Solution Key to Problem Set 3 ECN 134 Financial Economics Prof Farshid Mojaver Part A Financial Crisis Part 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 in monthly 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 PV then ArmT b C 1 1 1 ArmT 1 1 mT or PV C A where mT r m 1 r m r m 1 r m C PV 1 ArmT 1 1 360 0 08 1 12 12 0 08 thus C 1 000 000 ArmT 0 075 1 C 1 000 000 1 180 12 0 075 1 12 1 7 337 65 1 9 270 12 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 PV C 100 1666 67 r g 0 12 0 06 3 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 0 b PV 100K 1 C6 1 r 6 100K 2 100K 3 100K 4 100K 5 1000K 6 1 000 000 534 640 84 1 11 6 C r 1 1 r m m mT 100 000 5 1 1 0 11 369 589 70 0 11 c PV d NPV cost PV 369 589 70 534 640 84 165 051 14 5 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 it next 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 buy the house now or to buy it next year Answer SAIR Years Period yr SAIR m m T pv Price after subsidy Monthly mortgage payment SAIR Years Input 5 50 30 12 Output 222 000 1 260 49 PV SAIR m 1 1 1 SAIR m m T Input 6 50 30 Output Period yr SAIR m m T pv Price after 10 drop Monthly mortgage payment 12 207 000 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 Valuation 1 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 FV 1 r PV T or 1 r T 1 FV C r FV 1 r T C 1 1 r 1 r T 60 0 07 1 1 12 100 000 C 0 07 12 C 1 396 79 2 The combination of weak consumer spending and the traditional weakness of January sales 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 36 695 i C PV r 1 1 1 r T 695 0 04 12 1 1 36 0 04 1 12 PV 23 540 18 ii Finance it By financing we will actually make profit of 1 479 82 25 020 23 540 18 3 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 42 21 2 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 C 1 Par 1 T r 1 r 1 r T or PV 21 1 1 000 1 2 0271 1 0271 1 0 0271 2 PV 988 22 4 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 950 Answer 950 1 000 1 y 1 y 0 052632 5 2632 5 What is the future value of 100 continuously compounded for two …