Npv vs. Irr Essay Example

Npv vs. Irr Essay Versus IRR W. L. Silber I. Our favorite project A has the following cash flows: -1000 0 0 1 0 2 +300 3 +600 4 +900 5 We know that if the cost of capital is 18 percent we reject the project because the net present value is negative: 1000 + 300 600 900 + + = NPV 3 4 (1. 18) (1. 18) (1. 18)5 1000 + 182. 59 + 309. 47 + 393. 40 = -114. 54 We also know that at a cost of capital of 8% we accept the project because the net present value is positive: 1000 + 300 600 900 + + = NPV 3 4 (1. 08 ) (1. 08 ) (1. 08 )5 1000 + 238. 15 + 441 . 02 + 612 . 52 = 291. 69 II. Thus, somewhere between 8% and 18% we change our evaluation of project A from rejecting it (when NPV is negative) to accepting it (when NPV is positive). We can calculate the point at which NPV shifts from negative to positive by searching for the value of r, called the internal rate of return (IRR) in the following equation, which makes the NPV=0. 1000 + 300 600 900 + + =0 3 4 (1 + r ) (1 + r ) (1 + r )5 More generally, if CFi is the cash flow in period i, the IRR is that rate, r, such that: CF0 + CFt CF1 CF2 + +L+ =0 2 (1 + r ) (1 + r ) (1 + r )t In our case, CF0 = -1000, CF3 = 300, CF4 = 600 and CF5 = 900. All the other CFi = 0. III. The IRR can, in general, only be derived by trial and error. Putting our values for the CFi into a calculator (very carefully) we find the IRR= 14. 668%. We can check this result as follows: 1000 + 300 600 900 + + = 3 4 (1. 14668) (1. 14668) (1. 14668) 5 1000 + 198. 97 + 347 . 04 + 453 . 97 = -. 02 The sum is not exactly zero because of rounding. IV. We can now formulate an alternative rule to accepting the project if NPV gt; 0 and rejecting it if NPV lt; 0. In particular, we can recommend rejecting a project if the cost of capital is greater than the IRR (14. 68% in this case) and we can recommend accepting a project if the cost of capital is less than the IRR. These two rules are equally acceptable in this case for determining whether project A will increase the value of the firm. V. There are circumstances, however, where the IRR rule and the NPV rule provide conflicting advice. In particular, IRR and NPV may differ where there are two mutually exclus ive projects that must be ranked according to which one is best and where these two projects have very different timing of cash flows. Whenever there is a conflict between NPV and IRR the correct answer is provided by NPV. Let’s see why. VI. Suppose we want to compare project B with project A. The cash flows are described below, with B’s cash flows equally distributed over time, while A’s cash flow (as we saw) are delayed. A -1000 0 B -1000 1 +320 2 +320 +300 3 +320 +600 4 +320 +900 5 +320 We have already solved for the IRR of project A, i. e. , IRRA = 14. 668%. Solving for the IRR of project B produces, IRRB = 18. 03%. Thus, the IRR rule ranks project B better than A. We will write a custom essay sample on Npv vs. Irr specifically for you for only $16.38 $13.9/page Order now We will write a custom essay sample on Npv vs. Irr specifically for you FOR ONLY $16.38 $13.9/page Hire Writer We will write a custom essay sample on Npv vs. Irr specifically for you FOR ONLY $16.38 $13.9/page Hire Writer Let’s see whether that is also true for the NPV rule, i. e. , let’s see if NPVB is always greater than NPVA. To implement the NPV rule we must calculate the NPV of A and B for alternative values of the cost of capital. This is done in table 1: Table 1 Cost of Capital 20% 15% 10% 8% 5% NPVA -175 -12 +194 +291 +458 NPVB -43 +73 +213 +277 +385 Notice that project B is better (has a higher NPV) than project A when the cost of capital is above 10% (above 20% both have negative NPVs, but B is less bad), while project A is better when the cost of capital is below 8%. In fact, you can calculate the exact cost of capital at which the recommendation switches by setting NPVA = NPVB and solving (after some algebraic manipulations) for the IRR under those circumstances. This IRR turns out to be 8. 8169%. VII. We see that the NPV rule says that project B is better than project A (the same ranking as the IRR rule) only for â€Å"high† values for the cost of capital, i. e. , for a cost of capital greater than 8. 8169%. For values of the cost of capital below 8. 