Question

Joe’s Technology must choose between two repeatable methods of producing a new product. The initial costs and year-end cash benefits are as follows:

Year                                                   0                          1                                  2                                      3                                     4                                     5

Method M                     -$1,500,000                  600,000                        750,000                         550,000                         200,000    

Method N                      -$2,500,000                  1,200,000                      950,000                         700,000                         400,000                         300,000

Assume all cash flows occur at year-end and the company’s required return is 6.57 percent.

Please compute the net present value ______________ and the equivalent annuity ________________ for Method M

Please compute the net present value ______________ and the equivalent annuity ________________ for Method N

Which production method should be used? _______________

Answer 1

Computation of net present value and the equivalent annuity

- Method M

Year	Cashflow	[email protected]%	Cashflow*PVF
0	(1,500,000)	1	(1,500,000.00)
1	600,000	0.9384	563010.23
2	750,000	0.8805	660376.08
3	550,000	0.8262	454420.37
4	200,000	0.7753	155056.56

Net Present Value = PV of Inflows - PV of Outflows

= (563010.23+660376.08+454420.37+155056.56) - 1500000

= 1832863.23-1500000

=332,863.23

Equivalent Annuity Cash flow = (r(NPV)) / (1-(1+r)^-n)

where

r - rate per period

n - no. of periods

NPV - Net Present Value

Equivalent Annuity Cash flow = (.0657(332863.23)) / (1-(1.0657)^-4)

= 21869.114211/.22471722172

= 97,318.37

- Method N

Year	Cashflow	[email protected]%	Cashflow*PVF
0	(2,500,000)	1	(2,500,000.00)
1	1,200,000	0.9384	1126020.46
2	950,000	0.8805	836476.36
3	700,000	0.8262	578353.20
4	400,000	0.7753	310113.11
5	300,000	0.7275	218246.07

Net Present Value = PV of Inflows - PV of Outflows

= (1126020.46+836476.36+578353.20+310113.11+218246.07)-2500000

= 3069209.20-2500000

= 569,209.20

Equivalent Annuity Cash flow = (.0657(569209.20)) / (1-(1.0657)^-5)

= 37397.04444/0.27251311036

= 137,230.26

Decision: Both NPV and equivalent annuity is higher for Method N, so it should be accepted.