# Problem 5 net present value assume that project x

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Problem-5 :(Net Present Value)Assume that project -X costs Rs 2,500 and is expected togenerate year-end cash inflows of Rs 900, Rs 800, Rs 700Rs 600 and Rs 500 in years 1 to 5 years. The opportunitycost of the capital may be assumed to be 10%. Writecomments.Remember :Net Present Value problem can be solvedwith the help offormula by reference to table. If theproblem inthe examination has to solved with thehelp of formula, they apply the following formula .Present Value Factor(PVF) table is also knownPresentValue Interest Factor ( PVIF) table (available in the Fin.Mgmt bookat lastinAppendix pages).THIS IS IMPORTANT. (Refer to slides- 96 to98)(Refer to next slide for Working Notes):
30(Students should understand these twomethod s thoroughly. This is important)Working Notes for Problem-5Present Value Factor method (PVFmethod):Formula :PVCI1 + PVCI2 + PVCI3 +PVCI4(minus)Initial Investment(Cash outflow (CO)(PVF method asunder) :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 = Rs818.10(It means Rs 900 is valued at Rs Rs 818.10now)(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 = Rs660.80
31(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 = Rs409.90(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 = Rs310.00
33Calculations 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 = Rs661.15(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
34(5) CI5 = 5th year =500 / (1.10 x 1.10 x 1.10 x 1.10 x 1.10) =500 / 1.6105 = Rs. 310.46NPV Calculation under PVFtable 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 2,725.51Net Present Value (NPV)=TPV CI1 to CI5 (minus) Initial Investment (CO) =2,725.10 (minus) 2,500 = Rs 225.51NPV = Rs 225.51Comments :PTO
Comments :Project- X's Total present value of cash inflows(Rs 2,725) isgreater than that of cash outflow of (Rs 2,500). Thus, itgenerates a positive Net Present Value (NPV) of (+) Rs 225.Project-X adds to the wealth of owners, therefore it shouldbeaccepted.Note :To apply the above mentioned formula, when the initialinvestments, (or) outlay of funds (or) cash outflow is madeover a period of time or over number of years.These cashoutflows should be discounted to the present value tocalculate Net Present Value (NPV).35
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