Question

Economic questions. Answer questions 1 to 5 from the information below.

Paragon, a road construction company, must purchase a new paver to meet the growing demands for highway construction and resurfacing. The key parameters of the three pavers under scrutiny are provided below. Parameters A99 B88 C77 1. Initial Cost ($) 380,000 400,000 425,000 $290,000 at $300,000 at $310,000 from EOY1 increasing EOY1 EOY1 by $3,000 increasing by decreasing by 2. Revenues ($) annually 1% annually 3.0% annually thereafter thereafter. thereafter $125,000 at $175,000 at $185,000 at EOY1 EOY1 EOY1 3. Operating costs decreasing by decreasing by decreasing by ($) $1,000 annually 2% annually $2,500 annually thereafter. thereafter thereafter 4. End-of-life 45,000 -6,000 30,000 salvage value ($) 5. Useful life (years) 4 years 6 years All parameter values are fictitious. • EOY = End-of-year Industry Standard = 2.5 years MARR = 10% 3 years 1. A99's Net Present Worth (NPW). 2. 3. C77's net worth (NFW) at EOY6. Find the C77 paver's annual equivalent worth (AEW) if it was repeated and used during twenty-four (24) years with no changes to any of its initial parameter values. A99's annual equivalent worth (AEW). The best paver based on the AEW method. 4. 5.

Answer 1

1. A99’s Net Present worth (NPW)

NPW = Present worth of benefits - Present worth of costs

NPW = {[290000 + 3000(A/G,10%,3)](P/A,10%,3) - 6000(P/F,10%,3)} – [380000 + [125000 – 1000(A/G,10%,3)](P/A,10%,3)

Using DCIF Tables

NPW = (290000 + 3000(0.937))(2.487) - 6000(0.7513) – 380000 - (125000 – 1000(0.937))(2.487)

NPW = $35168.5

2. C77’s Net Future worth (NFW)

NFW = Future worth of benefits - Future worth of costs

NFW = [310000 - 9300(A/G,10%,6)](F/A,10%,6) + 30000 – 425000(F/P,10%,6) - [185000 – 2500(A/G,10%,6)](F/A,10%,6)

Using DCIF Tables

NFW = (310000 - 9300(2.224))*(7.716) + 30000 – 425000(1.772) - (185000 – 2500(2.224))(7.716)

NFW = $124709.38

3. C77’s Annual equivalent worth (AEW)

AEW does not change with the tenure. Therefore, the AEW can be estimated by using the NFW value computed above.

NAW = 124709.38 (A/F,10%,6)

Using DCIF Tables

NAW = 124709.38 *(0.1296)

NAW = $16162.33

4. A99’s Annual equivalent worth (AEW)

NAW = NPW (A/P,10%,3)

NAW = 35168.5 (A/P,10%,3)

Using DCIF Tables

NAW = 35168.5*(0.4021)

NAW = $14141.25

5. B88’s Net Future worth (NFW)

NFW = Future worth of benefits - Future worth of costs

NFW = [300000 + 3000(A/G,10%,4)](F/A,10%,4) + 45000 – 400000(F/P,10%,4) + [175000 – 3500(A/G,10%,4)](F/A,10%,4)

Using DCIF Tables

NFW = (300000 + 3000(1.381))(4.641) + 45000 – 400000(1.464) - (175000 – 3500(1.381))(4.641)

NFW = $81184.93

NAW = 81184.93(A/F,10%,4)

Using DCIF Tables

NAW = 81184.93*(0.2155)

NAW = $17495.35

Paver	A99	B88	C77
NAW	$14141.25	$17495.35	$16162.33

The Best Paver based on AEW method is B88 as it has the highest AEW among all the three alternatives.

Answer 2

1. A99’s Net Present worth (NPW)

NPW = Present worth of benefits - Present worth of costs

NPW = {[290000 + 3000(A/G,10%,3)](P/A,10%,3) - 6000(P/F,10%,3)} – [380000 + [125000 – 1000(A/G,10%,3)](P/A,10%,3)

Using DCIF Tables

NPW = (290000 + 3000(0.937))(2.487) - 6000(0.7513) – 380000 - (125000 – 1000(0.937))(2.487)

NPW = $35168.5

2. C77’s Net Future worth (NFW)

NFW = Future worth of benefits - Future worth of costs

NFW = [310000 - 9300(A/G,10%,6)](F/A,10%,6) + 30000 – 425000(F/P,10%,6) - [185000 – 2500(A/G,10%,6)](F/A,10%,6)

Using DCIF Tables

NFW = (310000 - 9300(2.224))*(7.716) + 30000 – 425000(1.772) - (185000 – 2500(2.224))(7.716)

NFW = $124709.38

3. C77’s Annual equivalent worth (AEW)

AEW does not change with the tenure. Therefore, the AEW can be estimated by using the NFW value computed above.

NAW = 124709.38 (A/F,10%,6)

Using DCIF Tables

NAW = 124709.38 *(0.1296)

NAW = $16162.33

4. A99’s Annual equivalent worth (AEW)

NAW = NPW (A/P,10%,3)

NAW = 35168.5 (A/P,10%,3)

Using DCIF Tables

NAW = 35168.5*(0.4021)

NAW = $14141.25

5. B88’s Net Future worth (NFW)

NFW = Future worth of benefits - Future worth of costs

NFW = [300000 + 3000(A/G,10%,4)](F/A,10%,4) + 45000 – 400000(F/P,10%,4) + [175000 – 3500(A/G,10%,4)](F/A,10%,4)

Using DCIF Tables

NFW = (300000 + 3000(1.381))(4.641) + 45000 – 400000(1.464) - (175000 – 3500(1.381))(4.641)

NFW = $81184.93

NAW = 81184.93(A/F,10%,4)

Using DCIF Tables

NAW = 81184.93*(0.2155)

NAW = $17495.35

Paver	A99	B88	C77
NAW	$14141.25	$17495.35	$16162.33

The Best Paver based on AEW method is B88 as it has the highest AEW among all the three alternatives.