8169% project A is better. This makes considerable sense. When the cost of capital is â€Å"high† the delayed cash flows of project A are penalized considerably, while when the cost of capital is â€Å"low† the delayed cash flows are not penalized. Indeed, the low cost of capital makes those â€Å"large but delayed† cash flows quite valuable. VIII. One way to understand the preference of NPV over IRR, more generally, is to recognize that NPV uses the â€Å"correct† rate, i. e. , the cost of capital, to discount the cash flows, rather than an â€Å"arbitrary† rate, i. e. , the IRR, that makes NPV =0. Another way to understand the superiority of the NPV rule is that the discounting process inherent in both the IRR and NPV techniques implicitly assumes the reinvestment of the cash flows at whatever discount rate is used, either IRR or the cost of capital. When the IRR is very high relative to the cost of capital it is unrealistic to assume reinvestment at that high rate. This is especially damaging when comparing two investments with very different timing of cash flows. We will revisit this reinvestment assumption later, under our discussion of yield to maturity on coupon bonds, where its meaning will become clearer.

Pointless death in war Essay Example

Pointless death in war Essay Example Pointless death in war Essay Pointless death in war Essay Good Evening/Morning Teachers and fellow students, today is the day that marks Wilfred Owens Inclusion into the War Poets Hall of Fame. Owens poetry was different to that of some other types of war poets of his time because he was courageous enough to make his attacks on the government and the significant loss of life. His Ideas and techniques are presented throughout the two poems Dulce et Decorum Est and Anthem for Doomed Youth. Owen explores the truths of war in these poems through themes such as; war as the horrific and savage scene it is, the disparity between reality of the battlefield and the perception of what war is at home. Owen shows the devastation of war on the human being and soul, not only the physical but the mental effects of war. The soldiers are influenced by government propaganda, they are told to die for their country; the betrayal, conspiracy and devastating loss of innocent youth. Owen is able to portray these truths through his powerful poetry. Throughout his poems he uses allusions, guttural consonants, onomatopoeia and other techniques to create powerful messages that war is, to quote Owen himself, to hell and back. Dulce et Decorum Est brings the realisation that war is not as it is portrayed to the public, but the allusion that the government gives to the country. This is shown through the title Dulce et Decorum Est. This title means that it is sweet and honorable to die for ones country this allusion throughout the poem shows through irony and sarcasm that it is the The old Lie; Dulce et Decorum est Pro patria mori. This shows how war is everything but sweet and honorable it is about the death and horror brought into peoples lives. War equals death. The description of the soldier drowning in the blood of his froth corrupted lungs certainly negates this. Owen shows the unknown fact that men are dying for their country in a horrible way. Owen is hiding it in another language, just as the government was hiding the truth from their country, letting people kill themselves. This is very different to the poets during Owens time, as he was not glorifying war, but exposing the devastating affect war had on humankind. This is used in conjunction with the disparity between war on the battlefront and the corruption of the perception of a courageous and glorious place to be. In the poem Anthem for Doomed Youth, Owen illustrates his theme of the devastating loss of youth. The title to brings to mind the hope of a song of praise, but Owen uses this to his advantage. He emphasises his theme through the words Anthem, Doomed Youth in the title of the poem are juxtaposed to highlight the brutality reality of war. The word Youth normally brings to mind happiness and joy. Owen places Youth next to the word Doomed which illustrates to the audience the stress and hopelessness of the youth during war. The word Anthem usually associates with a patriotic song or song of praise, Owen draws to mind the fact that these boys have nothing to sing about during the chaos of war. Owen effects the thoughts and feelings of people that have not experienced war for what it is, the major loss of innocent lives. Owen shows the significance of his poetry through the title, giving the audience a sense of feeling for the poem. Owen uses visual representations in Dulce to show the mental and