Question 3.17: From the undermentioned facts, compute the net present value......

Management Accounting and Financial Analysis for CA Final Examination [995093]

From the undermentioned facts, compute the net present values (NPVs) of the two projects for each of the possible cash flows, using sensitivity analysis.

$Project\>Y$ $(’000\>Rs)$	$Project\>X$ $(’000\>Rs)$
40	40	Initial cash outlays (t = 0)
0	6	Cash inflow estimates (t = 1 – 15) $\,$ Worst
8	8	Most-likely
16	10	Best
0.10	0.10	Required rate of return
15	15	Economic life (years)

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The NPV of each project, assuming a 10 per cent required rate of return, can be calculated for each of the possiblE cash flows. Table A-4 indicates that the present value interest factor annuity (PVIFA) of Re 1 for 15 years at 10 per cent discount is 7.606. Multiplying each possible cash flow by PVIFA, we get, (Table 3.9):
$\,$ Table 3.9 demonstrates that sensitivity analysis can produce some very useful information about projects that appear equally desirable on the basis of the most likely estimates of their cash flows. Project X is less risky than Project Y. The actual selection of the project (assuming that the projects are mutually exclusive) will depend on the decision maker’s attitude towards risk. If the decision maker is conservative, he will select Project X as there is no possibility of suffering losses. On the other hand, if he is willing to take risks, he will choose Project Y as it has the possibility of paying a very high return as compared to project X. Sensitivity analysis, in spite of being crude, does provide the decision maker with more than one estimate of the project’s outcome and, thus, an insight into the variability of the returns.

Table 3.9 Determination of NPV

$Project\>Y$		$Project\>X$		$\,$ $Expected\>cash\>inflows$
$NPV$	$PV$	$NPV$	$PV$	$\,$ $Expected\>cash\>inflows$
(Rs 40,000)	Nil	Rs 5,636	Rs 45,636	Worst
20,848	Rs 60,848	20,848	60,848	Most likely
81,696	1,21,696	36,060	76,060	Best

Table A-4 The Present Value of an Annuity of One Rupee

10%	9%	8%	7%	6%	5%	4%	3%	2%	1%	$Year$
.909	.917	.926	.953	.943	.952	.962	.971	.980	.990	1
1.736	1.759	1.783	1.808	1.833	1.859	1.886	1.913	1.942	1.970	2
2.487	2.531	2.577	2.624	2.673	2.723	2.775	2.829	2.884	2.941	3
3.170	3.240	3.312	3.387	3.465	3.546	3.630	3.717	3.808	3.902	4
3.791	3.890	3.993	4.100	4.212	4.329	4.452	4.580	4.713	4.853	5
4.355	4.486	4.623	4.767	4.917	5.076	5.242	5.417	5.601	5.795	6
4.868	5.033	5.206	5.389	5.582	5.786	6.002	6.230	6.472	6.728	7
5.335	5.535	5.747	5.971	6.210	6.463	6.733	7.020	7.326	7.652	8
5.759	5.995	6.247	6.515	6.802	7.108	7.435	7.786	8.162	8.566	9
6.145	6.418	6.710	7.024	7.360	7.722	8.111	8.530	8.983	9.471	10
6.495	6.805	7.139	7.499	7.887	8.306	8.760	9.253	9.787	10.368	11
6.814	7.161	7.536	7.943	8.384	8.863	9.385	9.954	10.575	11.255	12
7.103	7.487	7.904	8.358	8.853	9.394	9.986	10.635	11.348	12.134	13
7.367	7.786	8.244	8.746	9.295	9.899	10.563	11.296	12.106	13.004	14
7.606	8.061	8.560	9.108	9.712	10.380	11.118	11.938	12.849	13.865	15
7.824	8.313	8.851	9.447	10.106	10.838	11.652	12.561	13.578	14.718	16
8.022	8.544	9.122	9.763	10.477	11.274	12.166	13.166	14.292	15.562	17
8.201	8.756	9.372	10.059	10.828	11.690	12.659	13.754	14.992	16.398	18
8.365	8.950	9.604	10.336	11.158	12.085	13.134	14.324	15.679	17.226	19
8.514	9.129	9.818	10.594	11.470	12.462	13.590	14.878	16.352	18.046	20
8.649	9.292	10.017	10.836	11.764	12.821	14.029	15.415	17.011	18.857	21
8.772	9.442	10.201	11.061	12.042	13.163	14.451	15.937	17.658	19.661	22
8.883	9.580	10.371	11.272	12.303	13.489	14.857	16.444	18.292	20.456	23
8.985	9.707	10.529	11.469	12.550	13.799	15.247	16.936	18.914	21.244	24
9.077	9.823	10.675	11.654	12.783	14.094	15.622	17.413	19.524	22.023	25
9.427	10.274	11.258	12.409	13.765	15.373	17.292	19.601	22.397	25.808	30
9.644	10.567	11.655	12.948	14.498	16.374	18.665	21.487	24.999	29.409	35
9.779	10.757	11.925	12.332	15.046	17.159	19.793	23.115	27.356	32.835	40
9.863	10.881	12.108	13.606	15.456	17.774	20.720	24.519	29.490	36.095	45
9.915	10.962	12.234	13.801	15.762	18.256	21.482	25.730	31.424	39.197	50

