Question

Three mutualy exclusive das gn aternatives are being cons dered The estimated cash flows for each ater at e are g en below The MARR s 12% per year. At te ฉnd at the useful ft, te nvestment wil be sold. A decision maker can select one of these atarnatves or decide to select none of them Make recommandation using the PW method Investment cost Annual revenue Annual cost Usehd ife IRR Pw 275.000 $140.000 $79 397 548,669$96,112 $17.368510941 $22.744 15 years 15 years 15 years 21.3% 26.1% 182% $241908 $174 400 $241400 (a) Which altemative is the most economica? Choose the comedt answer below A. Atenative A B. None of the ahematives O C. Alternative C ( D. Abernativee (b) Calculate the discounted payback period of each aheroative (T yaas Round to the nearest doma) The discounted payback period of allamative A is The dscounted payback period af altenative B is years (Round to the nearest decimal The decounted paybtack parod of stemaive Cis s (Round to the nearest docimal) Based on the payback parlod, which aftemative is the most preleired? Choose the correct ansawer below O A. Alemative A ° C. Non* of the aherratiss O D. Altemative B (c) Why could the answers in (a) and (b) be dife A. because the payback pariod method ignores tre cash fows atoi the payback perilod use the payback period gives more weight to the cash fows after the payback period

Answer 1

(a) Option (B)

Alternative A has highest Present Worth, so this alternative is most economical.

(b) Discounted Payback Period (DPBP) is the year when the project's cumulative discounted cash flow is zero.

Net Cash Flow (NCF) ($) = Annual revenue - Annual cost

NCF, Alternative A = 79,397 - 17,368 = 62,029

NCF, Alternative B = 48,665 - 10,941 = 37,724

NCF, Alternative C = 96,112 - 22,944 = 73,168

Alternative - A
Year	NCF ($)	PV Factor @12%	Discounted NCF ($)	Cumulative Discounted NCF ($)
0	-2,75,000	1.0000	-2,75,000	-2,75,000
1	62,029	0.8929	55,383	-2,19,617
2	64,757	0.7972	51,624	-1,67,993
3	64,757	0.7118	46,093	-1,21,900
4	64,757	0.6355	41,154	-80,746
5	64,757	0.5674	36,745	-44,001
6	64,757	0.5066	32,808	-11,193
7	64,757	0.4523	29,293	18,099
Alternative - B
Year	NCF ($)	PV Factor @12%	Discounted NCF ($)	Cumulative Discounted NCF ($)
0	-1,40,000	1.0000	-1,40,000	-1,40,000
1	37,724	0.8929	33,682	-1,06,318
2	37,724	0.7972	30,073	-76,245
3	37,724	0.7118	26,851	-49,393
4	37,724	0.6355	23,974	-25,419
5	37,724	0.5674	21,406	-4,013
6	37,724	0.5066	19,112	15,099
Alternative - C
Year	NCF ($)	PV Factor @12%	Discounted NCF ($)	Cumulative Discounted NCF ($)
0	-3,70,000	1.0000	-3,70,000	-3,70,000
1	73,168	0.8929	65,329	-3,04,671
2	73,168	0.7972	58,329	-2,46,342
3	73,168	0.7118	52,080	-1,94,263
4	73,168	0.6355	46,500	-1,47,763
5	73,168	0.5674	41,517	-1,06,246
6	73,168	0.5158	37,743	-68,503
7	73,168	0.4689	34,312	-34,191
8	73,168	0.4263	31,193	-2,998
9	73,168	0.3876	28,357	25,359

If DPBP is between two successive years (N - 1) & N,

DPBP = (N - 1) + [Absolute value of cumulative discounted NCF in year (N - 1) / Discounted NCF in year N]

DPBP of Alternative A lies between year 6 and 7. DPBP of Alternative B lies between year 5 and 6. DPBP of Alternative C lies between year 8 and 9.

DPBP, Alternative A = 6 + (11,193 / 29,293) = 6 + 0.38 = 6.38 ~ 6 years

DPBP, Alternative B = 5 + (4,013 / 19,112) = 5 + 0.21 = 5.21 ~ 5 years

DPBP, Alternative C = 8 + (2,998 / 28,357) = 8 + 0.11 = 8.11 ~ 8 years

(ii) Option (D)

Alternative B has minimum DPBP, so this alternative preferred.

(c) Option (A)

The Payback period ignores cash flows after cut-off period and after the actual payback period, so its evaluation is different from that of PW method.