Question

Rafa and Sloane, tennis consultants, are interested in buying an automated system to analyze arm and leg movements for their tennis students. They feel that they could charge $100 per hour to students to use this machine. They have received three competing bids for such a system. But as their skills relate more to tennis, they are confused about which to accept. They have hired the USFSP Cost 1 class to analyze such. They think all the systems would have a useful life of 5 years.

Proposal A

Proposal B

Proposal C

Initial investment in equipment

$60,000

$100,000

$45,000

Working capital needs, returned at end of project life

5,000

1,000

7,000

Annual maintenance costs

10,000

3,000

12,500

Salvage value at end of year 5

10,000

35,000

0

Number of hours billed to students

250

300

200

1. Compute the net present value of each proposal with a discount rate of 12%.

2. Compute the payback of each.

3. Compute the accrual accounting rate of return (AAROR) on both a pretax and after-tax basis. As Rafa and Sloane are so successful on the tennis tour, their tax rate is 40%.

4. Which project would you recommend and why? Include both quantitative and qualitative factors. This is your conclusion.

5. Include a summary as follows (in input/summary tab):

SUMMARY

A

B

C

NPV

Payback

AAROR

pretax

after tax

HINTS

1. Set up your Excel spreadsheet with 4 tabs

• Input and conclusion (be sure to include the summary table)

• Net present value

• Payback

• Accrual accounting rate of return

You must link your inputs (from input tab) to your other spreadsheets. You must use the net present value excel function for the NPV calculation. You also must link your outputs (answers) back to the summary table.

Answer 1

1. Calculation of Net Present Value for proposal A

Year	Particulars	Cash flow	Disc. Rate @ 12%	Discounted Cash flow
0	Cost of equipment	-60000	1	-60000
0	Working capital requirement	-5000	1	-5000
1-5	Annual Cash receipts	25000	3.6	90000
1-5	Annual Cash operating costs	-10000	3.6	-36000
5	Working capital inflow	5000	0.57	2850
5	Salvage value of equipment	10000	0.57	5700
	Net Present Value (NPV)			-2450

2. Calculation of Net Present Value for proposal B

Year	Particulars	Cash flow	Disc. Rate @ 12%	Discounted Cash flow
0	Cost of equipment	-100000	1	-100000
0	Working capital requirement	-1000	1	-1000
1-5	Annual Cash receipts	30000	3.6	108000
1-5	Annual Cash operating costs	-3000	3.6	-10800
5	Working capital inflow	1000	0.57	570
5	Salvage value of equipment	35000	0.57	19950
	Net Present Value (NPV)			16720

3. Calculation of Net Present Value for proposal C

Year	Particulars	Cash flow	Disc. Rate @ 12%	Discounted Cash flow
0	Cost of equipment	-45000	1	-45000
0	Working capital requirement	-7000	1	-7000
1-5	Annual Cash receipts	20000	3.6	72000
1-5	Annual Cash operating costs	-12500	3.6	-45000
5	Working capital inflow	7000	0.57	3990
5	Salvage value of equipment	0	0.57	0
	Net Present Value (NPV)			-21010

Conclusion: Since the NPV is highest for Proposal B, therefore proposal B is selected.

4. Pay back period for proposal A

Initial investment = 60,000

Annual cash inflow (250 Hr. * $ 100 per Hr. ) = $ 25,000

Payback period = Initial investment / Annual cash inflow

= 60,000 / 25,000 = 2.4 years

5. Pay back period for proposal B

Initial investment = 100,000

Annual cash inflow (300 Hr. * $ 100 per Hr. ) = $ 30,000

Payback period = Initial investment / Annual cash inflow

= 100,000 / 30,000 = 3.3 years

6. Pay back period for proposal C

Initial investment = 45,000

Annual cash inflow (200 Hr. * $ 100 per Hr. ) = $ 20,000

Payback period = Initial investment / Annual cash inflow

= 45,000 / 20,000 = 2.25 years

7. Accounting rate of return

Particulars	Proposal A	Proposal B	Proposal C
Annual Earnings	25000	30000	20000
Annual operating cost	10000	3000	12500
Average annual net earnings	15000	27000	7500
Less: Tax @ 40%	6000	10800	3000
Average annual net earnings after tax	9000	16200	4500
Original investment	60000	100000	45000
Salvage value	10000	35000	0
Working capital	5000	1000	7000

Average investment 40000 68500 29500

Pre-tax accounting rate of return 37.5% 39.42% 25.42%

(Avg. annual earnings / Avg. investment )

After-tax accounting rate of return 22.5% 23.65% 15.25%

Avg. annual earnings after tax / Avg. investment )

Average investment = original investment - Scrap value + Working capital +Scrap value

2

Summary

PARTICULARS PROPOSAL A PROPOSAL B PROPOSAL C

NPV - 2450 16720 -21010

Payback period 2.4 3.3 2.25

Pre-tax accounting rate of return(%) 37.5 39.42 25.42

After-tax accounting rate of return(%) 22.5 23.65 15.25