Principles of Finance: IRR, NPV, Bond Pricing, Cash Flow, Savage Value, and NPV Calculation
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This article covers topics related to Principles of Finance such as IRR, NPV, Bond Pricing, Cash Flow, Savage Value, and NPV Calculation. It includes solved examples and calculations for better understanding.
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PRINCIPLES OF FINANCE
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SECTION A Question 1 (a) calculation of IRR Project 1 Discount rate (r)35% Year (t) Project 1 cash flowPresent value factor Present value of cash flow (1/1+r)^t (cash flow* present value factor) 0-200000 1100000.74074074077407.4074074074 2100000.5486968455486.9684499314 3100000.40644210744064.4210740233 4100000.30106822773010.6822770543 Total19969.4792084164 NPV-30.5207915836 IRR Discount rate (t)34.00% present value factorpresent value Year (t) Project 1 cash flow(1/1+r)^t (cash flow* present value factor) 0-200000 1100000.74626865677462.6865671642 2100000.5569169085569.1690799733 3100000.41560963284156.0963283383 4100000.31015644243101.564424133
20289.5163996087 NPV289.5163996087 The value of NPV is calculated by taking the difference of present value of cash inflow and cash- outflow. So at the rate of 35% (discount rate), the value of NPV is negative. IRR is existed where NPV is zero. Which means that IRR is existed between 34% and 35%. Moreover, the rate of IRR is 34.90%. project 2 Discount rate (r)31.00% Year (t)Cash flowPresent value factorPresent value (1/1+r)^t (cash flow* present value factor) 0-200000-0 100.76335877860 200.58271662490 300.44482185110 4600000.339558664920373.519896462 20373.519896462 NPV373.5198 Discount rate32.00% yearProject 2present value factorpresent value 0-200000-0 100.75757575760 200.57392102850
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300.43478865790 4600000.329385346919763.1208149615 Total19763.1208149615 NPV-236.8791850385 From the above analysis it can be interpreted that when discount rate is 31%, the value of NPV is positive. Moreover, as it is increased to 32% the value of NPV becomes negative. The rate of IRR lies at the place where the value of NPV becomes ZERO. Therefore, the rate of IRR lies between 31% and 32%. So the rate of IRR is 31.61%. (b) calculation of NPV Project 1 Discount rate (r)10.00% Year (t) Project 1 cash flowpresent value factorpresent value (1/1+r)^t (cash flow* present value factor) 0-200000 1100000.90909090919090.9090909091 2100000.8264462818264.4628099174 3100000.75131480097513.1480090158 4100000.68301345546830.1345536507 Total31698.6544634929 NPV11698.6544634929 NPV =31698.6544 – 20000 =11698.65 (positive is favourable) Project 2 Discount rate (r)10.00% Year (t)Cash flowpresent value factorpresent value (1/1+r)^t(cash flow* present
value factor) 0-200000-0 100.90909090910 200.8264462810 300.75131480090 4600000.683013455440980.8073219042 40980.8073219042 NPV20980.8073219042 NPV= 40980.807 – 20000 =20980.80 (Positive is favourable) When company select the project on the basis of positive and higher NPV. Moreover, NPV shows how much return company is getting back a positive NPV shows favourable project. In order to decide which project is more favourable( in terms of return ). Out of these two project, project 2 is providing higher return because it has better NPV then project A. Question 2 6% Risk Rf 10% 20% Exp. Return 30% 11%
