Question

Xavier c. wants to purchase a machine for $37,000 with a four year life and $1,000 salvage value. Xavier requires an 8% return on investment. The expected year-end net cash flows are $12,000 in each of the four years.
a) What is the machine's net present value (round to the nearest whole dollar?

b) What is the machine's internal rate of return?

Answer 1

(a) Net present value of machine
Pm=-C+V/(1+i)^n=37000-1000/1.08^4
=-36264.97
=-36265 (rounded to nearest dollar)

Cost of machine amortized over 4 years (annualized cost)
Ac=Pm(A/P,i,n)=-36264.97(A/P,0.08,4)=-36264.97(.08*(1.08^4)/(1.08^4-1)
=-10949.15

Expected year-end cash flow = annualized return - annualized cost  =>
12000=return - 10949.15

(b) Internal rate of return of machine
=return/cost - 1
=(12000-(-10949.15)/10949.15-1
=2.096-1
=1.096
=109.6%

Answer 2

A)
First find the present value of annuity ordinary
The formula is
Pv=pmt [(1-(1+r)^(-n))÷r]
Pv present value?
PMT payment per year 12000
R rate of return 0.08
N time 4 years
Pv=12,000×((1−(1+0.08)^(−4))÷(0.08))
pv=39,745

Net present value is
39745-37000=2745....answer

B)
internal rate of return=initial investment÷net cash flow

internal rate of return=37000÷12000
internal rate of return=3.083

Now see internal rate of return factor (3.083) in 4 years line of the present value of an annuity if $1 table.
3.083 is closest to 3.037
Now see the corresponding interest rate written at the top of the column
It's 12%
Internal rate of return is 12%


Here's the link of the table
http://www.accountingformanagement.org/present-value-of-an-annuity-of-1-in-arrear/

Sorry I couldn't upload the attachment because of the connection