7. Financial Maths

Question 1

Simple interest

Answer 1

interest is paid only on the original principle

v=p(1 + r x n)

p = principle amount

r = rate

n = number of years

Question 2

Compound interest

Answer 2

used more regularly, interest on balance brought forward

v=p(1 + r)^n

p = principle amount

r = rate

n = number of years

Question 3

equivalent rates

Answer 3

loan stated 8% interest per annum charged every 6 months = 4% would be charged every 6 months

£1 original amount

£1 x 1.04 = £1.04 June

£1.04 x 1.04 = £1.0816 December

(higher than 8% originally quoted)

Question 4

Depreciation

Answer 4

value of item goes down at a specified rate reflecting its usage and reduction in useful life

v= p x (1-r)^n

Question 5

terminal values

Answer 5

always draw a timeline work out how many years the original amount is going to earn interest on and at what rate then do the same for the additional amounts added add together to get final amount

Question 6

Sinking fund

Answer 6

constant amount is invested every year need to know when the first and last instalments are always draw a timeline work out as per terminal values

Also known as a geometric progression

Question 7

A

Answer 7

S = sum of money

R = rate

A = initial term

Question 8

The time value of money

Answer 8

money received today is worth more than the same sum received in the future due to;

potential earning

interest/ cost of finance

impact of inflation

effect of risk expressed as an interest rate for calculation purposes

Question 9

other terms for the time value of money

Answer 9

discount rate

required return

cost of capital

Question 10

Discounted cash flows - known present value

Answer 10

PV (1 + r)^n = FV

PV = present value

FV = future value

Question 11

Discounted cash flows - known future value

Answer 11

FV / (1 + r)^n

Question 12

Net Present Values NPV

Answer 12

if NPV is positive the project is viable

if NPV is zero the project breaks even

if NPV is negative the project is not financially viable

impacts on the shareholders wealth

Question 13

Annuity

Answer 13

where you receive a series of constant amounts until death or a set number of years

Question 14

How to calculate an annuity

Answer 14

use cumulative present value tables and net present value tables

Question 15

Perpetuity

Answer 15

An annuity that never finishes

1 / r

Question 16

internal rate of return IRR

Answer 16

NPV = 0 = IRR

if NPV is positive it will increase the share holders wealth

if discount rate is less than the IRR the project will have a positive NPV

Question 17

IRR formula

MUST LEARN

Answer 17

Question 18

Mortgages

Answer 18

The PV of the amount borrowed must equal to the PV of what you repay

is an annuity

use cumulative present value tables

Question 19

How to reval your mortgage after x years

Answer 19

eg 30,000 borrowed over 25 yrs at 12%

PV of loan = 30,000

PV of what you repay = 30,000 x 1 - r^-n / r (formula of formula sheet)

30,000 / 7.843 = 3825 annual payments

Interest rates go up to 14% at the end of year 2

Today = 30,000

1 yr = 30,000 x 1.12 = 33,660

less repayments = (3825)

balance =29,775

2 yr = 29,775 x 1.12 = 33,348

less repayments = (3825)

balance =29,523

refollow step 1 to work out annual payments at 14%

Question 20

how to calculate sinking fund payments

Answer 20

eg we want 50,000 in 6 years time 5.5%

1. Work out PV of 50,000 in 6 yrs time = 50,000 x 1/1.055^6

= 50,000 x 0.725 = 36,250

2. draw out timeline
3. t1 - t5 can use cumulative present values or annuity formula from table as t0 = 1
4. p (df @ t0 + df t1 - t5)

= 1 + 4.270

= 5.270