Corporate Finance, Module 2: "How to Calculate Present Values"
The homework exercises are modeled after the practice problems for this module. The cover the basic formulas needed for net present value calculations. The final exam tests the financial theory, not the background mathematics, but these methods are needed to solve the financial problems.
Exercise 2.1: Compounding Intervals
What is the value of $6,000 after 6 years invested at 3% a quarter?
Exercise 2.2: Doubling Investments
How long will it take a dollar to double if it is invested at
Use logarithms to compute the answer: $2 = $1 × (1 + r)t A ln 2 = t × ln (1 + r).
Exercise 2.3: Net Present Value
What is the net present value of an investment of $2,500 that produces income of $670 a year for 5 years at a discount rate of 10% per annum? Show the solution with discount factors and with the annuity formula.
Exercise 2.4: Net Present Value
What is the net present value of an investment costing $2,000 that produces cash flows of $700 in year 1, $700 in year 2, and $900 in year 3 if the discount rate is 10%?
Exercise 2.5: Savings and Consumption
A worker now has $10,000 and expects to save an $5,000 next year and then pay $4,000 in 2 years’ time and $3,000 in 3 years’ time for a new car. How much of the present savings can the worker spend now on a dining room set if savings earn 7%?
Exercise 2.6: Perpetuity
A lottery winner receives $750 in 1 year’s time and annually thereafter in perpetuity. What is the value of this perpetuity at an interest rate of 10%?
Exercise 2.7: Delayed Perpetuity
How much is the previous perpetuity worth if it begins in 10 years time instead of in 1?
Exercise 2.8: Growing Perpetuity
If the lottery winner receives $750 in 1 year’s time and this amount increases 5% per annum, what is the present value of this growing income stream at a 10% interest rate?