Lecture 4 - NPVs of annuities and perpetuities Flashcards
(36 cards)
What is the general formula for calculating NPV?
The general NPV formula discounts a series of future cash flows (C0, C1, …, Cn) at a constant discount rate, k, over time.
How do you value several cash flows occurring over a number of years?
The value is the sum of the present values of all cash flows, discounted by the appropriate rate for each period.
What is the Principle of Value Additivity?
The value of a set of independent cash flows is the sum of their individual present values.
What is an annuity?
An annuity is a series of equal cash flows (C) occurring at regular intervals over a fixed period.
How do you calculate the NPV of an annuity?
What is a perpetuity?
A perpetuity is a series of equal cash flows that continue indefinitely.
How do you calculate the NPV of a perpetuity?
Why are annuity and perpetuity formulae important in finance?
These formulae are essential for investment appraisal, estimating rates of return, and determining the cost of capital.
What is the annuity factor, and how is it used?
The annuity factor is a multiplier used to simplify the calculation of the NPV of an annuity. It is derived from annuity tables.
How do you interpolate the rate of return if it isn’t provided in the annuity table?
You can interpolate between values in the table or use a financial calculator to determine the exact factor.
What is the timeline approach for annuities and perpetuities?
The timeline approach illustrates when cash flows occur and helps calculate their NPVs at specific points in time.
How do you calculate the present value of a delayed perpetuity?
What is the present value of future present values (FPV)?
It is the present value of cash flows that occur after a certain period, discounted back to the present time.
What happens to the NPV when the discount rate changes over time?
The NPV calculation adjusts for the varying discount rates by applying each rate to the respective cash flow period.
How do you calculate the NPV with a variable discount rate?
The NPV is calculated by discounting each cash flow by its corresponding discount rate for that specific period.
What is the formula for the present value (PV) when the discount rate changes over time?
The concept is very similar to the traditional Net Present Value (NPV) formula, but instead of using a single, constant discount rate across all periods, you apply different discount rates to each cash flow based on the specific period they occur in
How does the changing discount rate affect the NPV calculation?
The changing discount rate requires each cash flow to be discounted by its specific rate for the period, resulting in a more complex NPV calculation that reflects the varying cost of capital over time.
What is an example of an NPV calculation with a variable discount rate?
A project with a 4-year life, net annual cash flows of £150,000, an initial investment of £500,000, and discount rates of 20%, 15%, and 10% for the respective years will have its NPV calculated by discounting each cash flow at the respective rate and summing the results.
What is the importance of using the correct discount rate in NPV calculations?
The correct discount rate reflects the opportunity cost of capital and risk. Using the correct rate ensures that the NPV calculation accurately reflects the present value of future cash flows, which is critical for sound investment decisions.
How do you calculate the present value of a delayed perpetuity?
The present value of a delayed perpetuity is calculated by first finding the future present value at the start of the perpetuity and then discounting it back to the present period. The formula is: PV(delayedperpetuity)=Ck×(1+k)nPV (delayed perpetuity) = \frac{C}{k \times (1+k)^n}PV(delayedperpetuity)=k×(1+k)nC, where C is the cash flow, k is the discount rate, and n is the number of periods of delay.
What is the significance of the annuity and perpetuity formulas in finance?
The annuity and perpetuity formulas are crucial for investment appraisal, determining the cost of capital, and estimating rates of return for investors. They simplify the calculation of the present value of cash flows that occur regularly over time.
How does the timeline approach help in NPV calculations for annuities and perpetuities?
The timeline approach helps visualize when cash flows occur, making it easier to apply the correct discount rate and formula (for annuity or perpetuity) to calculate their NPVs at specific points in time.
What is the example of ABC plc’s project for opening a store?
ABC plc plans to open a store with cash flows of -£10 million in year 0, -£6 million in year 1, and perpetual cash flows of £4 million starting from year 2. The project’s NPV can be calculated by summing the present values of these cash flows using the perpetuity formula for the cash flows from year 2 onwards .
How do you calculate the present value (PV) of perpetual cash flows for ABC plc’s project?
The PV of perpetual cash flows starting in year 2 can be calculated using the formula PV(P)=CkPV(P) = \frac{C}{k}PV(P)=kC, where C is the annual cash flow (£4 million) and k is the discount rate (5%). The PV of £4 million perpetuity is £80 million, which is the future present value viewed from the end of year 1 .
