A ) An entrepreneur invests $40,454.00 into a start-up business today. He expect
ID: 2621269 • Letter: A
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?
Explanation / Answer
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
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
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