Question

1. A firm is considering replacing the existing industrial air conditioning unit. They will pick one of two units. The first, the AC360, costs $26,081.00 to install, $5,081.00 to operate per year for 7 years at which time it will be sold for $7,075.00. The second, RayCool 8, costs $41,244.00 to install, $2,161.00 to operate per year for 5 years at which time it will be sold for $9,015.00. The firm’s cost of capital is 6.92%. What is the equivalent annual cost of the AC360?

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2. A firm is considering replacing the existing industrial air conditioning unit. They will pick one of two units. The first, the AC360, costs $26,822.00 to install, $5,108.00 to operate per year for 7 years at which time it will be sold for $6,926.00. The second, RayCool 8, costs $41,517.00 to install, $2,098.00 to operate per year for 5 years at which time it will be sold for $9,026.00. The firm’s cost of capital is 6.56%. What is the equivalent annual cost of the RayCool8?

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3. 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 $26,669.00 per year for 8 years and costs $98,113.00. The UGA-3000 produces incremental cash flows of $28,224.00 per year for 9 years and cost $125,952.00. The firm’s WACC is 9.08%. What is the equivalent annual annuity of the GSU-3300?

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4. 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 $25,014.00 per year for 8 years and costs $100,758.00. The UGA-3000 produces incremental cash flows of $28,890.00 per year for 9 years and cost $123,024.00. The firm’s WACC is 9.39%. What is the equivalent annual annuity of the UGA-3000?

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Answer 1

Brief Introduction:

The Equivalent Annual Annuity Method is used for decision making in case of mutually exclusive projects with different life span. The formula for arriving at Equivalent Annual Annuity is r*NPV/1-(1+r)^-nwhere

r is the discount rate to arrive at present value, which is usually the WACC of the firm.

n is the useful life of the project

NPV is the Net Present value of the project

Answer for 1:

Calculation of NPV:

The present value of Net Cash Outflow of AC360 for 7 years is $ 49111.44.The WACC of 6.92% is used to discount the future cash flows to the present value. The present value factor is calculated accordingly below.

Year	Cash Flows	PVIF (r,i)	NPV of Cash Flows
0	$ -26,081.00	1	$ -26,081.00
1	$   -5,081.00	0.9353	$   -4,752.15
2	$   -5,081.00	0.8747	$   -4,444.59
3	$   -5,081.00	0.8181	$   -4,156.93
4	$   -5,081.00	0.7652	$   -3,887.88
5	$   -5,081.00	0.7157	$   -3,636.26
6	$   -5,081.00	0.6693	$   -3,400.91
7	$   -5,081.00	0.626	$   -3,180.80
7	$    7,075.00	0.626	$    4,429.08
			$ -49,111.44

Calculation of Equivalent Annual Cost:

$=(0.069*49111.44)/(1-(1.069)^-7)$

= 9081.04

Therefore the equivalent annual cost of the AC360 is $ 9,081.04

Answer for 2:

Calculation of NPV:

The present value of Net Cash Outflow of Raycool 8 for 5 years is $ 43652.14.The WACC of 6.56% is used to discount the future cash flows to the present value. The present value factor is calculated accordingly below.

Year	Cash Flows	PVIF (r,i)	NPV of Cash Flows
0	$ -41,517.00	1	$ -41,517.00
1	$   -2,098.00	0.9384	$   -1,968.84
2	$   -2,098.00	0.8807	$   -1,847.64
3	$   -2,098.00	0.8265	$   -1,733.90
4	$   -2,098.00	0.7756	$   -1,627.15
5	$   -2,098.00	0.7278	$   -1,526.98
5	$    9,026.00	0.7278	$    6,569.38
			$ -43,652.14

Calculation of Equivalent Annual Cost:

$=(0.0656*43652.14)/(1-(1.0656)^-5)$

= 10521.33

Therefore the equivalent annual cost of the Raycool8 is $ 10,521.33

Answer for 3:

Calculation of NPV:

The present value of Net Cash Flows of GSU-3300 for 8 years is $ 49,057.22.The WACC of 9.08% is used to discount the future cash flows to the present value. The present value factor is calculated accordingly below.

Year	Cash Flows	PVIF (r,i)	NPV of Cash Flows
0	$ -98,113.00	1	$ -98,113.00
1	$ 26,669.00	0.9168	$ 24,449.03
2	$ 26,669.00	0.8404	$ 22,413.85
3	$ 26,669.00	0.7705	$ 20,548.08
4	$ 26,669.00	0.7063	$ 18,837.63
5	$ 26,669.00	0.6476	$ 17,269.55
6	$ 26,669.00	0.5936	$ 15,832.01
7	$ 26,669.00	0.5442	$ 14,514.12
8	$ 26,669.00	0.4989	$ 13,305.94
			$ 49,057.22

Calculation of Equivalent Annual Annuity:

$=(0.0908*49057.22)/(1-(1.0908)^-8)$

= 8889.75

Therefore the equivalent annual annuity of GSU-3300 is $ 8,889.75

Answer for 4:

Calculation of NPV:

The present value of Net Cash Flows of UGA-3000 for 9 years is $ 47466.08.The WACC of 9.39% is used to discount the future cash flows to the present value. The present value factor is calculated accordingly below.

Year	Cash Flows	PVIF (r,i)	NPV of Cash Flows
0	$ -1,23,024.00	1	$ -1,23,024.00
1	$      28,890.00	0.9142	$      26,410.09
2	$      28,890.00	0.8357	$      24,143.06
3	$      28,890.00	0.764	$      22,070.63
4	$      28,890.00	0.6984	$      20,176.09
5	$      28,890.00	0.6384	$      18,444.18
6	$      28,890.00	0.5836	$      16,860.94
7	$      28,890.00	0.5335	$      15,413.60
8	$      28,890.00	0.4877	$      14,090.51
9	$      28,890.00	0.4459	$      12,880.98
			$      47,466.08

Calculation of Equivalent Annual Annuity:

$=(0.0939*47466.08)/(1-(1.0939)^-9)$

= 7149.63

Therefore the equivalent annual annuity of UGA-3000 is $ 7,149.63