Given the following mutually-exclusive alternatives and a Minimum Attractive Rat
ID: 1188593 • Letter: G
Question
Given the following mutually-exclusive alternatives and a Minimum Attractive Rate of Return
(MARR) of 5%, which should be chosen?
Solve as PV(Present Value), FV (Future Value)and AW (AW not graded, but I want to see your attempt) (3 separate analyses) and show which Design gets chosen in each. SHOW YOUR WORK with tool formulas, not tables at this time to ensure you are understanding the concepts.
I am reposting this question:
I get PV but I DO NOT UNDERSTAND WHY for Future Value how the equation is applies..I thought the equation was FV=P(1+i)^n .....so for FV for Design A be FV= -2500(1.05)^1+ 3100(1.05)^5??? please explain and write out eqaution. i also need the equation, and explanation for Annual Worth please. I will give lots of points....thanks
Table
Year Design A Design B Design C
Year
Design A
Design B
Design C
0(cost)
($2500)
($2700)
($3000)
1
$0
$650
$0
2
$0
$650
$350
3
$0
$650
$700
4
$0
$650
$1050
5
$3100
$650
$1400
Total
$600
$550
$500
Year
Design A
Design B
Design C
0(cost)
($2500)
($2700)
($3000)
1
$0
$650
$0
2
$0
$650
$350
3
$0
$650
$700
4
$0
$650
$1050
5
$3100
$650
$1400
Total
$600
$550
$500
Explanation / Answer
Design A:
Initial cost = $2,500
Cash inflow at 5th year>
Net present worth of design A = PW of Benefits %u2013 Pw of cost
PW of benefit = $3,100 (P/F, i, n)
=$3,100 (P/F, 5%, 5yrs)
=$3,100 x 0.7835
= $2,428.85
Pw of cost = $2500
Net present worth of design A = PW of Benefits %u2013 Pw of cost
=$2,428.85 %u2013$2,500
= %u2013 $71.15
------------------------------------------------------------------------------------------------------------------------------------
Design B:
Initial cost = $2,700
Regular annuity of = $650 for 5 years
Net present worth of design A = PW of Benefits %u2013 Pw of cost
PW of benefit = $650 (P/A, i, n)
=$650 (P/A, 5%, 5yrs)
=$650 x 4.329
= $2,813.85
Pw of cost = $2500
Net present worth of design A = PW of Benefits %u2013 Pw of cost
=$2,813.85 %u2013$2,500
=$313.85
------------------------------------------------------------------------------------------------------------------------------------------
Design C:
Initial cost = $3,000
The cash inflow can be split into a regular annuity of $350 from 2nd year onwards and a gradient factor of $350.
Regular annuity of = $350 for 4 years
Gradient factor of $350 for 4 years,
Net present worth of design A = PW of Benefits %u2013 Pw of cost
PW of benefit = [$350 (P/A, i, n) + $350( P/G, i,n)] (P/F, i,n)
= [$350 (P/A, 5%, 4 yrs ) + $350( P/G, 4%, 4 yrs)] x(P/F, 5%,1 yr)
=[$350 x(3.546 ) + $350 x ( 5.103)] x (0.9524)
= ($1,241.1 + $1,786.05 ) x (0.9524)
=$ 3,027.15 x 0.9524
= $2,883.05
Pw of cost = $3,000
Net present worth of design A = PW of Benefits %u2013 Pw of cost
=$2,883.05 %u2013$3,000
= %u2013$116
We can observe that, design A and C has negative net present worth making them unprofitable.
Thus, design B with a positve net present worth of $313 has to be chosen.
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