Capital Budgeting | Assignment-1

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Capital Budgeting

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Solution 1: Cost of Equity-CAPM
Formula of CAPM: Rf + Beta*(Rm-Rf)
Where:
Rf= Risk free rate of return
Rm= Market return
Rm-Rf = Market risk premium
Beta: Systematic risk
(Lalli, 2011)
Cost of Equity of XYZ, Inc
 Beta: 0.8
 Rm-Rf: 5.5%
 Rf: 7% (Yield on 10 year T-Bond will be appropriate to be take)
Using formula: 7 %+( 0.8*5.5%) = 7%+4.4% = 11.4%
Cost of equity of XYZ, Inc is 11.4%
Solution 2:
Given Data
Years Cash flows
Year 0 $ (60,000.00)
Year 1 $ 10,000.00
Year 2 $ 10,000.00
Year 3 $ 10,000.00
Year 4 $ 10,000.00
Year 5 $ 10,000.00
Year 6 $ 10,000.00
Year 7 $ 10,000.00
Year 8 $ 10,000.00
Cost of capital 12%
a) Net present value
Formula: Present value of cash inflow-Present value of cash outflows
(Moles & Kidwekk, 2011)
Net Present Value

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Years Cash flows PVF @12% Present Value
0 $ (60,000.00) 1.000 $ (60,000.000)
1 $ 10,000.00 0.893 $ 8,928.571
2 $ 10,000.00 0.797 $ 7,971.939
3 $ 10,000.00 0.712 $ 7,117.802
4 $ 10,000.00 0.636 $ 6,355.181
5 $ 10,000.00 0.567 $ 5,674.269
6 $ 10,000.00 0.507 $ 5,066.311
7 $ 10,000.00 0.452 $ 4,523.492
8 $ 10,000.00 0.404 $ 4,038.832
NPV $ (10,323.602)
b) Internal rate of return
Formula of IRR:
(Moles & Kidwekk, 2011)
Internal rate of return
Years Cash flows PVF
@5% PV @ 5% PVF
@10% PV @ 10%
0 $
(60,000.00) 1.000 $
(60,000.000) 1.000 $
(60,000.000)
1 $
10,000.00 0.952 $
9,523.810 0.909 $
9,090.909
2 $
10,000.00 0.907 $
9,070.295 0.826 $
8,264.463
3 $
10,000.00 0.864 $
8,638.376 0.751 $
7,513.148
4 $
10,000.00 0.823 $
8,227.025 0.683 $
6,830.135
5 $
10,000.00 0.784 $
7,835.262 0.621 $
6,209.213
6 $
10,000.00 0.746 $
7,462.154 0.564 $
5,644.739
7 $ 0.711 $ 0.513 $

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10,000.00 7,106.813 5,131.581
8 $
10,000.00 0.677 $
6,768.394 0.467 $
4,665.074
NPV $
4,632.128 NPV $
(6,650.738)
Lower discount rate 5%
Higher discount rate 10%
NPV at lower discount rate $ 4,632.128
NPV at higher discount rate $ (6,650.738)
Internal rate of return 7.05%
c) MIRR
(Moles & Kidwekk, 2011)
Cost of Capital=12%
Reinvestment rate=12%
MIRR= 9.39%
d) Profitability Index
Formula= (Net present value + Initial Outlay)/Initial outlay
(Moles & Kidwekk, 2011)
= (-$10,323.60+ $ 60000)/$60000
= 0.83
e) Payback period
Payback Period
Years Cash flows Cumulative CF
Year 0 $ (60,000.00) $ (60,000.00)
Year 1 $ 10,000.00 $ (50,000.00)
Year 2 $ 10,000.00 $ (40,000.00)
Year 3 $ 10,000.00 $ (30,000.00)
Year 4 $ 10,000.00 $ (20,000.00)

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Year 5 $ 10,000.00 $ (10,000.00)
Year 6 $ 10,000.00 $ -
Year 7 $ 10,000.00 $ 10,000.00
Year 8 $ 10,000.00 $ 20,000.00
Payback Period 6 years
f) Discounted payback period
Discounted Payback Period
Years Cash flows PVF @12% Present Value Cummu. CF
0 $ (60,000.00) 1.000 $ (60,000.000) $ (60,000.000)
1 $ 10,000.00 0.893 $ 8,928.571 $ (51,071.429)
2 $ 10,000.00 0.797 $ 7,971.939 $ (43,099.490)
3 $ 10,000.00 0.712 $ 7,117.802 $ (35,981.687)
4 $ 10,000.00 0.636 $ 6,355.181 $ (29,626.507)
5 $ 10,000.00 0.567 $ 5,674.269 $ (23,952.238)
6 $ 10,000.00 0.507 $ 5,066.311 $ (18,885.927)
7 $ 10,000.00 0.452 $ 4,523.492 $ (14,362.435)
8 $ 10,000.00 0.404 $ 4,038.832 $ (10,323.602)
Discounted payback period This project has failed to recover the initial outlay as
discounted value of cash inflows is less than the initial
outlay
Solution 3:
Year Project A Project B
1 $ 5,000,000.00 $ 20,000,000.00
2 $ 10,000,000.00 $ 10,000,000.00
3 $ 20,000,000.00 $ 6,000,000.00
Initial Outlay $ 20,000,000.00
A: Net Present value
Formula: Present value of cash inflow-Present value of cash outflows
(Moles & Kidwekk, 2011)
Year Project A PVF @5% PV @ 5%
0 $ (20,000,000.00) 1.000 $ (20,000,000.000)
1 $ 5,000,000.00 0.952 $ 4,761,904.762

