150,000 if the EAR of the loan is unchanged? Sol For every 2 weeks payment = 2000/2 = 1000. 1 year = 26 weeks. Therefore, (1. 0525)1/26 = 1. 001970. So, dismiss rate = 0. 1970%. Here, PV of loan payments is the outstanding balance. 150, 000= (1000/0. 001970)1- 1/(1. 001970)N If we solve for N,We get N= 177. 98. So, it takes 178 months to pay off the mortgage. If we determine to pay for 2 weeks, then 178*2= 356 weeks. 5-24. You have credit card debt of $25,000 that has an APR (monthly compounding) of 15%. Each month you pay the minimum monthly payment just. You are required to pay only the outstanding interest. You have received an offer in the mail for an otherwise identical credit card with an APR of 12%. After considering all your alternatives, you decide to switch cards, roll oer the outstanding balance on the octogenarian card into the mod card, and borrow additional money as well.How much can you borrow today on the new card without changing the minimum monthly payment you will be required to pay? Sol Here the snub rate = 15/12 = 1. 25%. Assuming that monthly payment is the interest we get, 25,000*0. 15/12= $312. 50. This is perpetui ty. So the bill can be borrowed at the new interest rate is this cash escape discounted at the new discount rate. The new discount rate is 12/12 = 1%. So, PV = 312. 50/0. 01 = $31,250. So by switching credit cards we are able to spend an especial(a) 31, 250 ? 25, 000 = $6, 250. We do not have to pay taskes on this amount of new borrowing, so this is our after-tax benefit of switching cards. -28. Consider a redact that requires an initial investment of $100,000 and will produce a single cash flow of $150,000 in five years. a. What is the NPV of this image if the five-year interest rate is 5% (EAR)? b. What is the NPV of this project if the five-year interest rate is 10% (EAR)? c. What is the highest five-year interest rate such that this project is still profitable? Sol a. NPV = 100,000 + 150,000 / 1. 055 = $17,529. b. NPV = 100,000 + 150,000 / 1. 105 = $6862. Here we need to take care the IRR. Therefore, IRR = (150,000 / 100,000)1/5 1 = 8. 45%. 5-32. Suppose the current ann ual interest rate is 6%.One year from now, you believe the economy will vary to slow and the one-year interest rate will fall to 5%. In two years, you expect the economy to be in the midst of a recession, causing the Federal Reserve to cut interest rank drastically and the one-year interest rate to fall to 2%. The one-year interest rate will then rise to 3% the following year, and continue to rise by 1% per year until it returns to 6%, where it will remain from then on. a. If you were certain regarding these future interest rate changes, what biyearly interest rate would be consistent with these expectations? . What current term complex body part of interest rates, for terms of 1 to 10 years, would be consistent with these expectations? c. dapple the yield curve in this case. How does the one-year interest rate oppose to the 10-year interest rate? Sol a. The one-year interest rate is 6%. If rates fall next year to 5%, then if you reinvest at this rate over two years you would earn (1. 06)(1. 05) = 1. 113 per dollar invested. This amount corresponds to an EAR of (1. 113)1/2 1 = 5. 50% per year for two years. Thus, the two-year rate that is consistent with these expectations is 5. 0%. b. Year Future Interest consider FV from re-investing EAR 1 6% 1. 0600 6. 00% 2 5% 1. 1130 5. 50% 3 2% 1. 1353 4. 32% 4 3% 1. 1693 3. 99% 5 4% 1. 2161 3. 99% 6 5% 1. 2769 4. 16% 7 6% 1. 3535 4. 42% 8 6% 1. 4347 4. 62% 9 6% 1. 5208 4. 77% 10 6% 1. 6121 4. 89% c. We can get the yield curve by considering all EARs above. It is an inverted curve. 5-36. You are enrolling in an MBA program. To pay your tuition, you can each take out a standard student loan (so the interest payments are not tax deductible) with an EAR of 5 ? or you can use a tax-deductible home equity loan with an APR (monthly) of 6%. You address being in a very low tax bracket, so your tax rate will be only 15%. Which loan should you use? Sol APR is given, So we can get EAR by, (1+0. 06/12)12 = 1. 06168. So, EAR = 6. 168%. We have to convert the before tax rate to after tax rate. 6. 168? (1- 0. 15) = 5. 243% Since student loan is higher after tax rate, it is better to use home equity loan. 5-40. You firm is considering the purchase of a new world power phone system. You can either pay $32,000 now, or $1000 per month for 36 months. . Suppose your firm currently borrows at a rate of 6% per year (APR with monthly compounding). Which payment plan is more beautiful? b. Suppose your firm currently borrows at a rate of 18% per year (APR with monthly compounding). Which payment plan would be more pleasant in this case? Sol a. The payments are as risky as the firms other debt. So, opportunity cost = debt rate. PV(36 month rente of 1000 at 6%/12 per month) = $32,871. So we need to pay cash. b. PV(annuity at 18%/12 per months) = $27,661. So we can pay over time.