Rumus NPV (Net Present Value): Pengertian, Rumus, Tabel FVIVA, dan Contoh Soal

Kali ini kita akan membahas rumus NPV.  

NPV atau Net Present Value sering digunakan dalam sebuah penganggaran modal untuk menganalisa suatu profitabilitas dari sebuah proyek ataupun proyeksi investasi.

Para pemilik modal ataupun manajemen perusahaan dapat menggunakan perhitungan NPV untuk mengevaluasi apakah akan berinvestasi atau tidak. 

Net Present Value atau NPV diartikan juga sebagai nilai bersih sekarang.

Pengertian NPV (Net Present Value)

Net Present Value (NPV) adalah selisih antara nilai sekarang dari arus kas yang akan masuk dengan nilai sekarang dari arus kas yang akan keluar pada periode waktu tertentu.

NPV mengestimasikan nilai sekarang pada sebuah proyek, aset ataupun investasi yang berdasarkan pada arus kas yang akan masuk karna diharapkan pada masa depan dan arus kas yang akan keluar akan disesuaikan dengan suku bunga dan harga pembelian awal.

Net Pressent Value menggunakan harga pembelian awal dan nilai waktu uang (time value of money) untuk menghitung nilai sebuah aset.

Jadi, NPV merupakan sebuah nilai sekarang dari aset yang akan dikurangi dengan harga pembelian awal.

Pengertian NPV Menurut Para Ahli

Berikut ini ialah beberapa definisi dan pengertian dari NPV menurut para ahli silahkan di baca :

  1. Menurut Syafaruddin Alwi (2001, 163), Net Present Value adalah model yang memperhitungkan suatu pola cash flows yang keseluruhan dari sebuah investasi, dalam kaitan nya dengan waktu, berdasarkan discount rate tertentu.
  2. Menurut Dr. Sobarsa Kosasih dalam buku nya yang berjudul “Manajemen Operasi (2009 : 99)”, NPV merupakan sebuah Kelebihan Present Value (PV) dari cash inflow yang dihasilkan oleh sebuah proyek atas sejumlah investasi awal.
  3. Menurut R. Agus Sartono (2010 : 195), Net Present Value merupakan sebuah selisih antara present value aliran kas yang bersih atau yang sering disebut juga dengan procceed dengan present value Investasi.
  4. Menurut Dian Wijayanto dalam buku nya yang berujudul “Pengantar Manajemen (2012 : 246)”, Net Present Value (NPV) ialah sebuah kombinasi antara present value penerimaan dan present value pengeluaran.

Rumus NPV

Rumus NPV menambahkan semua arus kas masa depan dari investasi, mendiskon arus kas tersebut dengan tingkat diskon dan menguranginya dengan Investasi awal.

Persamaan dan rumus dari Net Present Value ( NPV ) adalah sebagai berikut :

Rumus NPV Net Present Value

Atau

Rumus NPV Net Present Value 2

Keterangan :

  • NPV = Net Present Value (rupiah)
  • Ct = Arus kas per tahun pada periode t
  • C0 = Nilai investasi awal pada tahun ke 0 (rupiah)
  • r = Suku bunga atau discount rate (%)

Tabel PVIFA

Selain rumus NPV di atas, kita juga bisa menggunakan tabel PVIFA (Present Value Interest Factor for an Annuity) kemudian masukan hasil nya ke persamaan atau rumus NPV yang terdapat di bawah ini :

NPV = ( Ct x PVIFA ( r ) ( t ) ) – C0

Dan tabel FVIFA dapat dilihat pada gambar di bawah ini.

