Net present value$-$unequal lives

Dakota Mining Company has two competing proposals: a damond core drill or a hydraulic excavatoo. Both pieces of equipment have an initial investment of $$607,236.$ The net cash flows estimated for the two proposals are as follows:

$\backslash$table$[[$Net Cash Flow,Net Cash Flow$],[$Year$,$Diamond Core Drill,Hydraulic Excavator$],[1,$$$194,000,$$$243,000],[2,173,000,225,000],[3,173,000,208,000],[4,138,000,213,000],[5,105,000,],[6,87,000,],[7,76,000,0],[8,76,000]]$The estimated residual value of the diamond core drill at the end of Year $4$ is $$240,000.$

Present Value of $$1$ at Compound Interest

$\backslash$table$[[$Year$,6\%,10\%,12\%,15\%,20\%],[1,0\mathrm{.}943,0\mathrm{.}909,0\mathrm{.}893,0\mathrm{.}870,0\mathrm{.}833],[2,0\mathrm{.}890,0\mathrm{.}826,0\mathrm{.}797,0\mathrm{.}756,0\mathrm{.}694],[3,0\mathrm{.}840,0\mathrm{.}751,0\mathrm{.}712,0\mathrm{.}658,0\mathrm{.}579],[4,0\mathrm{.}792,0\mathrm{.}683,0\mathrm{.}636,0\mathrm{.}572,0\mathrm{.}482],[5,0\mathrm{.}747,0\mathrm{.}621,0\mathrm{.}567,0\mathrm{.}497,0\mathrm{.}402],[6,0\mathrm{.}705,0\mathrm{.}564,0\mathrm{.}507,0\mathrm{.}432,0\mathrm{.}335],[7,0\mathrm{.}665,0\mathrm{.}513,0\mathrm{.}452,0\mathrm{.}376,0\mathrm{.}279],[8,0\mathrm{.}627,0\mathrm{.}467,0\mathrm{.}404,0\mathrm{.}327,0\mathrm{.}233],[9,0\mathrm{.}592,0\mathrm{.}424,0\mathrm{.}361,0\mathrm{.}284,0\mathrm{.}194],[10,0\mathrm{.}558,0\mathrm{.}386,0\mathrm{.}322,0\mathrm{.}247,0\mathrm{.}162]]$

Determine which equipment should be favored, comparing the net present values of the two proposals and assuming a minimum rate of return of $12\%.$ Use the present value table appearing above$\mathrm{.}10,0\mathrm{.}558,0\mathrm{.}386,0\mathrm{.}322,0\mathrm{.}247,0\mathrm{.}162$

Determine which equipment should be favored, comparing the net present values of the two proposals and assuming a minimum rate of return of $12\%.$ Use the present value table appearing above.

$\backslash$table$[[,$Diamond Core Drill Hydraulic Excavator,$],[$Present value of net cash flow total,$$,$$