Question

1. A) A firm is considering replacing the existing industrial air conditioning unit. They will pick one of two units. The first, the AC360, costs $26,294.00 to install, $5,151.00 to operate per year for 7 years at which time it will be sold for $6,930.00. The second, RayCool 8, costs $41,464.00 to install, $2,183.00 to operate per year for 5 years at which time it will be sold for $8,907.00. The firm’s cost of capital is 5.33%. What is the equivalent annual cost of the AC360?

B) A firm is considering replacing the existing industrial air conditioning unit. They will pick one of two units. The first, the AC360, costs $26,129.00 to install, $5,184.00 to operate per year for 7 years at which time it will be sold for $7,101.00. The second, RayCool 8, costs $41,159.00 to install, $2,022.00 to operate per year for 5 years at which time it will be sold for $9,080.00. The firm’s cost of capital is 5.49%. What is the equivalent annual cost of the RayCool8?

2. A) A firm is must choose to buy the GSU-3300 or the UGA-3000. Both machines make the firm’s production process more efficient which in turn increases incremental cash flows. The GSU-3300 produces incremental cash flows of $25,033.00 per year for 8 years and costs $101,232.00. The UGA-3000 produces incremental cash flows of $27,533.00 per year for 9 years and cost $124,285.00. The firm’s WACC is 8.57%. What is the equivalent annual annuity of the GSU-3300?

Answer 1

AC360

Initial cost

=

$26,294

Life

=

7 years

annual cost

=

$5,151

Salvage

=

$6,930

Rate

=

5.33% or 0.0533

Equivalent cost

=

PV of all cost/PVAF(5.33%,7 years)

=

[$26294+annual cost*PVAF(5.33%,7 years)-PVF(5.33%,7 years)*salvage value]/PVAF(5.33%,7 years)

=

$26294+(5151*5.7178)-(6930*0.6952)]/5.7178

=

(26294+29452-4817)/5.7178

=

$8,907.10

Raycool 8

Initial cost

=

$41,159

Life

=

5 years

annual cost

=

$2,022

Salvage

=

$9,080

Rate

=

5.49% or 0.0549

Equivalent cost

=

PV of all cost/PVAF(5.49%,5 years)

=

[$41159+annual cost*PVAF(5.49%,5 years)-PVF(5.49%,5 years)*salvage value]/PVAF(5.49%,5 years)

=

[41159+(2022*4.2715)-(9080*0.7655)]/4.2715

=

(42844/4.2715)

=

$10,030.48

GSU 300

Initial cost

=

$101,232

Life

=

8 years

annual incremental cashflow

=

$25,033

Salvage

=

nil

Rate

=

8.57%

PV of incremental cashflow

=

PVAF(8.57%,8years)*incremental cashflow

=

5.6244*25033

=

$140,795.32

NPV

=

$39,563.32

Equivalent annuity of NPV

=

npv/PVAF(8.57%,8 years)

=

$39563/5.6244

=

$7,034.24

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