Tabel FVIFA 1% – 10%

Periods1%2%3%4%5%6%7%8%9%10%
10.99010.98040.97090.96150.95240.94340.93460.92590.91740.9091
219.70419.41619.13518.86118.59418.33418.08017.83317.59117.355
329.41028.83928.28627.75127.23226.73026.24325.77125.31324.869
439.02038.07737.17136.29935.46034.65133.87233.12132.39731.699
548.53447.13545.79744.51843.29542.12441.00239.92738.89737.908
657.95556.01454.17252.42150.75749.17347.66546.22944.85943.553
767.28264.72062.30360.02157.86455.82453.89352.06450.33048.684
876.51773.25570.19767.32764.63262.09859.71357.46655.34853.349
985.66081.62277.86174.35371.07868.01765.15262.46959.95257.590
1094.71389.82685.30281.10977.21773.60170.23667.10164.17761.446
11103.67697.86892.52687.60583.06478.86974.98771.39068.05264.951
12112.551105.75399.54093.85188.63383.83879.42775.36171.60768.137
13121.337113.484106.35099.85693.93688.52783.57779.03874.86971.034
14130.037121.062112.961105.63198.98692.95087.45582.44277.86273.667
15138.651128.493119.379111.184103.79797.12291.07985.59580.60776.061
16147.179135.777125.611116.523108.378101.05994.46688.51483.12678.237
17155.623142.919131.661121.657112.741104.77397.63291.21685.43680.216
18163.983149.920137.535126.593116.896108.276100.59193.71987.55682.014
19172.260156.785143.238131.339120.853111.581103.35696.03689.50183.649
20180.456163.514148.775135.903124.622114.699105.94098.18191.28585.136
21188.570170.112154.150140.292128.212117.641108.355100.16892.92286.487
22196.604176.580159.369144.511131.630120.416110.612102.00794.42487.715
23204.558182.922164.436148.568134.886123.034112.722103.71195.80288.832
24212.434189.139169.355152.470137.986125.504114.693105.28897.06689.847
25220.232195.235174.131156.221140.939127.834116.536106.74898.22690.770
26227.952201.210178.768159.828143.752130.032118.258108.10099.29091.609
27235.596207.069183.270163.296146.430132.105119.867109.352100.26692.372
28243.164212.813187.641166.631148.981134.062121.371110.511101.16193.066
29250.658218.444191.885169.837151.411135.907122.777111.584101.98393.696
30258.077223.965196.004172.920153.725137.648124.090112.578102.73794.269
31265.423229.377200.004175.885155.928139.291125.318113.498103.42894.790
32272.696234.683203.888178.736158.027140.840126.466114.350104.06295.264
33279.897239.886207.658181.476160.025142.302127.538115.139104.64495.694
34287.027244.986211.318184.112161.929143.681128.540115.869105.17896.086
35294.086249.986214.872186.646163.742144.982129.477116.546105.66896.442
36301.075254.888218.323189.083165.469146.210130.352117.172106.11896.765
37307.995259.695221.672191.426167.113147.368131.170117.752106.53097.059
38314.847264.406224.925193.679168.679148.460131.935118.289106.90897.327
39321.630269.026228.082195.845170.170149.491132.649118.786107.25597.570
40328.347273.555231.148197.928171.591150.463133.317119.246107.57497.791
41334.997277.995234.124199.931172.944151.380133.941119.672107.86697.991
42341.581282.348237.014201.856174.232152.245134.524120.067108.13498.174
43348.100286.616239.819203.708175.459153.062135.070120.432108.38098.340
44354.555290.800242.543205.488176.628153.832135.579120.771108.60598.491
45360.945294.902245.187207.200177.741154.558136.055121.084108.81298.628
46367.272298.923247.754208.847178.801155.244136.500121.374109.00298.753
47373.537302.866250.247210.429179.810155.890136.916121.643109.17698.866
48379.740306.731252.667211.951180.772156.500137.305121.891109.33698.969
49385.881310.521255.017213.415181.687157.076137.668122.122109.48299.063
50391.961314.236257.298214.822182.559157.619138.007122.335109.61799.148