(Contd.)

20%	19%	18%	17%	16%	15%	14%	13%	12%	11%	$Year$
.833	.850	.847	.855	.862	.870	.877	.885	.893	.901	1
1.528	1.547	1.566	1.585	1.605	1.626	1.647	1.668	1.690	1.713	2
2.106	2.140	2.174	2.210	2.246	2.283	2.322	2.361	2.402	2.444	3
2.589	2.639	2.690	2.743	2.798	2.855	2.914	2.974	3.037	3.102	4
2.991	3.058	3.127	3.199	3.274	3.352	3.433	3.517	3.605	3.696	5
3.326	3.410	3.498	3.589	3.685	3.784	3.889	3.998	4.111	4.231	6
3.605	3.706	3.812	3.922	4.039	4.160	4.288	4.423	4.564	4.712	7
3.837	3.954	4.078	4.207	4.344	4.487	4.639	4.799	4.968	5.146	8
4.031	4.163	4.303	4.451	4.607	4.772	4.946	5.132	5.328	5.537	9
4.192	4.339	4.494	4.659	4.833	5.019	5.216	5.426	5.650	5.889	10
4.327	4.487	4.656	4.836	5.029	5.234	5.453	5.687	5.938	6.207	11
4.439	4.611	4.793	4.988	5.197	5.421	5.660	5.918	6.194	6.492	12
4.533	4.715	4.910	5.118	5.342	5.583	5.842	6.122	6.424	6.750	13
4.611	4.802	5.008	5.229	5.468	5.724	6.002	5.303	6.628	6.982	14
4.675	4.876	5.092	5.324	5.575	5.847	6.142	6.462	6.811	7.191	15
4.730	4.938	5.162	5.405	5.669	5.954	6.265	6.604	6.974	7.379	16
4.775	4.990	5.222	5.475	5.749	6.047	6.373	6.729	7.120	7.549	17
4.812	5.033	5.273	5.534	5.818	6.128	6.467	6.840	7.250	7.702	18
4.843	5.070	5.316	5.585	5.877	6.198	6.550	6.938	7.366	7.839	19
4.870	5.101	5.353	5.628	5.929	6.259	6.623	7.024	7.469	7.963	20
4.891	5.127	5.384	5.665	5.973	6.312	6.687	7.102	7.562	8.075	21
4.909	5.149	5.410	5.696	6.011	6.359	6.743	7.170	7.645	8.176	22
4.925	5.167	5.432	6.723	6.044	6.399	6.792	7.230	7.718	8.266	23
4.937	5.182	5.451	5.747	6.073	6.434	6.835	7.283	7.784	8.348	24
4.948	5.195	5.467	5.766	6.097	6.464	6.873	7.330	7.843	8.422	25
4.979	5.235	5.517	5.829	6.177	6.566	7.003	7.496	8.055	8.694	30
4.992	5.251	5.539	5.858	6.215	6.617	7.070	7.586	8.176	8.855	35
4.997	5.258	5.548	5.871	6.233	6.642	7.105	7.634	8.244	8.951	40
4.999	5.261	5.552	5.877	6.242	6.654	7.123	7.661	8.283	9.008	45
4.999	5.262	5.554	5.880	6.246	6.661	7.133	7.675	8.305	9.042	50

