Page 50 - DMGT409Basic Financial Management

Unit 3: Time Value of Money

Present Value of a Series of Cash Flows Notes

Illustration 18: From the following information, calculate the present value at 10 per cent interest
rate.

Year 0 1 2 3 4 5
Cash infl ow (`) 2,000 3,000 4,000 5,000 4,500 5,500
Solution:
2000 3000 4000 5000 4500 5500
P = + + + + +
+
+
+
v
+
+
+
(1 0.10) 0 (1 0.10) 1 (1 0.10) 2 (1 0.10) 3 (1 0.10) 4 (1 0.10) 5
= 2000 + 2727 + 3304 + 3755 + 3073.5 + 3415.5 = ` 18.275
Present value can also be calculated by the following way:
Years Cash infl ow (`) PV Factor 10 per cent Present value (`)
0 2000 1.00 2000.0
1 3000 0.909 2727.0
2 4000 0.826 3304.0
3 5000 0.751 3755.0
4 4500 0.683 3073.5
5 5500 0.621 3415.5
Total present value 18275.0
(c) Present value of even cash flows (annuity)
Present Value of Deferred Annuity

CIF CIF CIF CIF
PVA = 1 + 2 + ............ n +
n 1 2 n− 1 n
+
+
+
+
(1 I ) (1 I ) (1 I ) (1 I )
or
⎛ (1 I+ ) − 1⎞
n
CIF ⎜ n ⎟ = CIF (PVIFA 1.n )
+
⎝ I (1 I ) ⎠
Where,
PVA = Present value of annuity.
I = Discounting factor or interest rate.
CIF = Cash infl ows.
n = Duration of the annuity.
Illustration 18: Mr. Bhat wishes to determine the PV of the annuity consisting of cash fl ows of
` 40,000 per annum for 6 years. The rate of interest he can earn from this investment is 10 per
cent.

Solution:
= ` 40,000 × PVIFA
I . n
= ` 4000 × 4.355 = ` 17,420

Note: See present value of annuity table for 6 year at 10 per cent.

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