Tabel FVIFA 11% – 20%

Periods11%12%13%14%15%16%17%18%19%20%
10.90090.89290.88500.87720.86960.86210.85470.84750.84030.8333
217.12516.90116.68116.46716.25716.05215.85215.65615.46515.278
324.43724.01823.61223.21622.83222.45922.09621.74321.39921.065
431.02430.37329.74529.13728.55027.98227.43226.90126.38625.887
536.95936.04835.17234.33133.52232.74331.99331.27230.57629.906
642.30541.11439.97538.88737.84536.84735.89234.97634.09833.255
747.12245.63844.22642.88341.60440.38639.22438.11537.05736.046
851.46149.67647.98846.38944.87343.43642.07240.77639.54438.372
955.37053.28251.31749.46447.71646.06544.50643.03041.63340.310
1058.89256.50254.26252.16150.18848.33246.58644.94143.38941.925
1162.06559.37756.86954.52752.33750.28648.36446.56044.86543.271
1264.92461.94459.17656.60354.20651.97149.88447.93246.10544.392
1367.49964.23561.21858.42455.83153.42351.18349.09547.14745.327
1469.81966.28263.02560.02157.24554.67552.29350.08148.02346.106
1571.90968.10964.62461.42258.47455.75553.24250.91648.75946.755
1673.79269.74066.03962.65159.54256.68554.05351.62449.37747.296
1775.48871.19667.29163.72960.47257.48754.74652.22349.89747.746
1877.01672.49768.39964.67461.28058.17855.33952.73250.33348.122
1978.39373.65869.38065.50461.98258.77555.84553.16250.70048.435
2079.63374.69470.24866.23162.59359.28856.27853.52751.00948.696
2180.75175.62071.01666.87063.12559.73156.64853.83751.26848.913
2281.75776.44671.69567.42963.58760.11356.96454.09951.48649.094
2382.66477.18472.29767.92163.98860.44257.23454.32151.66849.245
2483.48177.84372.82968.35164.33860.72657.46554.50951.82249.371
2584.21778.43173.30068.72964.64160.97157.66254.66951.95149.476
2684.88178.95773.71769.06164.90661.18257.83154.80452.06049.563
2785.47879.42674.08669.35265.13561.36457.97554.91952.15149.636
2886.01679.84474.41269.60765.33561.52058.09955.01652.22849.697
2986.50180.21874.70169.83065.50961.65658.20455.09852.29249.747
3086.93880.55274.95770.02765.66061.77258.29455.16852.34749.789
3187.33180.85075.18370.19965.79161.87258.37155.22752.39249.824
3287.68681.11675.38370.35065.90561.95958.43755.27752.43049.854
3388.00581.35475.56070.48266.00562.03458.49355.32052.46249.878
3488.29381.56675.71770.59966.09162.09858.54155.35652.48949.898
3588.55281.75575.85670.70066.16662.15358.58255.38652.51249.915
3688.78681.92475.97970.79066.23162.20158.61755.41252.53149.929
3788.99682.07576.08770.86866.28862.24258.64755.43452.54749.941
3889.18682.21076.18370.93766.33862.27858.67355.45252.56149.951
3989.35782.33076.26870.99766.38062.30958.69555.46852.57249.959
4089.51182.43876.34471.05066.41862.33558.71355.48252.58249.966
4189.64982.53476.41071.09766.45062.35858.72955.49352.59049.972
4289.77482.61976.46971.13866.47862.37758.74355.50252.59649.976
4389.88682.69676.52271.17366.50362.39458.75555.51052.60249.980
4489.98882.76476.56871.20566.52462.40958.76555.51752.60749.984
4590.07982.82576.60971.23266.54362.42158.77355.52352.61149.986
4690.16182.88076.64571.25666.55962.43258.78155.52852.61449.989
4790.23582.92876.67771.27766.57362.44258.78755.53252.61749.991
4890.30282.97276.70571.29666.58562.45058.79255.53652.61949.992
4990.36283.01076.73071.31266.59662.45758.79755.53952.62149.993
5090.41783.04576.75271.32766.60562.46358.80155.54152.62349.995