Question 3 a) Bond price = Coupon 1 / (1 + YTM / 2)1+ Coupon 2 / (1 + YTM / 2)2+........Coupon 40 / (1 + YTM / 2)40+ Face value / (1 + YTM)20 Coupon = 1000 * 5% = 50 / 2 = 25 every half year YTM = 6% / 2 = 3% = 25 / (1 + 3%)1+ 25 / (1 + 3%)2......25 / (1 + 3%)40+ 1000 / (1 + 6%)20 = 884.43 would be the bond price at issuance. b) The price of the bond at this point where coupon rate is equivalent to yield to maturity would be equals to its par or face value that is, 1000. Question 4 a Interest = 1000 * 8% = 800 Price of bond: interest / risk rate = 800 / 10% = 800 Question 4.b 5.548% Question 4.c (1) Bond C 6% = [80 + {(1000 – price) / 2 }] / [{1000 + Price} / 2] .06 = 160 + 1000 – price / 1000 + price = 785 Bond D 6% = [80 + {(1000 – price) / 8}] / [{1000 + Price} / 2] 6% = 640 + 1000 – Price / 4 (1000 + price) = 280 (2) 7
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Bond C 10% = [80 + {(1000 – price) / 2 }] / [{1000 + Price} / 2] = 963 Bond D 10% = [80 + {(1000 – price) / 8}] / [{1000 + Price} / 2] = 308 (3) The above stated calculation clearly indicate that yield to maturity certainly increases or decreases the value of the bond. If it is increased than the value of bond will also improve and in case it is decreased than the value of bond of reduce. The bond D has a greater risk element as the maturity is more which also reflect in the price of bond. The risk also depict in the prices of the bond. Question 5 Expected future cash flow: 40000 / 11% = 363636 Question 6 a) Calculation of Savage value of fixed assets The expenditure of the fixed assets at the beginning of the project which is also known as the actual cost of fixed assets would be = $1000. The depreciation on fixed assets in year 1 = $280, year 2 = $280 and year 3 = $280. So, the total depreciation on fixed asset over the three years = $280 + $280 + $280 = 840. Formula to calculate the carrying value of the fixed assets after three years = Original cost – Depreciation = $1000 - $840 = $160 Market value of the retired assets = $500 which is also known as salvage value before tax. The after-tax savage value of the fixed assets = market value of the retired assets * (1 – tax rate) = $500* (1 – 0.3) = $500* 0.7 = $350 8
The after-tax savage value of the fixed assets is $350. b) Calculation of operating cash flow of each year of the project ParticularsYear 1Year 2Year 3 Operating income540540540 Add Depreciation280280280 Less investment in net working capital -500-100-100 Addrecoveredfrom net working capital --700 Less Income tax-162-162-162 Operating cash flow1585581258 c) Calculation of Cash flow from assets or financing activities in each year of the projects ParticularsYear 1Year 2Year 3 Purchase of assets-100000 Sale of assets00500 Cash flow from assets-10000500 d) Calculation of NPV YearsCash flowDiscountingfactor @10% Present value of cash flow 0-15000-1500 9
1658 – 100 = 5580.9502.2 2658 – 100 = 5580.82457.56 3658 – 100 + 350 + 500 = 1408 0.751056 Present value of cash inflow – Initial investment = 2015.76 – 1500 = 515.76. If the required rate of return of this project is 10%, then it is advisable to the company to accept this project because at 10% return the company will earn profit. It is because the net present value of the three-year project is positive. Question 7 DateCipl a RtIdeaRtWon derla RtPVRRtAlke m RtCiplaIdeaWon derla PVRAlke m 21- 02-17 593. 1 0.06 % 108. 35 - 0.09 % 374.1 5 0.32 % 1268- 0.04 % 2000 .05 - 1.73 % 0.00%- 0.66 % 0.26 % - 0.19 % - 2.02% 22- 02-17 589. 25 - 0.65 % 112. 6 3.92 % 374.4 5 0.08 % 1263. 35 - 0.37 % 2022 .55 1.12 % - 0.71% 3.36 % 0.02 % - 0.52 % 0.84% 23- 02-17 592. 4 0.53 % 119. 6 6.22 % 373.4- 0.28 % 1260. 1 - 0.26 % 2076 .85 2.68 % 0.47%5.65 % - 0.34 % - 0.41 % 2.40% 27- 02-17 585. 25 - 1.21 % 114. 55 - 4.22 % 373.8 5 0.12 % 1278. 1 1.43 % 2154 .75 3.75 % - 1.27% - 4.79 % 0.06 % 1.27 % 3.46% 28- 02-17 583. 7 - 0.26 % 115. 85 1.13 % 372.4- 0.39 % 1295. 55 1.37 % 2141 .55 - 0.61 % - 0.33% 0.57 % - 0.45 % 1.21 % - 0.90% 1-03-586.0.45113.-373.80.381296.0.0521440.120.38%-0.32-- 10
