Part A: Financial CrisisPart B: Present ValueFor simplicity it is assumed that no down payment is paid in either of the two cases.Part B: Present Value and Bond ValuationPart D: Interest Rate RiskSolution Key to Problem Set 3ECN 134Financial Economics Prof. Farshid MojaverPart A: Financial CrisisPart B: Present Value 1. Marjan is shopping for a mortgage to cover a $1,000,000 loan on her house.a. She has been offered a 30 year loan at 8% stated annual interest to be repaid inmonthly installments beginning exactly one month after she closes on the house. What will her payments be on this loan?b. She also found a 15 year loan at 7.5% stated annual interest to be repaid in monthly installments beginning exactly one month after she closes on the house. What will her payments be on this loan?c. What are Marjan’s total payments on the 30 year $1,000,000 loan? What are her total payments on the 15 year $1,000,000 loan?Answer)(a)  mTmrmrCPV/111/ or PV = C.A, where  mTmTrmrmrA/111/1 then )/1(mTrAPVC  65.337,7$000,000,108.0121208.01111360mTrmTrACthusA(b) 12.270,9$12075.011112075.0)000,000,1(1180C(c) 30- year loan: Total paid=7,337.65360=$2,641,554 15-year loan: Total paid=9,270.12180=$1,668,612.60(But actually, this calculation is not meaningful in finance because it does not consider discount factor for the future payment.)2. Bahram’s Bonds assembles mortgage bonds into portfolios and sells shares (trenches) based on when the underlying mortgage are paid off. The company plans to issue stock that promises profits per share of $100 next year, growing at 6% per year indefinitely. Profits will be distributed annually. The market discount rate for assets of comparable risk is 12%. What is the present value of the income stream associated with a share of Bahram’s Bonds?Answer) 67.1666$06.012.0100grCPV3. Young Joon is considering the purchase of a troubled econometric consulting company. He thinks he can resurrect it if he puts $100,000 per year in at the end of each of the first 5 years. He plans to sell it for $1,000,000 at the end of the sixth year. The market interest rate for loans of comparable risk is 11%, which is the same as Young Joon’s discount rate for this property.a. Draw the timeline of the cash flows, showing costs as negative cash.b. What is the present value of the expected sale at the end of six years?c. What is the present value of the expected cash infusions over the next five years?d. What is the maximum that Young Joon would be willing to pay for the derelict company (to just break even)?Answer) (a) PV -$100K -$100K -$100K -$100K -$100K $1000K 0 1 2 3 4 5 6 (b)    84.640,534$11.1000,000,11666rCPV(c)   70.589,369$11,01111.0000,10011/5 mTmrmrCPV(d) NPV= -cost + PV=-369,589.70+534,640.84=$165,051.145. Buy This Year or Next As a first time home buyer you can buy a home now when interest rates are low (5.5%) and received the $8,000 tax credit $8,000 for a $230,000 home or you can wait and buy itnext year when prices are projected to decrease another 10%. But if you wait you will lose the subsidy and interest rates may increase to 6.5%. What is the best decision; to buythe house now or to buy it next year? Answer)Input OutputSAIR 5.50%Years 30Period/yr 12SAIR/mm.Tpv (Price after subsidy) $222,000 Monthly mortgage payment $1,260.49 <=PV*(SAIR/m)/[1-1/(1+SAIR/m)^m.T]Input OutputSAIR 6.50%Years 30Period/yr 12SAIR/mm.Tpv (Price after 10% drop) $207,000 Monthly mortgage payment $1,308.38 Under these assumptions it is better to buy the house now.For simplicity it is assumed that no down payment is paid in either of the two cases. Part B: Present Value and Bond Valuation1. Whitney wants to put $100,000 down on a house five years from now. She plans to make monthly payments at the end of each month (beginning 30 days from now) into an account that pays a stated annual rate of 7% interest compounded monthly. What are her monthly payments?Answer)  PVrFVT.1 or   TTrrCrFV111.1  rrCFVT11  100,000=1207.011207.0160C  C=$1,396.792. The combination of weak consumer spending and the traditional weakness of Januarysales has led automobile manufacturers to offer zero interest financing or cash back options to stimulate sales. Suppose you can buy the car of your choice for its negotiated price of $25,020 less $500 cash back, or you can finance the entire $25,020 car cost for 36 months at zero interest. You have the cash necessary to pay for the car in an account that earns a stated annual interest rate of 4%, compounded monthly. You will either finance it or pay cash depending on which is the best deal.(i) What is the cost of the financed car to you right now?(ii) Should you pay cash, or finance the car, and why?Answer)The monthly financed car payment with no interest is: $25,020/36=$695i) PV= 361204.01111204.0695111TrrC  PV=$23,540.18ii) Finance it. By financing, we will actually make profit of: $1,479.82=$25,020- $23,540.183. How much would you pay per $1,000 face value for a bond with a coupon rate of 4.2% per year and two semi-annual payments remaining? The return on assets of comparable risk is 5.5% per year.Answer)Coupon rate=4.2%  0.42 $1,000=$42  C=21$242, Note that here, “the return is 5.5% per year” must be interpreted as effective annual rate and not stated, so EAIR=0.055. We need effective semi-annual interest rate or ESIR. 1.055 = (1+ESIR)2 => ESIR=0.0271 PV=  TTrParrrC)1(111 or PV=  22)0271.01(000,10271.1110271.21 PV = $988.224. For a 1-year pure discount bond, compute the yield to maturity if the bond’s face value is $1,000 and the price is