2b. Present and Future Values (extended) Flashcards
What is the difference between Future Value and Present Value?
- Future value looks at what an investment made today will grow to at a specific point in the future, given a certain rate of interest (or growth rate).
- Present value calculates how much a future sum of money is worth today, given a certain discount rate. It’s the inverse of future value.
What is the formula for Present Value
Where Ct is the cash flow of dollars at the end of year t,
and r is the discount rate
What does the discount factor really measure?
The present value of a dollar received at the end of year t.
What does this principle mean? “A safe dollar is worth more than a
risky dollar”
Most investors dislike risky ventures and won’t invest in them unless they see
the prospect of a higher return. The riskier the venture, the less that they will be prepared to
pay and the higher the return that they will demand.
What is the opportunity cost of capital?
The opportunity cost of capital is the rate of return that the shareholders could get by investing on their own at the same level of risk
What should you not forget about opportunity cost of capital?
that it looks at the rate of return at the SAME LEVEL of risk!!!
What are the 2 rules that can be used to justify a particular investment?
Net Present Value rule - Accept investments that have positive NPVs
Rate of Return Rule - Accept investments that offer rates of return in excess of their opportunity costs of capital
What other formula can be used when it comes to present values with multiple cash flows?
DCF - Discounted Cash Flow formula
The Σ refers to the sum of the series of discounted cash flows
To use NPV, add the (usually negative) initial cash flow
If you are considering a construction project of $700k, and the bank lends at 8% interest. Does this mean the cost of capital is 8%?
NO!!
- The interest rate on your loan has NOTHING to do with the risk of the project
–> it just reflects the (in this case good) health of your business - Whether you take the loan or not, you still face the choice between the office building and an equally risky investment.
IF you loan $700k from the bank and invest it into the building, whilst an equally risky portfolio in the stock market would generate greater returns - YOU ARE A FOOL
A normal perpetuity is distributed at the end of each year (and thus the first payment is only after just a little less than a year), but what do you call a perpetuity that starts IMMEDIATELY?
A “perpetuity due”
How do you calculate a “perpetuity due”?
Just add on the first years cash flow to a regular perpetuity
What is (r) - the annual rate of return on a perpetuity?
The promised annual payment divided by the present value
eg. 10 million present value, annual payment of 1m = 0.1
How do you calculate a delayed perpetuity?
Imagine a $1B in perpetuity for 10y, but payments only start in year 3…
It basically turns into a normal perpetuity from year 3… to find the “delayed” perpetuity, we would discount the figure by (1 + r)^3
A normal annuity is distributed at the end of each year (and thus the first payment is only after just a little less than a year), but what do you call an annuity that starts IMMEDIATELY?
An “annuity due”
What does “amortizing” mean?
part of the regular payment is used to pay interest on the loan and part is used to
pay off or “amortize” the loan
Why is growing perpetuities used?
think back to your plans to donate $10 billion to fight malaria and other infectious diseases. Unfortunately, you made no allowance for the growth in salaries and other costs, which will probably average about 4% a year starting in year 1. Therefore, instead of providing $1 billion a year in perpetuity, you need to provide $1 billion in year 1, 1.04 × $1 billion in year 2, and so on.
The perpetual stream of income in the above calculation would keep pace with the growth rate in costs