Tabel FVIFA 21% – 30%

Periods21%22%23%24%25%26%27%28%29%30%
10.82640.81970.81300.80650.80000.79370.78740.78120.77520.7692
215.09514.91514.74014.56814.40014.23514.07413.91613.76113.609
320.73920.42220.11419.81319.52019.23418.95618.68418.42018.161
425.40424.93624.48324.04323.61623.20222.80022.41022.03121.662
529.26028.63628.03527.45426.89326.35125.82725.32024.83024.356
632.44631.66930.92330.20529.51428.85028.21027.59427.00026.427
735.07934.15533.27032.42331.61130.83330.08729.37028.68228.021
837.25636.19335.17934.21233.28932.40731.56430.75829.98629.247
939.05437.86336.73135.65534.63133.65732.72831.84230.99730.190
1040.54139.23237.99336.81935.70534.64833.64432.68931.78130.915
1141.76940.35439.01837.75736.56435.43534.36533.35132.38831.473
1242.78441.27439.85238.51437.25136.05934.93333.86832.85931.903
1343.62442.02840.53039.12437.80136.55535.38134.27233.22432.233
1444.31742.64641.08239.61638.24136.94935.73334.58733.50732.487
1544.89043.15241.53040.01338.59337.26136.01034.83433.72632.682
1645.36443.56741.89440.33338.87437.50936.22835.02633.89632.832
1745.75543.90842.19040.59139.09937.70536.40035.17734.02832.948
1846.07944.18742.43140.79939.27937.86136.53635.29434.13033.037
1946.34644.41542.62740.96739.42437.98536.64235.38634.21033.105
2046.56744.60342.78641.10339.53938.08336.72635.45834.27133.158
2146.75044.75642.91641.21239.63138.16136.79235.51434.31933.198
2246.90044.88243.02141.30039.70538.22336.84435.55834.35633.230
2347.02544.98543.10641.37139.76438.27336.88535.59234.38433.254
2447.12845.07043.17641.42839.81138.31236.91835.61934.40633.272
2547.21345.13943.23241.47439.84938.34236.94335.64034.42333.286
2647.28445.19643.27841.51139.87938.36736.96335.65634.43733.297
2747.34245.24343.31641.54239.90338.38736.97935.66934.44733.305
2847.39045.28143.34641.56639.92338.40236.99135.67934.45533.312
2947.43045.31243.37141.58539.93838.41437.00135.68734.46133.317
3047.46345.33843.39141.60139.95038.42437.00935.69334.46633.321
3147.49045.35943.40741.61439.96038.43237.01535.69734.47033.324
3247.51245.37643.42141.62439.96838.43837.01935.70134.47333.326
3347.53145.39043.43141.63239.97538.44337.02335.70434.47533.328
3447.54645.40243.44041.63939.98038.44737.02635.70634.47733.329
3547.55945.41143.44741.64439.98438.45037.02835.70834.47833.330
3647.56945.41943.45341.64939.98738.45237.03035.70934.47933.331
3747.57845.42643.45841.65239.99038.45437.03235.71034.48033.331
3847.58545.43143.46241.65539.99238.45637.03335.71134.48133.332
3947.59145.43543.46541.65739.99338.45737.03435.71234.48133.332
4047.59645.43943.46741.65939.99538.45837.03435.71234.48133.332
4147.60045.44143.46941.66139.99638.45937.03535.71334.48233.333
4247.60345.44443.47141.66239.99738.45937.03535.71334.48233.333
4347.60645.44643.47241.66339.99738.46037.03635.71334.48233.333
4447.60845.44743.47341.66339.99838.46037.03635.71434.48233.333
4547.61045.44943.47441.66439.99838.46037.03635.71434.48233.333
4647.61245.45043.47541.66539.99938.46137.03635.71434.48233.333
4747.61345.45143.47641.66539.99938.46137.03735.71434.48333.333
4847.61445.45143.47641.66539.99938.46137.03735.71434.48333.333
4947.61545.45243.47741.66639.99938.46137.03735.71434.48333.333
5047.61645.45243.47741.66639.99938.46137.03735.71434.48333.333

Contoh Soal NPV

Berikut adalah contoh soal NPV beserta pembahasan jawabannya.

Contoh

Sebuah Perusahaan Z ingin membeli sebuah mesin produksi. Diperkirakan untuk harga mesin tersebut adalah Rp. 160 juta dengan mengikuti aturan suku bunga pinjaman yakni sebesar 12% per tahun. Untuk Arus Kas yang masuk pada perusahaan itu diestimasikan sekitar Rp. 60 juta per tahun selama 5 tahun. Hitung nilai NPV nya!

Penyelesaiannya

Diketahui :

Ct = Rp. 60 juta

C0 = Rp. 160 juta

r = 12% (0,12)

Jawaban :

Contoh Soal NPV Net Present Value

NPV = 53,57 + 47,83 + 42,71 + 38,13 + 34,05 – 160,00

NPV = 56,29

Jadi nilai untuk NPV-nya adalah Rp. 56,29 juta.

Itulah penjelasan lengkap tentang rumus NPV beserta pengertian dan rumus nya semoga bermanfaat.

Pelajari Lebih Lanjut

Rumus ROE

Rumus ROA

Elastisitas Permintaan dan Penawaran

Bunga Majemuk

Bunga Tunggal

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