Question

Question 2 2.1. 2.2. Explain why discounted cash flow (DCF)methods are regarded as superior to non DCF approaches to project evaluation. (20%) A householder currently operates an inefficient gas fired boiler which is increasingly expensive to operate. A modern condensing combi boiler would reduce gas consumption by 20% but would cost £2400 to install. His estimated cost for gas over the next year using the current boiler is £1250. It is also anticipated that future gas prices will rise by 2% per year. Answer the following using appropriate cash flow diagrams. What would be the simple payback period for the proposed boiler replacement? If the discount rate is 5% and the anticipated life of the replacement is 20 years would you recommend replacement and if so what would be the NPV and IRR for the project? (80%)

Answer 1

2.1-	Discounted cash flow method are considered as better methods over non discounted cash flow methods because discounted cash flow methods consider the risk due to inflation and time associated with the cash flow. Discounted cash flow method consider time value of money concepts to evaluate the performance of project while non discounted cash flow methods do not consider concept of time value of money.
2.2-
Year	cost of gas consumption of old boiler over the years = current year consumption*(1+inflation rate) inflation rate =2%	Annual saving from the use of new boiler =20% of the gas consumption of old boiler	Accumulated annual savings		Year	Annual saving from the use of new boiler =20% of the gas consumption of old boiler	present value factor = 1/(1+r)^n r =5%	present value of annual savings = annual savings*present value factor at 5%
0					0	-2400	1	-2400
1	1250	250	250		1	250	0.952381	238.0952381
2	1275	255	505		2	255	0.907029	231.292517
3	1300.5	260.1	765.1		3	260.1	0.863838	224.6841594
4	1326.51	265.302	1030.402		4	265.302	0.822702	218.264612
5	1353.0402	270.60804	1301.01004		5	270.60804	0.783526	212.0284802
6	1380.101	276.020201	1577.030241		6	276.0202008	0.746215	205.9705236
7	1407.703	281.540605	1858.570846		7	281.5406048	0.710681	200.0856515
8	1435.8571	287.171417	2145.742263		8	287.1714169	0.676839	194.3689186
9	1464.5742	292.914845	254.2577375	amount to be recovered in year 10 =2400-2145.74	9	292.9148453	0.644609	188.8155209
10	1493.8657	298.773142			10	298.7731422	0.613913	183.4207918
11	1523.743	304.748605			11	304.748605	0.584679	178.1801977
12	1554.2179	310.843577			12	310.8435771	0.556837	173.0893349
13	1585.3022	317.060449			13	317.0604486	0.530321	168.1439254
14	1617.0083	323.401658			14	323.4016576	0.505068	163.3398132
15	1649.3485	329.869691			15	329.8696908	0.481017	158.6729614
16	1682.3354	336.467085			16	336.4670846	0.458112	154.1394482
17	1715.9821	343.196426			17	343.1964263	0.436297	149.735464
18	1750.3018	350.060355			18	350.0603548	0.415521	145.4573079
19	1785.3078	357.061562			19	357.0615619	0.395734	141.3013848
20	1821.014	364.202793			20	364.2027931	0.376889	137.2642024
Payback period = year before final year of recovery+(amount to be recovered in year 10/annual savings of year 10)	9+(254.2577/298.77)	9.85			Net present value =sum of present value of annual savings			1266.35
					IRR	Using IRR function in MS excel	IRR(J850:J870)	10.20% C. - = New Microsoft Office Excel Worksheet (2) - Microsoft Excel Home Insert Page Layout Formulas Data Review View * Cut Calibri - 11 - A A Dr Wrap Text Percentage 1 D 3 AutoSum" AT A La Copy Paste Format Painter B I U - - > A +0.00 E EFF Merge & Center - $ - % , 8.09 Conditional Format Conditional Format Cell Cell Insert Delete Format Insert Delete Format Sort & Find & Formatting as Table Styles 2 Clear Filter Select Clipboard Font Alignment Number Styles Cells Editing L872 fx =IRR(1850:1870) Document Recovery C D E F G H I L M N O P Excel has recovered the following files. Save 849 Year cost of gas Annual savin Accumulated annual Year Annual saving from the us present value present value of annual savings = annual savings*present the ones you wish to keep. -2400 -2400 Available files 1250 250 250 250 0.952380952 238.0952381 1275 255 505 255 0.907029478 231.292517 New Microsoft Office Excel W... 3 1300.5 260.1 765.1 260.1 0.863837599 224.6841594 Version created from the last ... 7:48 AM Wednesday, Februar... 4 1326.51 265.302 1030.402 265.302 0.822702475 218.264612 5 1353.0402 270.60804 1301.01004 270.60804 0.783526166 212.0284802 New Microsoft Office Excel W... 6 1380.101 276.020201 1577.030241 276.0202008' 0.746215397 205.9705236 Version created last time the ... 7 1407.703 281.540605 1858.570846 281.5406048 0.71068133 200.0856515 5:30 AM Monday, January 01... 8 1435.8571 287.171417 2145.742263 287.1714169 0.676839362 194.3689186 9 1464.5742 292.914845 254.2577375 amoun 292.9148453 0.644608916 188.8155209 10 1493.8657 298.773142 298.7731422 0.613913254 183.4207918 11 1523.743 304.748605 304.748605 0.584679289 178.1801977 12 1554.2179 310.843577 310.8435771 0.556837418 173.0893349 13 1585.3022 317.060449 317.0604486 0.530321351 168.1439254 14 1617.0083 323.401658 323.4016576 0.505067953 163.3398132 15 1649.3485 329.869691 329.8696908 0.481017098 158.6729614 16 1682.3354 336.467085 336.4670846 0.458111522 154.1394482 17 1715.9821 343.196426 343.1964263 0.436296688 149.735464 18 1750.3018 350.060355 350.0603548 0.415520655| 145.4573079 19 1785.3078 357.061562 357.0615619 0.395733957| 141.3013848 20 1821.014 364.202793 364.2027931 0.376889483 137.2642024 Payback pe 9+254.257 9.85 Net present value =sum of present value of annud 1266.35 Which file do I want to save? IRR Using irr function in ms excel IRR(J850:1870) L 1 0.20%|| Close BEHEEEE 160.00 40 ulawwalo Sheet Sheet Sheet