Question

Perform a future value analysis for the following investment alternatives, using an interest rate of 8% and a useful life of 10 years.

First cost

Annual benefits

Annual costs

Update cost in year 5

Residual value

Team A

$ 21,500

$ 3,000 the first year with a $ 500 annual increase

$ 2,000

$ 3,200

$ 4,000

Team B

$ 27,000

$ 4,000 the first year with a $ 400 annual increase

$ 3,500

$ 4,500

$ 3,500

Answer 1

ANSWER:

I = 8% AND N = 10 YEARS

1) Team a:

pv = first cost + annual benefits(p/a,i,n) + increase in annual benefits(p/g,i,n) + annual costs(p/a,i,n) + update cost in year 5(p/f,i,n) + residual value(p/f,i,n)

pv = - 21,500 + 3,000(p/a,8%,10) + 500(p/g,8%,10) - 2,000(p/a,8%,10) - 3,200(p/f,8%,5) + 4,000(p/f,8%,10)

pv = - 21,500 + 3,000 * 6.71 + 500 * 25.977 - 2,000 * 6.71 - 3,200 * 0.6806 + 4,000 * 0.4632

pv = - 21,500 + 20,130 + 12,988.5 - 13420 - 2,177.92 + 1,852.8

pv = -2,126.62

fv = pv(f/p,i,n)

fv = - 2,126.62(f/p,8%,10)

fv = - 2,126.62 * 2.159

fv = -4,591.37

2) Team b:

pv = first cost + annual benefits(p/a,i,n) + increase in annual benefits(p/g,i,n) + annual costs(p/a,i,n) + update cost in year 5(p/f,i,n) + residual value(p/f,i,n)

pv = - 27,000 + 4,000(p/a,8%,10) + 400(p/g,8%,10) - 3,500(p/a,8%,10) - 4,500(p/f,8%,5) + 3,500(p/f,8%,10)

pv = - 27,000 + 4,000 * 6.71 + 400 * 25.977 - 3,500 * 6.71 - 4,500 * 0.6806 + 3,500 * 0.4632

pv = - 27,000 + 26,840 + 10,390.8 - 23,485 - 3,062.7 + 1,621.2

pv = -14,695.7

fv = pv(f/p,i,n)

fv = - 14,695.7(f/p,8%,10)

fv = - 14,695.7 * 2.159

fv = - 31,728.01

based on future analysis we should select team a.