1. CALCULATIONS…

2. Calculation examples (I.)
What is the rate of return if $1,000 investment yields $1,200? (20%)
What will be the future amount if we invest $500 at 12%? ($560)
What will be the future amount in 3 years if we invest $500 at 12% compounded annually? ($702)
What is the average annual compounded rate if $800 investment grows to $1,500 in 6 years? (11.05%)
How much $ will accrue to $10,000 in 5 years if the yearly (compounded) rate of return is 10%? ($6,209)

3. Calculation examples (II.)
Approximately what yearly (compounded) rate of return will double or triple a given amount in 10 years? (double: 7.18%; triple: 11.61%)
Approximately in how many years will a given amount accrue to ten times its starting value if the yearly (compounded) rate of return is 15%? (16.5 years)
How many times as much is an amount that will be compounded for 20 years from now at a rate of return of 15% as it would be if its returns were not compounded? (4.1 times)

4. Calculation examples (III.)
At least how many periods from now should an F = 100 cash flow occur so that its present value is smaller than 50, if the discount rate is 10%? (7.27 periods)
What discount rate makes the present value of an F = 150 cash flow due in 8 periods equal to 90? (6.59%)
What is the real rate of return if the nominal rate of return is 10% and the rate of inflation is 3%? (6.8%)
What will be the future amount, in nominal terms, if $1,000 grows for 3 years at an annual real rate of 5%, and the rates of inflation are 2%, 4%, and 3%, for the 1st, 2nd, and 3rd year, respectively? ($1,265)

5. Calculation examples (IV.)
What will be the future amount, in real terms, if $1,000 grows for 2 years at an annual nominal rate of 10%, and the rates of inflation are 4% and 7%, for the 1st and 2nd year, respectively? ($1,087)
There is an investment opportunity with the following possible cash flow outcomes and their respective probabilities: F1 = $5,000, F2 = –$3,000, F3 = $2,000, p1 = 10%, p2 = 20%, p3 =70%. The utility function of the investor is U(W) = lnW, and his starting wealth (W0) is $5,000. Should this opportunity be taken (and why)? What are the certainty equivalent and the risk premium of this opportunity? (The inverse function of lnW is eW.) (YES; CE: $646; RP: $654)

6. Calculation examples (V.)
… run the same for F1 = $10,000, F2 = –$3,000, F3 = –$1,000, p1 = 20%, p2 = 30%, p3 = 50%, and W0 = $8,000. (NO; CE: –$356; RP: $956)
What is the expected return of the project that generates $2 million future cash flow in one period from $1.6 million initial investment? Should this project be accepted if its cost of capital is 15%? What is the NPV and IRR of the project? (25%; YES; NPV: $0.14 million; IRR: 25%)

7. Calculation examples (VI.)
What is the net present value of the following cash flow series: F0 = –$6,000, F1 = $2,000, F2 = $5,000, F3 = $4,000, if the cost of capital is 15%? Should this project be undertaken (and why)? (NPV: $2,150; YES)
… run the same for F0 = –$10,000, F1 = $3,000, F2 = $4,000, F3 = $5,000, and r = 20%. (NPV: –$1,829; NO)