For all problems involving computation, you must show your work to receive any credit. Two points will be deducted for arithmetic errors, if all other components of your answer are correct.
1.Find the future value of $500, invested at 6% annual interest, compounded monthly, for three years?
2. Find the present value of $374, paid exactly nine years from now, if the required rate of return is 9%.
3. You're saving for your daughter's college expenses. She's now seven years of age, and you assume she'll start college at age eighteen. You figure that the total for four years of college will be $150,000. If you can earn 2% interest on a college savings account, how much will you need to put in the account now to have $150,000 when your daughter starts college?
4.If the present discounted value of $139 received a year from today is $125, what is the discount rate?
5. A factory costs $800,000. You reckon that it will produce an inflow after operating costs of $170,000 a year for 10 years. If the opportunity cost of capital is 14%, what is the net present value (NPV) of the factory?
6. 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 $150,000, payable up front, while revenues are expected to be $7,500 per year, forever.
a.If the interest rate on comparable assets is 4%, is this project worthwhile? Show your calculations.
b. What is the project's internal rate of return (IRR)? Show your calculations.
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 in return for an up-front payment from them of $15,000. You figure it will cost you $5,000 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: $15,000
Costs in Year 1: $ 5,000
Costs in Year 2: $ 5,000
Costs in Year 3: $ 5,000
c. Find this project's internal rate of return (IRR). Show your calculations.