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Summary IB114_FM_Week 1b_Financial Arithmetic
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Financial Arithmetic. Notes summarising all the content from lectures and include worked examples to better understand concepts. Grade attained: 83%
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[T1W1] - FINANCIAL ARITHMETICCOMPOUND GROWTH
DISCOUNT FACTORS AND PRESENT VALUES
The opportunity cost of capital is r
The discount factor, 1/(1+r)n reflects the time value of money
ANNUITIES
An annuity is a finite stream of N equal future cash flows, C, at regular intervals
● Annuity Factor, AN,R is the sum of the corresponding N present-value factors, calculated using R
as discount rate
● Present Value of Annuity is the product of annual cash flow, C and annuity factor
Delayed Annuity - Annuity begins at a date many periods in the future
1. Calculate Present Value of the annuity
Since the formula values the annuity as one period prior to first payment, E.g. If first payment is paid
out at date 6, the annuity is valued at date 5
2. Discount the PV of the annuity back to date 0
, E.g. Because annuity formula brings back the annuity to date 5, the second calculations must discount
over remaining 5 periods (n = 5) to discount PV of annuity to date 0.
Annuity Due - First annuity payment begins at date 0
PV = Payment at date 0 + Present value of Annuity
E.g. If 20 year annuity with payments of £50,000 starting at Year 0, discount rate is 8%
£50,000 + £50,000 x A19,0.08 = £530,180
Infrequent Annuity - Annuity payments occurring less frequently than once a year
1. Determine the interest rate over the period between payments, where annual interest rate is, r, and
number of periods between payments is n.
Interest rate over n periods = (1+r)n - 1
E.g Annuity of £450 payable once every 2 years over a 20-year period. Annual interest rate is 6%.
Interest rate of 2-year period = (1.06)2 -1 = 12.36%
2. Find PV of annuity over [total number of periods / number of periods between payments]
E.g. Annuity of £450 payable once every 2 years over a 20-year period. PV = 450 x A 10,0.1236 =
£2,505.57 where r in AN,R is the interest rate over n periods.
Equating PV of Two Annuities - Equating PV of inflow with PV of outflows
Question requires current inflow over n number of years to equate the outflow over the following m
years. (Page 256 of Corporate Finance)
1. Calculate the PV of the outflow over m years
2. Discount the PV of the outflow at date 0,
3. Annuity of cash inflow will equate PV of outflow at date 0,
Growing Annuity
A Growing Annuity is a finite steam of growing cash flows
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