In: Finance
Following are the 2 projects Richard Soderberg is thinking about investing in:
Project 1
Year |
Free Cash Flow |
0 |
($900) Initial Investment |
1 |
($90) |
2 |
$241 |
3 |
$273 |
4 |
$283 |
5-15 |
$280 |
*Project 1 initial investment at time zero is $900 (Outflow)
Project 2
Year |
Free Cash Flow |
0 |
($1900) Initial Investment |
1 |
($1400) |
2 |
$116 |
3 |
$635 |
4 |
$690 |
5 |
$755 |
6 |
$826 |
7-15 |
$849 |
*Project 2 initial investment at time zero is $1900 (Outflow)
Question) Find the following:
1) Discounted payback period of project 1 and 2 at the following rates: 8%,20%
2) Net Present Value of project 1 and 2 at the following rates: 8%, 20%
3) Profitability Index of both project 1 and 2
Note: Please do not solve using excel sheet formula or financial calculator
1] | Project 1 | |||||||
Year | Cash flow | PVIF at 8% | PV at 8% | Cumulative PV at 8% | PVIF at 10% | PV at 10% | Cumulative PV at 10% | |
0 | $ -900.00 | 1 | $ -900.00 | $ -900.00 | 1 | $ -900.00 | $ -900.00 | |
1 | $ -90.00 | 0.92593 | $ -83.33 | $ -983.33 | 0.90909 | $ -81.82 | $ -981.82 | |
2 | $ 241.00 | 0.85734 | $ 206.62 | $ -776.71 | 0.82645 | $ 199.17 | $ -782.64 | |
3 | $ 273.00 | 0.79383 | $ 216.72 | $ -560.00 | 0.75131 | $ 205.11 | $ -577.54 | |
4 | $ 283.00 | 0.73503 | $ 208.01 | $ -351.99 | 0.68301 | $ 193.29 | $ -384.24 | |
5 | $ 280.00 | 0.68058 | $ 190.56 | $ -161.42 | 0.62092 | $ 173.86 | $ -210.38 | |
6 | $ 280.00 | 0.63017 | $ 176.45 | $ 15.03 | 0.56447 | $ 158.05 | $ -52.33 | |
7 | $ 280.00 | 0.58349 | $ 163.38 | $ 178.40 | 0.51316 | $ 143.68 | $ 91.35 | |
8 | $ 280.00 | 0.54027 | $ 151.28 | $ 329.68 | 0.46651 | $ 130.62 | $ 221.97 | |
9 | $ 280.00 | 0.50025 | $ 140.07 | $ 469.75 | 0.42410 | $ 118.75 | $ 340.72 | |
10 | $ 280.00 | 0.46319 | $ 129.69 | $ 599.44 | 0.38554 | $ 107.95 | $ 448.67 | |
11 | $ 280.00 | 0.42888 | $ 120.09 | $ 719.53 | 0.35049 | $ 98.14 | $ 546.81 | |
12 | $ 280.00 | 0.39711 | $ 111.19 | $ 830.72 | 0.31863 | $ 89.22 | $ 636.03 | |
13 | $ 280.00 | 0.36770 | $ 102.96 | $ 933.68 | 0.28966 | $ 81.11 | $ 717.13 | |
14 | $ 280.00 | 0.34046 | $ 95.33 | $ 1,029.01 | 0.26333 | $ 73.73 | $ 790.87 | |
15 | $ 280.00 | 0.31524 | $ 88.27 | $ 1,117.27 | 0.23939 | $ 67.03 | $ 857.90 | |
$ 1,117.27 | $ 857.90 | |||||||
Discounted payback at 8% = 5+161.42/176.45 = | 5.91 | Years | ||||||
Discounted payback at 10% = 6+134.15/143.68 = | 6.93 | Years | ||||||
Project 2 | ||||||||
Year | Cash flow | PVIF at 8% | PV at 8% | Cumulative PV at 8% | PVIF at 10% | PV at 10% | Cumulative PV at 10% | |
0 | $ -1,900 | 1 | $ -1,900.00 | $ -1,900.00 | 1 | $ -1,900.00 | $ -1,900.00 | |
1 | $ -1,400 | 0.92593 | $ -1,296.30 | $ -3,196.30 | 0.90909 | $ -1,272.73 | $ -3,172.73 | |
2 | $ 116 | 0.85734 | $ 99.45 | $ -3,096.84 | 0.82645 | $ 95.87 | $ -3,076.86 | |
3 | $ 635 | 0.79383 | $ 504.08 | $ -2,592.76 | 0.75131 | $ 477.08 | $ -2,599.77 | |
4 | $ 690 | 0.73503 | $ 507.17 | $ -2,085.59 | 0.68301 | $ 471.28 | $ -2,128.50 | |
5 | $ 755 | 0.68058 | $ 513.84 | $ -1,571.75 | 0.62092 | $ 468.80 | $ -1,659.70 | |
6 | $ 826 | 0.63017 | $ 520.52 | $ -1,051.23 | 0.56447 | $ 466.26 | $ -1,193.44 | |
7 | $ 849 | 0.58349 | $ 495.38 | $ -555.85 | 0.51316 | $ 435.67 | $ -757.77 | |
8 | $ 849 | 0.54027 | $ 458.69 | $ -97.16 | 0.46651 | $ 396.06 | $ -361.71 | |
9 | $ 849 | 0.50025 | $ 424.71 | $ 327.55 | 0.42410 | $ 360.06 | $ -1.65 | |
10 | $ 849 | 0.46319 | $ 393.25 | $ 720.80 | 0.38554 | $ 327.33 | $ 325.68 | |
11 | $ 849 | 0.42888 | $ 364.12 | $ 1,084.93 | 0.35049 | $ 297.57 | $ 623.25 | |
12 | $ 849 | 0.39711 | $ 337.15 | $ 1,422.07 | 0.31863 | $ 270.52 | $ 893.76 | |
13 | $ 849 | 0.36770 | $ 312.18 | $ 1,734.25 | 0.28966 | $ 245.93 | $ 1,139.69 | |
14 | $ 849 | 0.34046 | $ 289.05 | $ 2,023.30 | 0.26333 | $ 223.57 | $ 1,363.26 | |
15 | $ 849 | 0.31524 | $ 267.64 | $ 2,290.94 | 0.23939 | $ 203.24 | $ 1,566.50 | |
$ 2,290.94 | $ 1,566.50 | |||||||
Discounted payback at 8% = 8+97.16/424.71 = | 8.23 | Years | ||||||
Discounted payback at 10% = 9+1.65/327.33 = | 9.01 | Years | ||||||
2] | NPV: | AT 8% | AT 10% | |||||
Project 1 | $ 1,117.27 | $ 857.90 | ||||||
Project 2 | $ 2,290.94 | $ 1,566.50 | ||||||
3] | PI: | |||||||
Project 1: | AT 8% | AT 10% | ||||||
PV of cash inflows | $ 2,017.27 | $ 1,757.90 | ||||||
Initial investment | $ 900.00 | $ 900.00 | ||||||
PI [PV of cash inflows/Initial investment] | 2.24 | 1.95 | ||||||
Project 2: | AT 8% | AT 10% | ||||||
PV of cash inflows | $ 4,190.94 | $ 3,466.50 | ||||||
Initial investment | $ 1,900.00 | $ 1,900.00 | ||||||
PI [PV of cash inflows/Initial investment] | 2.21 | 1.82 |