Problem 5 net present value assume that project x

Problem-5 :
(Net Present Value)
Assume that project -X costs Rs 2,500 and is expected to
generate year-end cash inflows of Rs 900, Rs 800, Rs 700
Rs 600 and Rs 500 in years 1 to 5 years. The opportunity
cost of the capital may be assumed to be 10%. Write
comments.
Remember : Net Present Value problem can be solved
with the help of formula by reference to table. If the
problem in the examination has to solved with the
help of formula, they apply the following formula .
Present Value Factor(PVF) table is also known Present
Value Interest Factor ( PVIF) table (available in the Fin.
Mgmt book at last in Appendix pages).
THIS IS IMPORTANT. (Refer to slides- 96 to 98)
(Refer to next slide for Working Notes):

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(Students should understand these two
method s thoroughly. This is important)
Working Notes for Problem-5
Present Value Factor method (PVF
method):
Formula : PVCI1 + PVCI2 + PVCI3 +PVCI4
(minus)
Initial Investment
(Cash outflow (CO)
(PVF method as
under) :
Present Value of following cash inflows
(CIs) :
(1) CI1 = 1st year = 1 / [1+(r / 100)^1] =
1 / [1+ (10/100)^1 = 1 / 1.10 = 0.909 =
Present Value amount of CI1 =
900 x 0,909 = Rs
818.10
(It means Rs 900 is valued at Rs Rs 818.10
now)
(2) CI2 = 2nd year = 1 / [1 + (10/100)^2 ] =
1 / (1.10 x 1.10) = 0.826
=
Present Value amount of CI2 =
800 x 0.826 = Rs 660.80

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(3) CI3 = 3rd year = 1 / [1 + 10/100)^3 ] =
1 / (1.10 x 1.10 x 1.10) = 0.751 =
Present Value of amount of CI3 =
700 x 0.751 = Rs.
525.70
(4) CI4 = 4th year = 1 / [1 + 10/100)^4] =
1 / (1.10 x 1.10 x 1.10 x 1.10) =
(1 / 1.4641) = 0.683 =
Present value of amount of CI4 =
600 x 0.683 = Rs
409.90
(5) CI5 = 5th year = 1 / [1 + 10/100)^5 =
1 / (1.10 x 1.10 x 1.10 x 1.10 x 1.10) =
(1 /1.6105) = 0.620 =
Present value of amount of CI5 =
500 x 0.620 = Rs
310.00

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Comments :

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Calculations under NPV Formula method :
(1) CI1 = 1st year = (900 / 1.10) = Rs 818.18
(2) CI2 = 2nd year = 800 / (1.10 x 1.10) =
= 800 / 1.21 = Rs
661.15
(3) CI3 = 3rd year = 700 / (1.10 x1.10x 1.10)
=
= 700 / 1.331 = Rs 525.92
(4) CI4 = 4th year =
600 / (1.10 x 1.10 x 1.10 x 1.10) =
600 / 1.4641 = Rs.
409.80

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(5) CI5 = 5th year =
500 / (1.10 x 1.10 x 1.10 x 1.10 x 1.10) =
500 / 1.6105 = Rs. 310.46
NPV Calculation under PVF
table method:
Total Present Value of CI1 to CI5 =
CI1 + CI2 + CI3 + CI4 + CI5 =
818.18 + 661.15 + 525.92 = 409.80 + 310.46
=
TPV of CI1 to CI 5 = Rs 2,725.51
Net Present Value (NPV)
=
TPV CI1 to CI5 (minus) Initial Investment (CO) =
2,725.10 (minus) 2,500 = Rs 225.51
NPV = Rs 225.51
Comments :
PTO

Comments :
Project- X's Total present value of cash inflows (Rs 2,725) is
greater than that of cash outflow of (Rs 2,500). Thus, it
generates a positive Net Present Value (NPV) of (+) Rs 225.
Project-X adds to the wealth of owners, therefore it should
be accepted.
Note :
To apply the above mentioned formula, when the initial
investments, (or) outlay of funds (or) cash outflow is made
over a period of time or over number of years. These cash
outflows should be discounted to the present value to
calculate Net Present Value (NPV).
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