Some Answers & Explanations Test#2-A Winter 2001 FINC434 - Prof: David Eagle (a) Exercising Now: Time 0 time 0 tax basis Price #shares tax situation cash flow current $6 85,000 $510,000 $510,000 exercise price $3 85,000 $255,000 ($255,000) taxable income @ 35% $255,000 less taxes ($89,250) ($89,250) Problem 1 Time 2 $165,750 ($344,250) Price proceeds from sale 16 85,000 $1,360,000 $1,360,000 less tax basis ($510,000) capital gains @ 20% $850,000 less taxes ($170,000) ($170,000) $680,000 $1,190,000 profit on investment $845,750 (ANSWER to part (a) (b) Exercising in two years: Time 2 Price proceeds from sale $16 85,000 $1,360,000 exercise price $3 85,000 $255,000 taxable income @ 35% $1,105,000 less taxes ($386,750) profit on investment $718,250 = cash flow at time 2 (ANSWER to part (b) (c) NPV ( exercising now) relevant discount rate = 9% time cash flows PV(cash flows) 0 ($344,250) $ (344,250) 2 $1,190,000 $ 1,001,599 $ 657,349 = NPV (ANSWER to part (c) (d) NPV (exercising two years from now) relevant discount rate = 5% (when compared to option of exercising now) time cash flows PV(cash flows) 2 $718,250 $ 651,474 $ 651,474 (e) Exercising now (but just barely) (f) The risk of exercising now may be less than the 9% rrr indicates because the company may let us rescind our stock purchase. Problem 6 interest principal total Tranch 1 $7,215 $ 13,355 $20,570 Tranch 2 $7,215 $7,215 Tranch 3 $7,215 $7,215 Z Tranch $0 $35,000 Question 7 The appraisal value would have to be less than the cost of the house for this not to be a conforming loan. Question 8 PV because the discount rate is higher r prepayments duration PV Since the value of the PO is the present value of the future principal payments, its value will go up. Note: as long as there is no default, the PO will receive the same amount of principal payments. It is just a question of when thoses payments will come and what the discount rate will be that we should use to compute PV. Question 9 If the market interest rate increases from 7.3% to 10%, the prepayments on the 7% fixed-rate mortgages will decrease. Prepayments from refinancing will almost disappear because homeowners would be refinancing with higher interest rates. Some prepayments will nevertheless continue because some people will still be selling their homes. However, people considering selling their homes and moving up to a bigger home will become more reluctant to do so, because they would be replacing their 7% mortgage with a 10% one. Problem 10 When the market interest rate decreases from 5.5% to 4.7%, the prepayment of 7% fixed-rate mortgages will increase because more people will choose to refinance their mortgages at the lower rate. Note: The payments that people are required to make on these fixed-rate mortgages stays the same unless the prepay. As a result, the lower market interest rate does not decrease people’s monthly payment unless they refinance.. Essay #11 See Quiz #9 and Chapter 9 in the Crash Book. Question 12. (c) The futures sold will result in a $15,750 profit. (a) buy stock and sell (1275-1212)*250 stock index futures. For The stock bought will result in an $8750 loss. each future contract they (1212-1247)*250 sell at 1275, they should The overall profit will be $7000. buy $311,750 worth of (15,750-8750) the stock in the S&P500 (1247*250) (d) The futures sold will result in a $8250 loss. (1275-1308)*250 (b) The futures sold will result in a $1250 loss. The stock bought will result in an $15,250 profit. (1275-1280)*250 (1308-1247)*250 The stock bought will result in an $8250 profit. The overall profit will be $7000. (1280-1247)*250 (15,250-8250) The overall profit will be $7000. (8250-1250) Note that the expiration value of S&P 500 stock index futures contract is now based on the opening S&P 500 on expiration day, not the closing. Question 13 See Chapter 7 in the Crash Book Remember that index arbitrage is a subset of program trading, but it does not mean the same as program trading. Question 14: D Question 15 • Suppose that there would be more hedgers wanting to buy T-bond futures than hedgers wanting to sell T-bond futures if the futures price of the T- bond equaled the expected price of the T-bond at expiration. Therefore, in order to induce speculators to fill the gap, the futures price would need to be greater than the expected expiration price of the T-bond. As the expiration of this futures contract approaches, the difference between the futures prices and the expected price at expiration would diminish. On the other hand, suppose instead that there would be more hedgers wanting to sell T-bond futures than hedgers wanting to buy T-bond futures if the futures price equaled the expected price of the T-bond at expiration. Therefore, in order to induce speculators to fill the gap, the futures price would need to be less than the expected expiration price of the T-Bond. As the expiration of this futures contract approaches, the difference between the futures prices and the expected price at expiration would diminish. Question 16 According to Van Horne, interest rate swaps are marked to market now. Question 17 Buying a stock index futures contract at 1300 is the same as buying $325,000 worth of stock. If the S&P 500 increases, you will gain the same whether you bought the SIF or the stock. For example, if the S&P 500 increases to 1367, then the stock should now be worth $341,750, which is a gain of $16,750. If you had bought stock index futures your cash settlement would be $16,750. On the other hand, if the S&P 500 decreases you will lose the same regardless whether you bought stock index futures or the stock. For example, if the S&P 500 decreases to 1175, then the stock should now be worth $293,750 which is a loss of $31,250. This is also the loss you would get if you had bought SIF. Selling a stock index futures contract at 1300 is equivalent to selling $325,000 worth of stock short. If the S&P 500 increases, you will lose money regardless whether you sold stock index futures or stock. For example if the S&P 500 increases to 1367, the short seller of stock would lose $16,750 and so would the seller of the futures contract. On the other hand, if the S&P 500 decreases you will gain regardless whether you sold stock index futures or stock. For example, if the S&P 500 decreases to 1175, the short seller of stock will gain $31,250 and so will the seller of the futures contract. Question 18 $20 C $15 B $10 $5 A 80 90 100 110 120 market price -$5 at expiration -$10 -$15 -$20 buying stock and buying stock index futures also have profit- loss graphs like C. This is the basis for put-call parity (See Appendix A of Chapter 10 in Van Horne).