Question

You have been observing the progressive gentrification of your city with interest. You realize that the time is ripe for you to open and run an aerobic exercise center. You find an abandoned warehouse which will meet your needs and rent for $58,000/year. You estimate that it will initially cost $130,000 to renovate the place and buy Nautilius equipment for the center. You will depreciate the equipment using straight-line depreciation to ZERO. You have spent $15,000 on market research, which indicates that you can expect to get 400 members, each paying $500/year. You have also found five instructors you can hire for $24,000 a year each. Your tax rate, if you start making profits, will be 40% and you choose to use straight-line depreciation on your initial investment. If your cost of capital is 15% and you expect to retire to the Bahamas in 10 years. You expect that you will be able to sell the equipment for $50,000 in 10 years.

Estimate the net present value and internal rate of return for this investment. Would you take it?

Answer 1

Depreciation on initial investment = Initial cost/Useful life = $ 130,000/10 = $ 13,000

Computation of annual cash inflow:

Revenue ($ 500 x 400)		$ 200,000
Less: Cost
Rent	$58,000
Salaries for instructors	$24,000
Total cost		$ 82,000
Gross profit		$ 118,000
Less: Depreciation		$ 13,000
PBT		$ 105,000
Tax @ 40%		$ 42,000
Net profit		$ 63,000
Add: Depreciation		$ 13,000
Annual cash flow		$ 76,000

Terminal year cash flow = Annual cash flow + [Salvage value x (1 – Tax rate)]

                                            = $ 76,000 + [$ 50,000 x (1 – 0.4)]

                                            = $ 76,000 + ($ 50,000 x 0.6)

                                            = $ 76,000 + $ 30,000 = $ 106,000

Computation of Net Present Value:

NPV = PV of cash inflows – Initial investment

Year	Cash Flow (C)	Computation of PV Factor	PV Factor @ 15 % (F)	PV (C x F)
0	($130,000)	1/(1+0.15)0	1	($130,000.00)
1	$76,000	1/(1+0.15)1	0.86956521739	$66,086.9565
2	$76,000	1/(1+0.15)2	0.75614366730	$57,466.9187
3	$76,000	1/(1+0.15)3	0.65751623243	$49,971.2337
4	$76,000	1/(1+0.15)4	0.57175324559	$43,453.2467
5	$76,000	1/(1+0.15)5	0.49717673530	$37,785.4319
6	$76,000	1/(1+0.15)6	0.43232759591	$32,856.8973
7	$76,000	1/(1+0.15)7	0.37593703992	$28,571.2150
8	$76,000	1/(1+0.15)8	0.32690177385	$24,844.5348
9	$76,000	1/(1+0.15)9	0.28426241204	$21,603.9433
10	$106,000	1/(1+0.15)10	0.24718470612	$26,201.5788
			NPV	$258,841.9567

Computations of IRR using excel:

	A	B
1	Year	Cash Flow
2	0	($130,000)
3	1	$76,000
4	2	$76,000
5	3	$76,000
6	4	$76,000
7	5	$76,000
8	6	$76,000
9	7	$76,000
10	8	$76,000
11	9	$76,000
12	10	$106,000
13	IRR	58.00%

If excel sheet look like above table, insert formula “=IRR(B2:B12)” in cell B13 to get IRR as 58 %

NPV of the project is $ 258,841.96 and IRR of the project is 58 %.

Project can be accepted as NPV is positive and IRR is higher than the required return.