Financial Maths

Question 1

What is interest? (4)

Answer 1

• The cost for borrowing and the reward for saving
• Compound interest is when interest is accumulated
• Simple interest is when interest is received periodically
• Also referred to as ‘cost of capital’ or ‘time value of money’

Question 2

How do you calculate simple interest?

Answer 2

FV = original principal amount x [1 x (r x n)]
E.g. 5% pa over 3 years on £1000
FV = 1000 x [1 x (0.05 x 3)
FV = £1150

Question 3

What is compound interest? (2)

Answer 3

• Interest earned is ‘rolled over’ into subsequent periods e.g. yearly
• Assumes that interest is reinvested

Question 4

How do you calculate compound interest?

Answer 4

• FV = PV (1+r)^2
• FV = future value / PV = amount deposited / r = interest / n = number of years/period

Question 5

What is an annuity and how do you calculate it? (4)

Answer 5

• Equal cash payments
• Received or made at regular intervals
• Over a specified period of time
• PV of annuity = £X x 1/r [1-1/(1+r)^n)
• £X - annuity payment each year / r - rate of interest / n - number of years /
  E.g. regular mortgage payments

Question 6

What is a perpetuity and how do you calculate it? (6)

Answer 6

• Equal cash payments
• Received or made at regular intervals
• Over an unspecified amount of time (into perpetuity)
• PV value of perpetuity = £x/r
• £x - annual payments / r - discount rate
• Used to value investments that have fixed periodic cash flows that are paid indefinitely e.g. standard preference share

Question 7

What are annualised rates? (4)

Answer 7

• Some credit statements do not state annual rates and therefore this is charged monthly
• The annual rate is a simple rate and assumes no compounding has occurred.
• To work out the monthly charge, simply divide annual APR by 12
• Annual percentage rate = APR e.g. 18%/12= 1.5% on outstanding balance a month. If paid, the amount is nothing. If not paid, the amount owed will compound

Question 8

How do you calculate APR and monthly rate? (2)

Answer 8

• APR = (1+monthly rate)^12-1
• Monthly rate = 12 square route APR-1

Question 9

When might discounting be applied? (4)

Answer 9

• To test the viability of a project such as the construction of a building or the purchase of a financial
• There are two main discounted cash flow (DCF) techniques used for project appraisal purposes:
• Net present value (NPV)
• Internal rate of return (IRR)

Question 10

What is the net present value approach? (3)

Answer 10

• Measures the present value of cash inflows against cash outflows to determine viability of investments
• NPV = PVi - PVo
• PVi - present value of all inflows / PVo - present value of all outflows

Question 11

What is the net present value approach? (5)

Answer 11

• Measures the present value of cash inflows against cash outflows to determine viability of investments
• NPV = PVi - PVo
• PVi - present value of all inflows / PVo - present value of all outflows
• If NPV is equal to or greater than 0, it is viable
• If NPV is less than 0, it is not viable

Question 12

What is the internal rate of return approach? (5)

Answer 12

• It is the discount rate that will equate the net present value of an investment as 0
• Present value of inflows equals the present value of outflows
• IRR of the project must be compared to the company’s cost of capital (the cost of equity and the cost of debt).
• If a company’s cost of capital is less than or equal a projects IRR, investment should be accepted
• If a company’s cost of capital is more than a projects IRR, investment should not be rejected

E.g. if an investment has an IRR of 15% and the cost of capital was only 10%, it would be accepted

Question 13

What is the internal rate of return approach? (5)

Answer 13

• It is the discount rate that will equate the net present value of an investment as 0
• Present value of inflows equals the present value of outflows
• IRR of the project must be compared to the company’s cost of capital (the cost of equity and the cost of debt).
• If a company’s cost of capital is less than or equal a projects IRR, investment should be accepted
• If a company’s cost of capital is more than a projects IRR, investment should not be accepted

Question 14

What are the problems with IRR? (5)

Answer 14

• IRR ignores the quantity of earnings e.g if a firms has limited choice of Project A which returns 20% on £100k and Project B which returns 40% on £10k, the lower IRR project is likely to be more appealing since it generates higher actual earnings
• IRR cannot be used when the discount rate is variable - though it would still be possible to calculate the NPV
• If the project has a number of inflows and outflows over time, then it may result in multiple IRRs
• If there is a big difference between the IRR and the project discount rate, may result in conflicting decisions
• Because IRR has limitations, NPV technique provides a superior method to evaluate the viability of a project

Question 15

How do you calculate the IRR in an exam? (2)

Answer 15

• You use all the multiple choice answers
• PV annuity formula