physical effects on the soldiers going through the punishment of war and how this changes the young soldiers. The harshness of the simile bent double like old beggars illustrates how the soldiers look, showing them as crestfallen and disheartened, bent. This is not how soldiers are normally depicted they should have their heads held high and marching tall. Owen shows how the young men of war have now become old beggars; they have aged and are begging for their lives; lives that may be taken away from them at any time. This along with an ecstasy of fumbling shows the urgent need for the salvation of ones life. The ecstasy of fumbling to put on their gas masks shows the audience how the soldiers have been forced into the bent and begging state to save their lives. The soldiers are beyond exhaustion, they have to find the energy to put on their gas mask or they will face death. The innocence of youth has been lost. Some have lost their lives; others have lost their mental state. Owen also shows the mental effects on the young soldiers as they are killed and thrown away to die through the poem Anthem for Doomed Youth. Owens main theme is the fact that the young soldiers do not get the proper funeral they deserve. The opening line What passing bells for those who die as cattle? the use of this rhetorical question illustrates numbers of soldiers massacred as if they were cattle, shredding the blood of youth, their pain, and death in large numbers. Owen uses onomatopoeia and personification in the bombs to represent the harshness of the battlefield, as the soldiers had to endure the sounds of wailing shells as they brutally diminish the soldiers mind. Owen compares the funeral at home compared to the funeral on the battlefield. The holy glimmers interpreted as tears, in the eyes of the soldiers, and funeral bells are replaced with the sounds of weapons firing. Owen shows that during war soldiers deaths are seen to be insignificant. Owen shows the insignificance of human life and the mental horrors as young men are brought to tears, the devastation of war and the savage mean to kill people. The use of Guttural consonants throughout Owens poem Dulce et Decorum Est are shown through words such as guttering, choking, drowning the use of t k and d emphasise the harshness of war. These words describe how a young soldier is dies in war; there is nothing smooth and flowing about the death of a soldier. It tells of the death of a young soldier just because he wasnt quick enough to put on his gas mask. The harsh sound when these words are spoken help set the theme of a pointless death in war. This coupled with the present participle, ing make the poem powerful to the reader showing that the scene is not in the past, its happening now, putting the reader at the scene of the horror and illustrates the urgency and death of the battlefield. Owen used this to convey his message to the home front, to show the effects of war through the harshness of his language, depicted with the loss of innocent life within our society. Owen uses onomatopoeia in Anthem through stuttering rifles rapid rattle this line demonstrates the continuing slaughter of men. The use of the word rapid infers not only the speed of the guns but the speed of which lives are being taken away. The use of onomatopoeia is also used in conjunction with alliteration in the rifles rapid rattle. This line depicts the sound of the guns. Also how the line not easily orated, and this implies that it is a hard time, a time of disparity. The sounds of guns fire also replaces the grieving people you would normally find when a death occurs. Owen significantly changes the audiences opinion of the war showing that there is no time to grieve when people are dying quicker than a gun can fire. Through the use of harsh consonants in his language, Owen conveys his message of hardship for soldiers during war, the loss of innocent lives, the reality of the battlefield and the horror and savagery of war. In conclusion Wilfred Owen uses many complex themes that show the world the significant horrors of war, major losses of war and the disparity of the battlefield and the effects of war at home. Throughout Dulce et Decorum Est and Anthem for Doomed Youth Owen has shown several techniques to justify his arguments to the audience and what has just been illustrated to you. Based on the crux of the arguments presented, I trust that Wilfred Owen will be included into the War Poets Hall of Fame.