paper 3 formulas

Question 1

gearing %

Answer 1

non-current liabilities/ capital employed x100
capital employed= non-current liabilities + total equity
total equity= retained earnings/reserves and share capital

above 50%= high gearing (more than half of long term funding borrowed)
below 50%= low gearing (less than half of long term funding borrowed)

Question 2

return on capital employed %

Answer 2

operating profit/capital employed x100

Question 3

time series analysis

Answer 3

too complicated- use notes from class

Question 4

payback years and months

Answer 4

1. unless provided, calculate net cash flow for each year (inflows-outflows)
2. from initial investment costs, deduct year 1 cash flow. Have you paid it off?
3. continue to deduct each years’ cash flow from what is remaining until what is left to pay off is LOWER number than the cash flow in the following year. at this point you will have your full number of years
   4 to calculate the months, use the formula (amount to pay/amount received in the following year x12)

e.g. initial costs= £10m.
cash flow: yr1: £2m, yr2: £3m, yr3: £4m, yr4: £5m
yr1: 10-2=8mil, yr2: 8-3=5mil yr3: 5-4=1mil. By end of year 3 there is 1mil left to pay and 5mil coming in yr4 so… 1/5 x12= 2.4 months.
ANSWER: 3yrs and 2.4 months

Question 5

average rate of return (ARR) %

Answer 5

1. total net cash flow-investment= project lifetime “profit”
2. “profit”/number of yrs life of project= average annual return
3. average annual return/initial investment x100

e.g. initial costs= £10m.
cash flow: yr1: £2m, yr2: £3m, yr3: £4m, yr4: £5m
so total cash flow= 2+3+4+5= £14-10= total profit of £4m.
£4m/4yrs= £1m annual profit
£1m/10m (initial costs) x100= 10%

Question 6

net present value (discounted cash flow) £

Answer 6

1. unless provided, calculate the net cash flow for each year
2. apply relevant discount factor for each year as provided in the exam extract to calculate the discounted net cash flow
3. add up the discounted net cash flow figures across the life of the project to reach an overall net present value of the project at the end of its life
4. • the initial costs of investment

e.g. initial costs= £10m
discount factors: yr1:£0.98 yr2:£0.95m yr3:£0.92 yr4:£0.87
net cash flow: yr1:£2m x 0.98= 1.96 yr2: £3m x 0.95= 2.85 yr3: £4m x 0.92= 3.68 yr4: £5m x 0.87= 4.35 TOTAL: £12.84m
£12.84m-£10m.
ANSWER: £2.84m