Chapter 4 财务管理(英语)作业
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Chapter 4 Time Value of Money: Valuing Cash Flow Streams
14. Perpetuities The British government has a consol bond outstanding paying £1,000 per year forever. Assume the current interest rate is 8% per year.
a. What is the value of the bond immediately after a payment is made?
Answer: p = C/r = 1000 / 8% = £ 12500
b. What is the value of the bond immediately before a payment is made?
Answer: p = 1000/8%+1000 = £ 13500
*18. Annuities When you purchased your car, you took out a five-year
annual-payment loan with an interest rate of 6% per year. The annual payment on the car is $5000. You have just made a payment and have now decided to pay off the loan by repaying the outstanding balance. What is the payoff amount for the following scenarios?
You have owned the car for one year (so there are four years left on the loan)? Answer: Present value of an annuity:
PV=C*(1/r)(1-1/(1+r)^n)=$5000*(1/0.06)(1-(1/1.06)^4)=17325.53
b. You have owned the car for four years (so there is one year left on the loan)? Answer: PV=$5000*(1/0.06)(0.06/1.06)=$4716.98
26. Growing Cash Flows You work for a pharmaceutical company that has developed
a new drug. The patent on the drug will last 17 years. You expect that the drug’s profits will be $2 million in its first year and that this amount will grow at a rate of 5% per year for the next 17 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 10% per year?
Answer: Present value of a growing annuity:
pv=c*(1/r-g)(1-(1+g/1+r)^n)=2*(1/0.05)(1-(1.05/1.10)^17)=$21.861million *35. You are saving for retirement. To live comfortably, you decide you will need to save $2 million by the time you are 65. Today is your 22nd birthday, and you decide, starting today and continuing on every birthday up to and including your 65th birthday, that you will put the same amount into a savings account. If the interest rate is 5%, how much must you set aside each year to ensure that you will have $2 million in the account on your 65th birthday?
Answer: $2 billion=FV(annuity)=c*(1/0.05)(1.05^44-1)=c*(7.56/0.05) Therefore, C=$13233 Thus, I need to save $13233 each year.