Introduction (w1)

Question 1

What are the 3 things that shareholders want?

Answer 1

• Maximise current wealth
• Transform wealth into consumption in the most desirable way
• Manage risk

Question 2

Why is profit maximisation problematic? (2 reasons)

Answer 2

• Prioritising profits in a short term damages long term value
• Profits can be manipulated by decreasing dividend

Question 3

What is a cost of capital?

Answer 3

A minimum rate of return accepted by the investors (shareholders)

Question 4

What is the opportunity cost of capital?

Answer 4

The foregone return from investing in an alternative project

Question 5

What is the equation for future value of £x?

Answer 5

Future Value = £x * (1+r) ^t

where t = number of times compounding occurs during the period
if compounded annually, t = years

Question 6

What is the equation for present value of £x?

Answer 6

Present Value = discount factor * value in period t

where DF = 1 / (1+r)^t

Question 7

What are the steps in calculating NPV?

Answer 7

1. Forecast cash flows in t0 and tn
2. Estimate the discount rate using opportunity cost of capital
3. Discount future cash flows
4. Sum the discounted payoffs

Question 8

How to calculate the rate of return on an investment?

Answer 8

Return = profit / investment

where profit = payoff - investment

Accept the project if return > opportunity cost

Question 9

What is the difference between perpetuity and annuity?

Answer 9

Perpetuity is an annuity with an infinite number of cash flow periods

Question 10

What is a today’s value of perpetuity if the annual cash flow (received for eternity) is £100 and the discount rate is 10%?

Answer 10

Present value of perpetuity = cash flow / discount rate

PV = £100 / 0.10 = £1000

Question 11

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?

Answer 11

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)

Question 12

What is the equation for calculating present value of an annuity?

Answer 12

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

Question 13

How to calculate an annual loan payment, when the value of loan, rate and no of years is given?

Answer 13

Annual loan payment = value of loan / annuity factor

where annuity factor = 1/r - 1 / r(1+r)^t

Question 14

How to calculate the value of the loan when the annual payment, no of years and the rate is given?

Answer 14

PV of loan = annual loan payment * annuity factor

where annuity factor = 1/r - 1 / r(1+r)^t

Question 15

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)?

Answer 15

Future value of annuity = C * [ (1+r)^t - 1 ] / r

Question 16

How to calculate a present value of a perpetuity which has an annual growth rate?

Answer 16

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

Question 17

What is annual percentage rate? How is it calculated?

Answer 17

Annualised interest rate, uses simple interest rate

APR = monthly rate * 12

Question 18

What is effective annual interest rate? How is it calculated?

Answer 18

Annualised interest rate which accounts for interest compounding

Often, APR needs to be converted into EAR

EAR = (1+ monthly rate) ^12 - 1

Question 19

What is the internal rate of return? Are projects with higher or lower IRR more desirable? When would an investment opportunity be accepted?

Answer 19

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

Question 20

What are the y-axis and x-axis of the IRR graph? Is the graph concave or convex and why?

Answer 20

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

Question 21

What are a 3 disadvantages of IRR?

Answer 21

1. As it is a quadratic function, for certain NPV the convex curve might intercept the NPV = 0 twice, giving 2 values for IRR
2. Subsequently, if the IRR curve is U-shaped, for certain values, the NPV increases as IRR increases
   - the 2 should have an inverse relationship
3. It assumes fixed rate throughout the project i.e., assumes that the funds generated in each year are reinvested at the IRR rate

Question 22

How is profitability index calculated? What are its benefits over NPV?

Answer 22

Profitability index = NPV / initial investment

It accounts for the size of the investments and weights the NPV proportionally to it