Question

Ch 11

Project L requires an initial outlay at t = 0 of $45,000, its expected cash inflows are $11,000 per year for 9 years, and its WACC is 10%. What is the project's NPV? Do not round intermediate calculations. Round your answer to the nearest cent.

$  

Project L requires an initial outlay at t = 0 of $45,464, its expected cash inflows are $9,000 per year for 8 years, and its WACC is 9%. What is the project's IRR? Round your answer to two decimal places.

  %

Project L requires an initial outlay at t = 0 of $50,000, its expected cash inflows are $15,000 per year for 9 years, and its WACC is 10%. What is the project's MIRR? Do not round intermediate calculations. Round your answer to two decimal places.

  %

Project L requires an initial outlay at t = 0 of $50,000, its expected cash inflows are $13,000 per year for 7 years, and its WACC is 12%. What is the project's payback? Round your answer to two decimal places.

  years

Project L requires an initial outlay at t = 0 of $60,000, its expected cash inflows are $14,000 per year for 9 years, and its WACC is 13%. What is the project's discounted payback? Do not round intermediate calculations. Round your answer to two decimal places.

  years

Answer 1

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

= [ 11000*1/(1.10)^1+11000*1/(1.10)^2+11000*1/(1.10)^3+11000*1/(1.10)^4+11000*1/(1.10)^5+11000*1/(1.10)^6+11000*1/(1.10)^7+11000*1/(1.10)^8+11000*1/(1.10)^9]-45000

= $ 18349.26

Answer = $ 18349.26

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Let the IRR be x.

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

45464= 9000/(1.0x) +9000/ (1.0x)^2 +9000/(1.0x)^3+...........+9000/(1.0x)^8      

Or x= 11.523%

Hence the IRR is 11.52 %

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Present Value of Cash Inflows = [ 15000*1/(1.10)^1+15000*1/(1.10)^2+15000*1/(1.10)^3+15000*1/(1.10)^4+15000*1/(1.10)^5+15000*1/(1.10)^6+15000*1/(1.10)^7+15000*1/(1.10)^8+15000*1/(1.10)^9]

= 86385.35724412720

Future Value = Present Value * (1+ Rate of Interest)^Time

= 86385.35724412720*(1+10%)^9

= $ 203692.15365

MIRR=[Future value of inflows/Present value of outflow]^(1/n)-1

= [203692.15365 / 50000]^(1/9)-1

= 16.89%

Answer = 16.89%

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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)]

= 3+(11000/13000)

= 3.85 years

Answer = 3.85 years

Note:

Year	Investment	Cash Inflow	Net Cash Flow
0	-50,000.00	-	-50,000.00	(Investment + Cash Inflow)
1	-	13,000.00	-37,000.00	(Net Cash Flow + Cash Inflow)
2	-	13,000.00	-24,000.00	(Net Cash Flow + Cash Inflow)
3	-	13,000.00	-11,000.00	(Net Cash Flow + Cash Inflow)
4	-	13,000.00	2,000.00	(Net Cash Flow + Cash Inflow)
5	-	13,000.00	15,000.00	(Net Cash Flow + Cash Inflow)
6	-	13,000.00	28,000.00	(Net Cash Flow + Cash Inflow)
7	-	13,000.00	41,000.00	(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+(4034.30/5950.85)

= 6.68 Years

Answer = 6.68 Years

	Cash Flow	Discounting Factor ( 13%)	Present Value (Cash Flow * Discounting Factor)	Cumulative Cash Flow (Present Value of Current Year+ Cumulative Cash Flow of Previous Year)
0	-60,000	1	-60,000.00	-60,000.00
1	14,000	0.884955752212	12,389.38	-47,610.62
2	14,000	0.783146683374	10,964.05	-36,646.57
3	14,000	0.693050162278	9,702.70	-26,943.86
4	14,000	0.613318727679	8,586.46	-18,357.40
5	14,000	0.542759935999	7,598.64	-10,758.76
6	14,000	0.480318527433	6,724.46	-4,034.30
7	14,000	0.425060643746	5,950.85	1,916.55
8	14,000	0.376159861722	5,266.24	7,182.78
9	14,000	0.332884833383	4,660.39	11,843.17