Chap 2 Flashcards
Why are cash flows discounted?
Because (1) a dollar today is worth more than a dollar tomorrow and (2) a safe dollar is worth more than a risky one. Formulas for PV and NPV are numerical expressions of these ideas.
What is the rate, r, in the PV calculation? What does the PV calculation give you?
The rate, r, in the formula is called the discount rate, and the present value is the discounted value of the cash flow, Ct.
What is the discount factor, what does it measure?
1/(1+r)^t
- It measures the present value of one dollar received in year t.
If valuing an investment project using PV calculations, what is the opportunity cost of capital?
That’s the rate of return that your company’s shareholders could get by investing on their own at the same level of risk as the proposed project.
- “the return foregone by not investing in financial markets.”
How do you calculate the NPV?
What is the formula?
Net present value equals present value minus the required investment
NPV = C0 + C1/(1 + r)
What is the rate of return on an investment?
How is this calculated?
The rate of return is simply the profit as a proportion of the initial outlay:
Return = ____profit____
investment
What are the two rules that you may justify investments by?
∙ Net present value rule. Accept investments that have positive net present values.
∙ Rate of return rule. Accept investments that offer rates of return in excess of their opportunity costs of capital.
What is the DCF formula?
When is this formula used?
PV = C1/(1+r) + … + Ct/ (1+r)^t
Discounting all future cash flows to time = 0
To value a stream of cash flows extending over a number of years
What is the difference between NPV and PV?
Just remember, present value is the value of the investment today; net present value is the addition that the investment makes to your wealth.
When you discount the expected cash flows by the opportunity cost of capital, you are asking what of investors?
You are asking how much investors in the financial markets are prepared to pay for a security that produces a similar stream of future cash flows.
What type of security is a consol?
Consols are perpetuities. These are bonds that the government is under no obligation to repay but that offer a fixed income for each year to perpetuity
How do you calculate the PV of a perpetuity?
PV = C / r
How do you calculate the PV of a “delayed” perpetuity?
PV = (C / r)*(1/r)^k
where k = delayed time
Need to multiply by the k-year discount factor
What is an annuity?
An annuity is an asset that pays a fixed sum each year for a specified number of years.
What is the t-year annuity factor?
A(angle n at i)
but in this case “n” is “t”
The expression shows the present value of $1 a year for each of t years. It is generally known as the t-year annuity factor.
What is an annuity due?
A level stream of payments starting immediately is called an annuity due. An annuity due is worth (1 + r) times the value of an ordinary annuity.
What are ammortizing loans?
Loans that involve a series of level payments are known as amortizing loans. “Amortizing” means that part of the regular payment is used to pay interest on the loan and part is used to reduce the amount of the loan.
What is the PV formula for growing perpetuities?
- What assumptions are made about r and g?
PV = C / (r-g)
This assumes that r (opportunity cost of capital) is greater than g (growth rate).
- This can be derived using a geometric series as well.
How is the PV of a growing annuity calculated?
Assumptions on r and g?
PV = [1/(r-g)] * [1 - ((1 + g)^t) / ((1+r))^t]
k i tried
- Must assume that the discount rate r is greater than the growth rate g. If r = g, the formulas blow up and are useless.
How often do France and Germany pay interest on its bonds?
What about the United States and Britain?
In France and Germany the government pays interest on its bonds annually. However, in the United States and Britain government bonds pay interest semiannually.
How do you find the effective annual interest rate given the m-thly compounded interest rate?
- Solving for (1+i) given the m-thly compounded interest.
Ex. An interest rate of 10% compounded semiannually is equivalent to 10.25% compounded annually. The effective annual interest rate on the bond is 10.25%.
What is the APR?
- Annual Percentage Rate
ex. Suppose a bank offers you an automobile loan at an APR of 12% with interest to be paid monthly. This means that each month you need to pay 1% interest.
Thus the bank is quoting a rate of 12%, but the effective annual interest rate on your loan is 1.0112 – 1 = .1268, or 12.68%
What is the difference between APR and the effective annual interest rate?
APR: quoted interest
EAR: effective interest
When interest is paid once a year, what is the difference between the quoted and effective rate? W
What about when interest is paid more frequently than once a year?
When interest is paid once a year, the quoted and effective rates are the same. When interest is paid more frequently, the effective interest rate is higher than the quoted rate.
What does it mean when interest is compounded continuously?
A situation where the payments are spread evenly and continuously throughout the year, so the interest rate is continuously compounded.
In this case “m” is infinite.
Why do financial managers “pretend” that payments are continuous?
because (1) it simplifies the calculations and (2) it gives a very close approximation to the NPV of frequent payments.
How do you calculate the equivalent interest payment when given the continuously compounded rate?
(1+i) = e^delta
delta = ln(1+i)
How can an annuity be interpreted in terms of perpetuities?
Remember that an annuity is simply the difference between a perpetuity received today and a perpetuity received in year t.
