Questions

1) Find the PV of a stream of payments lasting 4 years. Each payment is for $300, and the discount rate is 5%. The payments are all received at the end of the year, starting with the first payment, received exactly one year from the present. Show your work. 2) Find the PV of the following perpetuity: Yearly payment: $5000 (received at the end of each year) Discount rate : 8% Show your work. 3) You are negotiating to buy a small business. The seller assures you that the annual profits will be stable forever at 15,000 and that they have a present discounted value of 750,000. What is his asking price for the business? Calculate the discounted rate he must be using. Show your work. 4) After graduation from Harvard Extension, you decide to stay in the Cambridge area and start your own business. You think you see a couple of opportunities. Knowing first-hand the pressure Harvard students are under, you consider opening a business that allows them to let off steam and get rid of their aggression: A paintball center right in The Square. The cost of the project would be $250,000, payable up front, while revenues are expected to be $13,000 per year, forever. Assume profits are always received at the end of the year and the only cost for the project is its acquisition price, $250,000, payable immeadiately. A) If the rate of return on comparable projects is 4%, is this project worthwhile? Show your calculations. B) What is the projects internal rate of return (IRR)? Show your calculations. C) You are also considering a second business opportunity: Supplying fish, fresh from the bottom of the Charles River, to Harvard Dining Services, for the next three years. For this they will pay you $35,000 immediately. You figure it will cost you $14,000 a year in supplies to provide this culinary joy. So, the revenue and costs of the project can be summarized as follows: -Immediate and only revenue: 35,000 - Costs in Year 1 : 14,000 - Costs in Year 2 : 14,000 - Costs in Year 3 : 14,000 Find this project internal rate of return (IRR). Show your calculations 5) You are the manager of General- ford, a large north american car manufacturer. Demand for your product has been high and you are looking at the following three alternatives. Plan I. Spend 40 million dollar today on a factory in Alabama that will be completed in one year. You expect to receive $24.2 million in profits from this factory at the end of the second year, at which time you also expect to sell the factory to Toyhonda, a Japanese conpetitor, for $24.2 million. Plan II. Spend $100 million today in a joint venture with Nisubishi. You expect to begin generating yearly profits of $11 million at the end of the first year and every year thereafter. You expect the joint venture to last forever. Plan III. Spend $100 million today to buy stock in google on which you expect an annual rate of return of 12% which you expect to continue forever. The market interest rate is 10%. (Assume the inflation rate is constant at 0, and is expected to remain so for the duration of the above investments) A) which of the above plans would you undertake if you could undertake just one. Explain your answer and show any calculations. B) which of the pland would you do if you could do as many of them as you wish. Explain your answer and show any calculations C) if the prevailing market interest rate were 8%, and you could choose as many of the above plans as you liked. Which would you choose?