Question

A ) An entrepreneur invests $40,454.00 into a start-up business today. He expects the business will generate $60,003.00 per year for 14.00 years, and then it will generate $137,194.00 per year for the following 16.00 years. Suppose he wants a 9.00% annual return to run the business. What is the value of this business today if his forecasts are accurate? (HINT: Discount all cash flows to today and subtract start-up investment.)

B) A young graduate is planning on saving $600.00 each quarter for four years in an investment account paying 12.64% interest that is compounded quarterly. His first deposit will be made at the end of the next quarter, so this is a regular annuity. In 4 years, he also plans on being able to afford a 60-month car loan with $359.00 monthly payments at a 11.40% APR interest rate. Given the graduate’s plans, how expensive of a “dream car” will he expect to be able to purchase in four years?

Answer 1

	Year	cash inflow	present value of cash flow = cash flow/(1+r)6n r= 9%
	1	60003	55048.62
	2	60003	50503.32
	3	60003	46333.33
	4	60003	42507.64
	5	60003	38997.83
	6	60003	35777.83
	7	60003	32823.7
	8	60003	30113.48
	9	60003	27627.05
	10	60003	25345.92
	11	60003	23253.13
	12	60003	21333.15
	13	60003	19571.7
	14	60003	17955.69
	15	137194	37664.97
	16	137194	34555.02
	17	137194	31701.85
	18	137194	29084.27
	19	137194	26682.82
	20	137194	24479.65
	21	137194	22458.39
	22	137194	20604.03
	23	137194	18902.78
	24	137194	17342
	25	137194	15910.09
	26	137194	14596.41
	27	137194	13391.21
	28	137194	12285.51
	29	137194	11271.11
	30	137194	10340.47
	sum of present value of cash inflow		808463
	cash outflow		40454
	net present value		768009
2-	present value of annuity of 600
	present value of annuity at the of 2nd quarter	Using present value function in MS excel	pv(rate,nper,pmt,fv,type) rate = 4.16% nper = 4*4 =16 pmt = 600 type = 0	PV(4.16%,16,-600,0,0)	$6,909.58
	present value at todays time	fv/(1.0416)	6909.58/(1.0416)^2	6368.6841
	present value of loan amount at year 4	Using present value function in MS excel	pv(rate,nper,pmt,fv,type) rate = .95% nper = 12*5 =60 pmt = 359 type = 0	PV(.95%,60,-359,0,0)	$16,360.99
	total value of car he can afford at year 4	6909.58+16360.99	23270.57