Question

A local bike shop is considering opening a new coffee shop and to operate the shop over the next ten years. The coffee shop will occupy space next door in the same building. That space is currently being rented out to a tenant for $30,000 per year (paid at the end of each year). If you open the coffee shop, you will not be able to rent out the space and you will forgo the $30,000 rental income per year starting in one year. The project will require an upfront capital investment of $200,000 today in order to pay for remodeling the space and the new equipment. This capital investment can be expensed for tax purposes. At the end of the ten years, the store believes it can sell the equipment for $20,000. The store expects the new coffee shop to generate sales revenue from the project of $200,000 one year from today. The sales revenues are expected to grow annually at a rate of 5% over the next 10 years. The costs of goods sold amount to 30% of sales. Selling, general, and administrative (SG&A) costs are expected to amount to 40% of sales. The project will require an investment in net working capital of 10% of sales, to be in place at the beginning of each year (i.e., working capital in year 0 is based on the sales in year 1). The bike shop expects to remain very profitable in the future and to incur a marginal corporate tax rate of 20%. You plan to finance the project 40% with equity and 60% with debt. The bank offers you a loan with a fixed interest rate of 5%. The probability that you will default in any year on this loan is 1% and if you default creditors expect to recover 50% of the loan principal. You estimate the equity beta of the project to be 1.5, the Treasury bill rate to be 2%, and the market risk premium to be 8%.

a) Compute the NPV of the project.

b) The assumptions above state that the SG&A costs amount to 40% of sales. However, you are not completely sure about this assumption. What is the breakeven SG&A proportion relative to sales?

Answer 1

Initial investment	200000
Salvage Value	20000
Depreciation per year	18000	(200000-20000)/10
Revenue forgone	30000	p.a
Working capital requirement -10% of sales in the begging of the year
Tax Rate	40%

Finance Structure	Weight	Amount	Cost	WACC = Weight*Cost
Equity (ke)	40%	80000	0.14	5.60%
Debt @ 5% (kd)	60%	120000	0.035	2.10%
WACC				7.70%
Kd	(I)(1-t) + Credit Spread	0.035	(0.05*60/100)+0.005
Ke	Rf+B(Rm-Rf)	0.14	0.02+1.5*(0.08)
Credit spread for Debt	(1-Recovery Rate)*(Default probability)	0.005	(1-0.50)(1%) =0.005

Year	Sales	COGS - 30% of sales	SG&A - 40% of Sales	Depreciation	Rent forgone	PBT	Tax @ 40% of PBT	PAT (PBT-TAX)	Cash Flow (Dep+PAT)	Working Capital	Discount rate @7.70%	Discounted Cash Flow
0									-200000	-20000	1	-220000
1	200000	60000	80000	18000	30000	12000	4800	7200	25200	21000	0.9285	23398.2
2	210000	63000	84000	18000	30000	15000	6000	9000	27000	22050	0.8621	23276.7
3	220500	66150	88200	18000	30000	18150	7260	10890	28890	23152.5	0.8005	23126.45
4	231525	69457.5	92610	18000	30000	21457.5	8583	12874.5	30874.5	24310.1	0.7433	22949.02
5	243101	72930.3	97240.4	18000	30000	24930.3	9972.12	14958.18	32958.18	25525.6	0.6901	22744.44
6	255256	76576.8	102102.4	18000	30000	28576.8	11430.72	17146.08	35146.08	26801.9	0.6408	22521.61
7	268019	80405.7	107207.6	18000	30000	32405.7	12962.28	19443.42	37443.42	28142	0.595	22278.83
8	281420	84426	112568	18000	30000	36426	14570.4	21855.6	39855.6	29549.1	0.5524	22016.23
9	295491	88647.3	118196.4	18000	30000	40647.3	16258.92	24388.38	42388.38	31026.6	0.5129	21741
10	310266	93079.8	124106.4	18000	30000	45079.8	18031.92	27047.88	45047.88		0.4763	21456.31
10	Salvage Value								20000		0.4763	9526
10	Working Capital								31026.6		0.4763	14777.97
	NPV											29812.76