Page 52 - DMGT409Basic Financial Management

Unit 3: Time Value of Money

Solution: Notes

⎛ 0.10⎞ 4
ERI = 1 + 4 ⎠ ⎟ − 1
⎜
⎝
= 1.1038 – 1 = 0.1038 or 10.38 per cent.
Sinking Fund Factor

The financial manager may need to estimate the amount of annual payments so as to accumulate
a predetermined amount after a future date, to purchase assets or to pay a liability. The following
formula is useful to calculate the annual payment.
⎛ I ⎞
A = FVA
p n ⎜ n ⎟
⎝ (1 I+ ) − 1⎠
Where,
A = Annual payment.
p
VA = Future value after ‘n’ years.
n
I = Interest rate.
⎛ I ⎞
⎜ n ⎟ = FVIFA . In
+
⎝ (1 I ) − 1⎠
Illustration 22: 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 ⎟
+
p ⎝ (1 0.12 ) − 1⎠
= 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
Present Value of Perpetuity

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

PV = CIF X PVIFA
∝ I .∝
Where,
PV = Present value of a perpetuity.
∝
CIF = constant annual cash infl ow.

PVIFA = PV interest factor for a perpetuity.
I .∝
PV = CIF/I
∝

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