Question

Helsinki Co. is considering a new project that will cost $328,500. The expected net cash inflows from this project are $62,000 per year for 8 years. If Helsinki’s weighted average cost of capital (WACC) is 6%, what is the project’s net present value (NPV), IRR, Payback Period, and Discount Period?

Please show work.

Answer 1

NPV = Present Value of Cash Inflows - Present Value of Cash Outflows

=[$ 62000*1/(1.06) ^ 1 +$ 62000*1/(1.06) ^2+$ 62000*1/(1.06) ^3+$ 62000*1/(1.06) ^4+$ 62000*1/(1.06) ^5+$ 62000*1/(1.06) ^6+........+$ 62000*1/(1.06) ^8]-$ 328,500

= $ 56,507.22

Hence the correct answer is $ 56,507.22

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Let the IRR be y.

Now , Present Value of Cash Outflows=Present Value of Cash Inflows

328500=62000/(1.0y) + 62000/ (1.0y)^2  + 62000/(1.0y)^3 + .......+ 62000/(1.0y)^8

Or y= 10.189%

Hence the IRR is 10.189%

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Payback Period = ( Last Year with a Negative Cash Flow ) + [( Absolute Value of negative Cash Flow in that year)/ Total Cash Flow in the following year)]

= 5+ (18500/62000)

= 5.298387097 years

Hence the correct answer is 5.30 years

Note:

Year	Investment	Cash Inflow	Net Cash Flow
0	-3,28,500.00	-	-3,28,500.00	(Investment + Cash Inflow)
1	-	62,000.00	-2,66,500.00	(Net Cash Flow + Cash Inflow)
2	-	62,000.00	-2,04,500.00	(Net Cash Flow + Cash Inflow)
3	-	62,000.00	-1,42,500.00	(Net Cash Flow + Cash Inflow)
4	-	62,000.00	-80,500.00	(Net Cash Flow + Cash Inflow)
5	-	62,000.00	-18,500.00	(Net Cash Flow + Cash Inflow)
6	-	62,000.00	43,500.00	(Net Cash Flow + Cash Inflow)
7	-	62,000.00	1,05,500.00	(Net Cash Flow + Cash Inflow)
8	-	62,000.00	1,67,500.00	(Net Cash Flow + Cash Inflow)

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Discounted Payback Period =

( Last Year with a Negative Cumulative Cash Flow ) + [( Absolute Value of negative Cumulative Cash Flow in that year)/ Total Present Cash Flow in the following year)]

= 6 + (23,625.89178766590/ 41,233.541044585)

= 6.57 Years

Hence the correct answer is 6.57 Years

Note:

	Cash Flow	Discounting Factor ( 6%)	Present Value (Cash Flow * Discounting Factor)	Cumulative Cash Flow (Present Value of Current Year+ Cumulative Cash Flow of Previous Year)
0	-3,28,500	1	-3,28,500.00	-3,28,500.00000000000
1	62,000	0.943396226415	58,490.566037736	-2,70,009.43396226400
2	62,000	0.889996440014	55,179.779280883	-2,14,829.65468138100
3	62,000	0.839619283032	52,056.395548003	-1,62,773.25913337900
4	62,000	0.792093663238	49,109.807120757	-1,13,663.45201262100
5	62,000	0.747258172866	46,330.006717696	-67,333.44529492580
6	62,000	0.704960540440	43,707.553507260	-23,625.89178766590
7	62,000	0.665057113622	41,233.541044585	17,607.64925691900
8	62,000	0.627412371342	38,899.567023193	56,507.21628011220