Introduction (w1) Flashcards
What are the 3 things that shareholders want?
- Maximise current wealth
- Transform wealth into consumption in the most desirable way
- Manage risk
Why is profit maximisation problematic? (2 reasons)
- Prioritising profits in a short term damages long term value
- Profits can be manipulated by decreasing dividend
What is a cost of capital?
A minimum rate of return accepted by the investors (shareholders)
What is the opportunity cost of capital?
The foregone return from investing in an alternative project
What is the equation for future value of £x?
Future Value = £x * (1+r) ^t
where t = number of times compounding occurs during the period
if compounded annually, t = years
What is the equation for present value of £x?
Present Value = discount factor * value in period t
where DF = 1 / (1+r)^t
What are the steps in calculating NPV?
- Forecast cash flows in t0 and tn
- Estimate the discount rate using opportunity cost of capital
- Discount future cash flows
- Sum the discounted payoffs
How to calculate the rate of return on an investment?
Return = profit / investment
where profit = payoff - investment
Accept the project if return > opportunity cost
What is the difference between perpetuity and annuity?
Perpetuity is an annuity with an infinite number of cash flow periods
What is a today’s value of perpetuity if the annual cash flow (received for eternity) is £100 and the discount rate is 10%?
Present value of perpetuity = cash flow / discount rate
PV = £100 / 0.10 = £1000
What is today’s value of perpetuity if the annual cash flow is $100 and the discount rate is 10% but the investment only starts paying out in 3 years?
Regular calculation for present value of perpetuity must be adjusted by the discount factor, where DF = 1 / (1+r)^t
PV = (C / r) * 1 / (1+r)^t
PV = £100 / 0.10 * (1 / 1.10^3)
What is the equation for calculating present value of an annuity?
Present value of annuity = [ perpetuity factor - annuity factor ] * annual payoff
PV = [ ( 1/r ) - 1 / r(1+r)^t ] * C
note that the delayed payoff is usually calculated as (C / r) * 1 / (1+r) ^t, however if C = £1 (which is assumed when calculating a FACTOR), the equation simplifies to 1 / r(1+r)^t
How to calculate an annual loan payment, when the value of loan, rate and no of years is given?
Annual loan payment = value of loan / annuity factor
where annuity factor = 1/r - 1 / r(1+r)^t
How to calculate the value of the loan when the annual payment, no of years and the rate is given?
PV of loan = annual loan payment * annuity factor
where annuity factor = 1/r - 1 / r(1+r)^t
How to calculate a future value of an annuity (i.e., the total payoff in x years time, assuming a fixed annual rate of return)?
Future value of annuity = C * [ (1+r)^t - 1 ] / r
How to calculate a present value of a perpetuity which has an annual growth rate?
PV = C / (r-g)
As PV of a perpetuity = C / r or C * 1/r, growing perpetuity decreases the discount factor by reducing the denominator to account for the fact that the perpetuity is growing
What is annual percentage rate? How is it calculated?
Annualised interest rate, uses simple interest rate
APR = monthly rate * 12
What is effective annual interest rate? How is it calculated?
Annualised interest rate which accounts for interest compounding
Often, APR needs to be converted into EAR
EAR = (1+ monthly rate) ^12 - 1
What is the internal rate of return? Are projects with higher or lower IRR more desirable? When would an investment opportunity be accepted?
Discount rate (r), used in the calculation of NPV, which generates NPV = 0
The higher the IRR, the more desirable the investment as the project would have to reach a much higher discount rate to start generating losses
At a minimum, project’s IRR should exceed the cost of capital in order to be pursued
What are the y-axis and x-axis of the IRR graph? Is the graph concave or convex and why?
y-axis: NPV
x-axis: discount rate
The graph is convex and has diminishing marginal decrease as the absolute decrease in value, using the same discount rate, decreases as the NPV gets lower
What are a 3 disadvantages of IRR?
- As it is a quadratic function, for certain NPV the convex curve might intercept the NPV = 0 twice, giving 2 values for IRR
- Subsequently, if the IRR curve is U-shaped, for certain values, the NPV increases as IRR increases
- the 2 should have an inverse relationship - It assumes fixed rate throughout the project i.e., assumes that the funds generated in each year are reinvested at the IRR rate
How is profitability index calculated? What are its benefits over NPV?
Profitability index = NPV / initial investment
It accounts for the size of the investments and weights the NPV proportionally to it
