Question

Systems, Inc., 14.6 The director of capital budgeting for Big Sky Health Systems has estimated the following cash flows in thousands of dollars proposed new service: Year 0 Expected Net Cash Flow ($100) 70 50 20 The project's cost of capital is 10 percent. a. What is the project's payback period? b. What is the project's NPV? c. What is the project's IRR? Its MIRRY

Answer 1

Payback period is the period in which initial invetsment is recovered.

Year	Opening Bal	CF	Closing Bal
1	$ 100.00	$   70.00	$   30.00
2	$   30.00	$   50.00	$ -20.00
3	$ -20.00	$   20.00	$ -40.00

PBP = Year in which least +ve CB + [ CB In that year / Cf in Next year ]

= 1 + [ 30 / 50 ]

= 1 + 0.6

= 1.60 Years

NPV = PV of Cash Inflows - PV ofCash Outflows

Year	CF	PVF @10%	Disc CF
0	$ -100.00	1.0000	$ -100.00
1	$    70.00	0.9091	$      63.64
2	$    50.00	0.8264	$      41.32
3	$    20.00	0.7513	$      15.03
NPV			$      19.98

IRR is the Rate at which PV of Cash Inflows are equal to PV of Cash Outflows

Year	CF	PVF @23%	Disc CF	PVF @24%	Disc CF
0	$ -100.00	1.0000	$ -100.00	1.0000	$ -100.00
1	$    70.00	0.8130	$      56.91	0.8065	$    56.45
2	$    50.00	0.6610	$      33.05	0.6504	$    32.52
3	$    20.00	0.5374	$      10.75	0.5245	$    10.49
NPV			$        0.71		$     -0.54

IRR = Rate at which least +ve NPV + [ NPV at that rate / Change in NPV due to 1% inc in Disc Rate ] * 1%

= 23% + [ 0.71 / 1.25 ] * 1%

= 23% + 0.57%

= 23.57%

MIRR is similra to IRR. Here Intermediary CFs are assumed as reinvested at Cost of Capital.

Year	CF	FVF @10%	FV of CFs
1	$   70.00	1.2100	$   84.70
2	$   50.00	1.1000	$   55.00
3	$   20.00	1.0000	$   20.00
FV of CFs			$ 159.70

Thus $ 100 has become $ 159.7 in 3 years.

FV = PV(1+r)^n

= 159.70 = 100 ( 1 + r)^3

(1+r)^3 = 159.7 / 100

= 1.597

1+r = 1.597 ^ ( 1 /3)

= 1.1689

r = 1.1689 - 1

= 0.1689 i.e 16.89%