Question

1. Your firm is considering a project that will cost $3 million in initial investments. The project will earn cash flows of $750,000 for 6 years then terminate with no salvage value. If the WACC is 8%, what is the Net Present Value of the investment?

   $467,160
   		$487,993
   		$472,627
   		$503,679

   1. 
      A project calls for $5.5 million in initial investments. The project will return the following cash flows. What is the modified IRR if the WACC of 7% is applied as the reinvestment rate?
      ​​​​​​Year:   CF
      • 1              400k
      • 2              700k
      • 3              1.1 million
      • 4              1.7 million
      • 5              1.8 million
      • 6              1.5 million
      • 7              900k
      • 8              300k

		9.49%
		9.98%
		8.87%
		8.61%

Answer 1

Part A:

NPV :
NPV is the difference between Present value of Cash Inflows and Present value of cash outflows.

NPV = PV of Cash Inflows - PV of Cash Outflows
If NPV > 0 , Project can be accepted
NPV = 0 , Indifference point. Project can be accepted/ Rejected.
NPV < 0 , Project will be rejected.

Year	CF	PVF @8 %	Disc CF
0	$ -3,000,000.00	1.0000	$ -3,000,000.00
1	$      750,000.00	0.9259	$      694,444.44
2	$      750,000.00	0.8573	$      643,004.12
3	$      750,000.00	0.7938	$      595,374.18
4	$      750,000.00	0.7350	$      551,272.39
5	$      750,000.00	0.6806	$      510,437.40
6	$      750,000.00	0.6302	$      472,627.22
NPV			$     467,159.75

Option A is correct.

Part B:

Modified IRR:

It is similar to IRR. In IRR, we are assumed that intermediary cashflows are reinvested at IRR only. In MIRR, we assume that Intermediary CFs are reinvested at Reinvestment Rate rather than at IRR. Convert all cash flows in to Future value using reinvestment rate and calculate the growth rate between Current Value and Future value.
That growth rate is MIRR.

Year	Bal Years	CF	FVF @7 %	FV of CFs
1	7	$    400,000.00	1.6058	$       642,312.59
2	6	$    700,000.00	1.5007	$    1,050,511.25
3	5	$ 1,100,000.00	1.4026	$    1,542,806.90
4	4	$ 1,700,000.00	1.3108	$    2,228,353.22
5	3	$ 1,800,000.00	1.2250	$    2,205,077.40
6	2	$ 1,500,000.00	1.1449	$    1,717,350.00
7	1	$    900,000.00	1.0700	$       963,000.00
8	0	$    300,000.00	1.0000	$       300,000.00
Future Value of CFs				$ 10,649,411.36

Thus $5500000 has become $10649411.36 over a period of 8 Years
Future Value = Cash Flow * ( 1 + r )^n
$ 10649411.36 = $ 5500000 ( 1 + r) ^ 8
( 1 + r) ^ 8 = $10649411.36 / $ 5500000
( 1 + r) ^ 8 = 1.9363
( 1 + r) = 1.9363 ^ ( 1 / 8 )
( 1 + r) = 1.0861
r = 1.0861 -1
r = 0.0861
i.e MIRR is 8.61 %

Modified IRR is 8.61%

Option D is correct.