Question

Sales Cost of goods sold Gross margin Sales, general admin Interestepense Taxable income Jan 123 78 45 12 Feb Mar 131144 2399 48 55 13 12 30 33 Net income 24 25 1919 Balance Sheetſin M5) Jan Feb 625 814 Receivables 160 177 Inventory 105 123 Curr. Assets 890 1.114 PPSE 1,176 1.176 Total Assets 2,066 2.290 Payables Notes Payable Accruals 30 34 LTD 50 50 Curr. Liabilities 200 206 LTD 300 Equity 1,566 1.784 Total LGE 2,066 2,290 Mar 900 200 124 1.224 1,176 2,400 131 38 50 219 300 1,981 2,400 Problem 2 2. Apache seils maintenance services to various private jet operators. For these. Apache's demands payment within 30 days. Apache is considering changing this policy to 15.net 30. What is the implicit effective annual rate in this payment policy? b. Apache's maintenance service business grosses some $20M per year before discounts and its average days receivable is 30 (unlike the overall business where this number is -401 F25% of Apache's clients opt to pay earlier and get the discount what will be the change in the service business's receivables? If Apache's cost of capital is what are the projected savings of this change in policy? If Apache's gross marginis 40%, by how much will gross dollar revenues have to rise to offset the loss from discounts? in percent? A new dient from out of town is quoted 56,000 for a repair. The service people ask you to approve this. You do a Quick check on the client and assess a 15% default risk What is the NPV of the dient? What is the break-even probability? What is the minimum probability of collecting for you to approve the service?

Answer 1

a. Effective Annual rate			b. Average collection period			c. One-time client (Assumuing settlement in 30 days)
Notional purchase(assumed)	100		Gross revenue	20	20	Repair cost	6000
Discount %	1%		Avg. receivables before new policy	20/365*30=	1.64384	Default probability	15%
Days difference	30-5=25		% paying early	25%	25%	NPV of client (-6000+(6000*(1-15%)/1.000219^30))+(6000*20%/1.000219^30)	258.75
			Avg. receivables after new policy	(20*(1-25%))/365*30=	1.23288	Break-even probability     =-6000+(p*5100)+(6000*20%)=0,   solving for p,
Discount ($)	1		Change in receivables		0.41096	Extend credit if prob. Of getting paid is higher than, (p > )-- to break-even.	0.94
Rate(%)	1/99=	1.01%	Cost of capital	8% p.a./ 365= 0.0219%	8%		94%
Days difference in 1 year	365-(5*12)=	305	PV of Projected savings in capital costs	(1.64384-1.23287))/0.0219%=	1876.58
			minus: PV of discounts	(20*25%*1%)/0.0219%=	-228.31
EAR=	(1+1.01%)^(365/25)-1=	15.80%	Projected savings net of discounts		1648.26
			Gross margin	20*40%=	8
			Gross revenues must rise by:
			$	discount=(20*25%*1%)	0.05
			%	(20*25%*1%)/20=	0.25%