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Question 1 1. Find the PV of a stream of payments lasting 6 years. Each payment is for $450, and the discount rate is 3.5%. 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 = $125 (received at the end of each year) Discount rate = 6.25% 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 $75,000, and that they have a present discounted value of $2,000,000, which is his asking price for the business. Calculate the discount 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 $550,000, payable up front, while revenues are expected to be $42,000 per year, forever. Assume profits are always received at the end of the year, and the only cost of the project is its acquisition price, $550,000, payable immediately. 4(a). If the rate of return on comparable projects is 3%, is this project worthwhile? Show your calculations. 4(b). What is the project's internal rate of return (IRR)? Show your calculations. 4(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 $75,000 immediately. You figure it will cost you $27,500 a year in supplies to provide this culinary joy. 5. You are the manager of General-Ford, a large North American automobile manufacturer. Demand for your product has been high and you are looking at the following three alternative plans: Plan I: Spend $84 million today on a factory in Alabama that will be completed in 1 year. You expect to receive $30 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 competitor, for a further $60 million. Plan II: Spend $110 million today in a joint venture with Nisubishi. You expect to begin generating yearly profits of $12.5 million at the end of the first year and every year thereafter. You expect the joint venture to last forever. Plan III: Spend $120 million today to buy stock in Google on which you expect an annual rate of return of 10.25%, which you expect will continue forever. The market interest you could achieve if you do not invest in any of the three is 9.5%. (Assume the inflation rate is constant at 0, and is expected to remain so for the duration of the above investments.) 5(a). Which of the above plans would you undertake if you could undertake just one? 5(b). Which of the plans would you do if you could do as many of them as you wish? 5(c). If the prevailing market interest rate were 6.5%, and you could choose as many of the above plans as you liked, which would you choose