Page 40 - DMGT515_PERSONAL_FINANCIAL_PLANNING

Unit 2: Time Value of Money

⎛ I ⎞ Notes
A = FVA
p n ⎜ n ⎟
⎝ (1I+ ) − ⎠
1
Where,
A = Annual payment.
p
VA = Future value after ‘n’ years.
n
I = Interest rate.
⎛ I ⎞
⎜ n ⎟ = FVIFA I.n
⎝ (1I+ ) − ⎠
1
Illustration 28
The finance manager of a company wants to buy an asset costing ` 1,00,000 at the end of 10 years.
He requests to find out the annual payment required, if his savings earn an interest rate of 12 per
cent per annum.
Solution:

⎛ 0.12 ⎞
A = 1,00,000 ⎜ 10 ⎟
+
1
p ⎝ (10.12 ) − ⎠
= 1,00,000 (0.12 or 2 / 2.1058) = ` 5698.5
1
A = 1,00,000 ×
p
FVIFA
12%.10y
1
= 1,00,000 ×
17.548
= ` 5698.65

2.11.1 Present Value of Perpetuity

Perpetuity is an annuity of infinite duration. It may be expressed as:

PV = CIF × PVIFA
µ I .µ
Where,
PV = Present value of a perpetuity.
µ
CIF = Constant annual cash inflow.
PVIFA = PV interest factor for a perpetuity.
I .µ
PV = CIF / I
µ
Illustration 29
Mr. Bhat an investor, expects a perpetual amount of ` 1000 annually from his investment. What
is his present value of this perpetuity if the interest rate is 8 per cent?
Solution:
PV = CIF/I = 1000/0.08 = ` 12,500
µ

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