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Working capital – 9% of EBIT-1.125-1.2375-1.361-1.497-1.647-1.812-1.866 Net Cash Inflow5.756.336.967.658.429.269.54 WACC – 9.04%10.9170.8410.7710.7070.649 PV of Cash flow5.755.805.855.905.966.01 Present value of cash in year 6 =CF5/ (WACC–g) = $8,418,575(1 + .03) / (.0904 – .03) = $143,561,792 discounting cash flows and terminal value in terms of their present value. By Doing so, we find: V0= $5,750,000 / 1.0904 + $6,325,000 / 1.09042+ $6,957,500 / 1.09043 + $7,653,250 / 1.09044+ ($8,418,575 + 143,561,792) / 1.09045 V0= $119,969,144 Market value of equity = Market value of firm – market value of debt S= $119,969,144 – 30,500,000 S=$89,469,144 Maximum share price = market value of equity / no. of shares outstanding Share price = $89,469,144 / 1,850,000 Share price = $48.36 b) EV/EBITDA multiple = 8 Calculation of Terminal Value using EV/EBITDA multiple = Present EBITDA X 8 = ($12.60 + $ 1.01)million X 8 = $13.61 million X 8 = $ 108.86 million Therefore maximum share price can be offered = $108.86 million / 1.85 million = $58.84 per share 14
SECTION B Question 1 The internal rate of return technique do not provide the clearly picture of future. It ignore the overall size of project. It ignores future cost with calculation . Mutually exclusive projects got ignored while calculating the internal rate of return. Different term of project is not considered while evaluating the internal rate of return technique. In case the later cash inflow are not sufficient than the IRR is not possible to calculate in the project. Also the wealth of the project is not possible to measure with the support of internal rate of return method or technique. It does not account for investment. It suggests to keep match up with multiple cash (Kim, Kim and Yook, 2021). The disadvantage of the Internal rate of return technique can be solved with the use of other method or techniques like net present value and the payback period and other relevant techniques. To overcome the challenges of IRR time horizon can cut down to deal with the time related issues. Also the management can use this technique only for the projects contain only a shirt time duration. Question 3 Beta is a measure of a stock volatility in relation to the overall market. The Beta is one of the most popular indicator with the help of which investors can measure the risk of the securities. Beta is a concept that measures the expected move in a stock relative to movements in the overall market. A beta greater than 1.0 suggest that the particular stock and security is more volatile than the broader market. While in the case, when Beta is less than 1.0 indicate a stock with lower volatile. Beta is basically and probably a better indicator of the short-term risk not for the long term risk (Xiang and et.al., 2019). In order to calculate and estimate the beta of the securities, the two factors is need to be used. The two factors likely to determine its value is the risk free return rate and the other one is stocks rate of return. Beta = Covariance/ variance. Covariance = measure of a stocks return relative to that of the market Variance = measure of how the market moves relative to its mean 15
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REFERENCES Books and journals Kim, K., Kim, J. and Yook, D., 2021. Analysis of Features Affecting Contracted Rate of Return of Korean PPP Projects.Sustainability.13(6). p.3311. Xiang, J. and et.al., 2019. Hydroxycinnamic acid amide (HCAA) derivatives, flavonoid C- glycosides,phenolicacidsandantioxidantpropertiesoffoxtailmillet.Food chemistry.295.pp.214-223. 1