(Contd.)

30%	29%	28%	27%	26%	25%	24%	23%	22%	21%	$Year$
.769	.775	.781	.787	.794	.800	.806	.813	.820	.826	1
1.361	1.376	1.392	1.407	1.424	1.440	1.457	1.474	1.492	1.509	2
1.816	1.842	1.868	1.896	1.923	1.952	1.981	2.011	2.042	2.074	3
2.166	2.203	2.241	2.280	2.320	2.362	2.404	2.448	2.494	2.540	4
2.436	2.483	2.532	2.583	2.635	2.689	2.745	2.803	2.864	2.926	5
2.643	2.700	2.759	2.821	2.885	2.951	3.020	3.092	3.167	3.245	6
2.802	2.868	2.937	3.009	3.083	3.161	3.242	3.327	3.416	3.508	7
2.925	2.999	3.076	3.156	3.241	3.329	3.421	3.518	3.619	3.726	8
3.019	3.100	3.184	3.273	3.366	3.463	3.566	3.673	3.786	3.905	9
3.092	3.178	3.269	3.364	3.465	3.570	3.682	3.799	3.923	4.054	10
3.147	3.239	3.335	3.437	3.544	3.656	3.776	4.902	4.035	4.177	11
3.190	3.286	3.387	3.493	3.606	3.752	3.851	3.985	4.127	4.278	12
3.223	3.322	3.427	3.538	3.656	3.780	3.912	4.053	4.203	4.362	13
3.249	3.351	3.459	3.573	3.695	3.824	3.962	4.108	4.265	4.432	14
3.268	3.373	3.483	3.601	3.726	3.859	4.001	4.153	4.315	4.489	15
3.283	3.390	3.503	3.623	3.751	3.887	4.033	4.189	4.357	4.536	16
3.295	3.403	3.518	3.640	3.771	3.910	4.059	4.219	4.391	4.576	17
3.304	3.413	3.529	3.654	3.786	3.928	4.080	4.243	4.419	4.608	18
3.311	3.421	3.539	3.664	3.799	3.942	4.097	4.263	4.442	4.635	19
3.316	3.427	3.546	3.673	3.808	3.954	4.110	4.279	4.460	4.657	20
3.320	3.432	3.551	3.679	3.816	3.963	4.121	4.292	4.476	4.675	21
3.323	3.436	3.556	3.684	3.822	3.970	4.130	4.302	4.488	4.690	22
3.325	3.438	3.559	3.689	3.827	3.976	4.137	4.311	4.499	4.703	23
3.327	3.441	3.562	3.692	3.831	3.981	4.143	4.318	4.507	4.713	24
3.329	3.442	3.564	3.694	3.834	3.985	4.147	4.323	4.514	4.721	25
3.332	3.447	3.569	3.701	3.842	3.995	4.160	4.339	4.534	4.746	30
3.333	3.448	3.571	3.703	3.845	3.998	4.164	4.345	4.541	4.756	35
3.333	3.448	3.571	3.703	3.846	3.999	4.166	4.347	4.544	4.760	40
3.333	3.448	3.571	3.704	3.846	4.000	4.166	4.347	4.545	4.761	45
3.333	3.448	3.571	3.704	3.846	4.000	4.167	4.348	4.545	4.762	50