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2 $ 10,000,000.00 0.907 $ 9,070,294.785
3 $ 20,000,000.00 0.864 $ 17,276,751.971
$ 11,108,951.517
Year Project A PVF @10% PV @ 10%
0 $ (20,000,000.00) 1.000 $ (20,000,000.000)
1 $ 5,000,000.00 0.909 $ 4,545,454.545
2 $ 10,000,000.00 0.826 $ 8,264,462.810
3 $ 20,000,000.00 0.751 $ 15,026,296.018
$ 7,836,213.373
Year Project A PVF @15% PV @ 15%
0 $ (20,000,000.00) 1.000 $ (20,000,000.000)
1 $ 5,000,000.00 0.870 $ 4,347,826.087
2 $ 10,000,000.00 0.756 $ 7,561,436.673
3 $ 20,000,000.00 0.658 $ 13,150,324.649
$ 5,059,587.409
Year Project B PVF @5% PV @ 5%
0 $ (20,000,000.00) 1.000 $ (20,000,000.000)
1 $ 20,000,000.00 0.952 $ 19,047,619.048
2 $ 10,000,000.00 0.907 $ 9,070,294.785
3 $ 6,000,000.00 0.864 $ 5,183,025.591
$ 13,300,939.423
Year Project B PVF @10% PV @ 10%
0 $ (20,000,000.00) 1.000 $ (20,000,000.000)
1 $ 20,000,000.00 0.909 $ 18,181,818.182
2 $ 10,000,000.00 0.826 $ 8,264,462.810
3 $ 6,000,000.00 0.751 $ 4,507,888.805
$ 10,954,169.797
Year Project B PVF @15% PV @ 15%
0 $ (20,000,000.00) 1.000 $ (20,000,000.000)
1 $ 20,000,000.00 0.870 $ 17,391,304.348
2 $ 10,000,000.00 0.756 $ 7,561,436.673
3 $ 6,000,000.00 0.658 $ 3,945,097.395
$ 8,897,838.415
B: Internal Rate of return
Formula of IRR:

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(Moles & Kidwekk, 2011)
IRR of Project A
Year Project A PVF @35% PV @ 35%
0 $ (20,000,000.00) 1.000 $ (20,000,000.000)
1 $ 5,000,000.00 0.741 $ 3,703,703.704
2 $ 10,000,000.00 0.549 $ 5,486,968.450
3 $ 20,000,000.00 0.406 $ 8,128,842.148
$ (2,680,485.698)
Year Project A PVF @25% PV @ 25%
0 $ (20,000,000.00) 1.000 $ (20,000,000.000)
1 $ 5,000,000.00 0.800 $ 4,000,000.000
2 $ 10,000,000.00 0.640 $ 6,400,000.000
3 $ 20,000,000.00 0.512 $ 10,240,000.000
$ 640,000.000
Lower discount rate 25%
Higher discount rate 35%
NPV at lower discount rate $ 640,000.000
NPV at higher discount rate $ (2,680,485.698)
Internal rate of return 26.93%
IRR of Project B
Year Project B PVF @50% PV @ 50%
0 $ (20,000,000.00) 1.000 $ (20,000,000.000)
1 $ 20,000,000.00 0.667 $ 13,333,333.333
2 $ 10,000,000.00 0.444 $ 4,444,444.444
3 $ 6,000,000.00 0.296 $ 1,777,777.778
$ (444,444.444)
Year Project B PVF @40% PV @ 40%
0 $ (20,000,000.00) 1.000 $ (20,000,000.000)
1 $ 20,000,000.00 0.714 $ 14,285,714.286

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2 $ 10,000,000.00 0.510 $ 5,102,040.816
3 $ 6,000,000.00 0.364 $ 2,186,588.921
$ 1,574,344.023
Lower discount rate 40%
Higher discount rate 50%
NPV at lower discount rate $ 1,574,344.023
NPV at higher discount rate $ (444,444.444)
Internal rate of return 47.80%

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References
Lalli, W. (2011). Handbook of Budgeting. US: John Wiley & Sons.
Moles, P. & Kidwekk, D. (2011). Corporate finance. US: John Wiley &sons.