Hello, if possible, could you please do by tonight? My primary question is 4c. It asks for calculations, but in the lecture they said it is impossible to solve for IRR without a specialty calculator.

Problem Set 3 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. PV = Yearly Revenue $450 i=3.5% N=6 years PV = $366.15 Given a $450 payment at a discount rate of 3.5% for 6 years, the present value of the stream of payments is $366.15. 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. Yearly Payment = $125 i = 6.25% $1923.08 Given a yearly payment of $125 in a perpetuity at a discount rate of 6.25%, the Present Value of the payment would be $1923.08. 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. PDV = $2,000,000 Annual Profits = $75,000 i = 0.0375 Discount Rate = 3.375% With a Present Discounted Value of $2M and annual profits of $75,000 in perpetuity, the discount rate would equate to 3.375%. 4 (30 pts.). 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. PV of Cash outflows = $500,000 (one time) Cash Inflows = $42,000 (annually) Opportunity cost = i = 3% NPV = PV of Cash inflows - PV of Cash Outflows NPV = NPV = 1400000 - 550000 NPV = 850000 Given an opportunity cost of 3% for the exchange of a one time cost of $550,000 for an annual return of $42,000, the Net Present Value would equal $850,000. This would certainly be a worthwhile project to invest in, since the Net Present Value is not only positive, but a high value above the one time start up cost. 4(b). What is the project's internal rate of return (IRR)? Show your calculations. The Internal Rate of Return is the opportunity cost (i) value required for the Net Present Value to equal zero. NPV = 0 PV of Cash outflows = $500,000 (one time) Cash inflows = $42,000 (annually) NPV = PV of Cash inflows - PV of Cash Outflows 0= i = 7.64% For the Net Present Value to equal zero, the Internal Rate of Return would be 7.64%. 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. So, the revenue and costs of the project can be summarized as follows: Immediate and only revenue: $75,000 Costs in Year 1: $27,500 Costs in Year 2: $27,500 Costs in Year 3: $27,500 Find this project's internal rate of return (IRR). Show your calculations. NPV = 0 Cash Outflows = $27,500 (annually) Cash inflows = $75,000 (one time) NPV 0= 75000 = i = 0.0492 IRR = 4.92% Given the one-time Cash inflow of $75,000 and a Cash out flow of $27,500 annually for three years, the internal rate of return would have to equal 4.92%. This would mean that it would require a discount rate of 4.92% for the Cash inflow to equal the cash outflow in three years' time. 5. (40pts.) 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? NPV = Plan I - Cash Outflows = $84,000,000 NPV = Cash inflows total = $90,000,000 i = 9.5% NPV = Plan II - Cash Outflows = $110,000,000 $5.48M Cash inflows = $12.5M (perpetuity) i = 9.5% NPV = PV of Cash Inflows - PV of cash outflows NPV = NPV = $131.58 - $110M = $21.58M Plan III - Cash outflows = $120M Cash inflows = 10.25% (perpetuity) = $12.3 i = 9.5% NPV = NPV = $129.47M - $120M NPV = $9.47M When considering the calculations above for each of the plan options, I would chose to undertake Plan II. This is because Plan II has the greatest return at Net Present Value. 5(b). Which of the plans would you do if you could do as many of them as you wish? If there was no restriction to the number of plans I could proceed with, I would chose to proceed with all three plans. I would make this decision based on the fact that all three plans had a positive Net Present Value, therefore, in accordance with the Net Present Value Rule, one should undertake any project with a positive Net Present Value. 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? NPV = Plan I - Cash Outflows = $84,000,000 Cash inflows total = $90,000,000 i = 6.5% NPV = NPV = Plan II - Cash Outflows = $110,000,000 $5.64M Cash inflows = $12.5M (perpetuity) i = 6.5% NPV = PV of Cash Inflows - PV of cash outflows NPV = NPV = $192.31 - $110M = $82.31M Plan III - Cash outflows = $120M Cash inflows = 10.25% (perpetuity) = $12.3 i = 6.5% NPV = NPV = $189.23M - $120M NPV = $69.23M If there were to be a decrease in the interest rate in the market, I would still chose all three plans. This would be the proper course of action because all three plans had positive Net Present Value, and according to the Net Present Value Rule, one should undertake any project with a positive Net Present Value