Question

Please provide answer in the most simplest form, thank you.

Project K costs $52,125, it’s expected cash inflows are $12,000 per year for 8 years, and it’s WACC is 12%.

What’s the project’s NPV?

What’s the project’s IRR?

What’s the project’s MIRR?

What’s the project’s payback?

What’s the project’s discounted payback?

Answer 1

NPV = Present value of cash inflow - Initial investment,

Present value of cash inflow = Annual Cash inflow X Present Value Factor or Discount factor,

Present Value Factor or Discount factor = 1/(1+i)ⁿ,

i = WACC or cost of capital or discount rate = 12% or 0.12,

n is the number of corresponding year, here it is for year 1 = 1, Year 2 = 2,... and so on upto 8 years,

NPV

year	Cash inflow	Discount Factor @12%		Present Value
1	12000	0.8928571428571430		10714.285714285700
2	12000	0.7971938775510200		9566.326530612240
3	12000	0.7117802478134110		8541.362973760930
4	12000	0.6355180784048310		7626.216940857970
5	12000	0.5674268557185990		6809.122268623190
6	12000	0.5066311211773210		6079.573454127850
7	12000	0.4523492153368930		5428.190584042720
8	12000	0.4038832279793690		4846.598735752430
		Total PV		59611.677202063100
		InitialInvestment		52125.000000000000
		NPV		7486.677202063050,

IRR

To find IRR,
First, Devide initial investment by Annual Cash flow = %52,125 / $12,000 =						4.343750
Then , round it to 3 or 4 decimal places as per PVAnnuity Table, Then ,Look at PVAnnuity table for this 4.343750 for 8 years raw, Round it to 3 decimal places becuase table below is in 3 decimal places
Then, you can find the Rate, that rate is IRR

Here it is marked in light red pencil, So we know that in 8 year raw 3.344 represents 16%, so 16% is IRR,

MIRR,

In MIRR, it is based on the assumption that the intermediate cash flows are reinvested at WACC or cost of the fund employed by the organization, and apply formula for future value of single investment for 8 years, and equate it. Then solve the equation, we will get the answer of MIRR

So intermediate annual cash flows are reinvested at 12% for the end of the project period, so formula for compounding = (1+i)ⁿ, Where n is the number of years reinvested, for example $12,000 of the first year, we can reinvest it for 7 years (the remaining life of project),

"i" is the Cost of capital or WACC = 12% or 0.12,

year	Cash inflow	investment period in yrs	Cmpound Value per $	Compounded Cash flow
1	12000	7	2.210681407406080	26528.17688887300
2	12000	6	1.973822685184000	23685.87222220800
3	12000	5	1.762341683200000	21148.10019840000
4	12000	4	1.573519360000000	18882.23232000000
5	12000	3	1.404928000000000	16859.13600000000
6	12000	2	1.254400000000000	15052.80000000000
7	12000	1	1.120000000000000	13440.00000000000
8	12000	0	1.000000000000000	12000.00000000000
		Total Future Value		147596.31762948100

that means our first investment of $52,125 became $147,596.317629481 after 8 years.

and apply Future value of single investment for 8 years, Future Value = A (1+i)ⁿ, where A is the first deposit = $52,125,

i = Actual rate of return

$147,596.317629481 = $52,125 X (1 + i)⁸,

$147,596.317629481 / $52,125 = (1 + i)⁸,

2.83158403126103 = (1 + i)⁸,

1+i = 2.83158403126103^(1/8),

1+i = 1.13894743746002,

i = 1.13894743746002 -1 = 0.13894743746002 or 13.894743746002%,

Pay back period When annual cash flows are uniform = Cost of project / Annual cash inflow ,

=$52,125 / $12,000,

= 4.343750 years.

Discounted Pay back period,

first we have to calculate present value of annual cash inflow, then calculate Cumulative cash inflow to identify in which year , the Present value of cash inflows are crossing the initial investments,

year	Cash inflow	Discount Factor @12%	Present Value	Cumulative Present Value
1	12000	0.8928571428571430	10714.285714285700	10714.285714285700
2	12000	0.7971938775510200	9566.326530612240	20280.612244898000
3	12000	0.7117802478134110	8541.362973760930	28821.975218658900
4	12000	0.6355180784048310	7626.216940857970	36448.192159516900
5	12000	0.5674268557185990	6809.122268623190	43257.314428140100
6	12000	0.5066311211773210	6079.573454127850	49336.887882267900
7	12000	0.4523492153368930	5428.190584042720	54765.078466310600
8	12000	0.4038832279793690	4846.598735752430	59611.677202063100

We know that Present value of cash inflows are crossing the initial investment in 7^th year, so deduct 6^th year cumulative cash inflow from initial investments = $52,125 - $49,336.887882267900 =$2,788.1121177321,

and devide the above amount by 7^th year present value =$2,788.1121177321 / $5,428.190584042720,

= 0.513635635036162,

So the discounted payback period = 6.513635635036162 years.

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