Question

Please solve it by hand so that I can understand the steps.

6. A project has the following total (or net) after-tax cash flows.

               ____________________________________________________

        Year             Total (or net) after-tax cash flow

               ____________________________________________________

                  1 $1,000,000
2 1,500,000
3 2,000,000
4 2,500,000      

            _______________________________________________________

The required rate of return on the project is 15 percent. The initial investment (or initial cost or initial outlay) of the project is $4,000,000.
a) Find the (regular) payback period of the project.
b) Compute the discounted payback period of the project.
c) Find the net present value (NPV) of the project.
d) Find the profitability index (PI) of the project.
e) Calculate the modified internal rate of return (MIRR) of the project.

Answer 1

Part A:

Payback period is the period in which Initial Investment is recovered.

Year	Opening Bal	Cash Flow	Closing Balance
1	$ 40,00,000.00	$ 10,00,000.00	$   30,00,000.00
2	$ 30,00,000.00	$ 15,00,000.00	$   15,00,000.00
3	$ 15,00,000.00	$ 20,00,000.00	$    -5,00,000.00
4	$ -5,00,000.00	$ 25,00,000.00	$ -30,00,000.00

PBP = Year in which least +ve Closing Bal+ [ Closing Bal at that Year / CF in next year ]

= 2 + [ 1.5M / 2 M ]

= 2.75 Years

Part B:

DIsc PBP is similar to PBP where in PBP CFs are considered , Here DIsc CFs are considered.

Year	Opening Bal	Cash Flow	pvf @15%	Disc CF	Closing Balance
1	$ 40,00,000.00	$ 10,00,000.00	0.8696	$    8,69,565.22	$   31,30,434.78
2	$ 31,30,434.78	$ 15,00,000.00	0.7561	$ 11,34,215.50	$   19,96,219.28
3	$ 19,96,219.28	$ 20,00,000.00	0.6575	$ 13,15,032.46	$     6,81,186.82
4	$    6,81,186.82	$ 25,00,000.00	0.5718	$ 14,29,383.11	$    -7,48,196.30

Disc PBP = Year in which least +ve Closing Bal+ [ Closing Bal at that Year / CF in next year ]

= 3 + [ 681186.82 / 1429383.11]

= 3 + 0.48

= 3.48 Years

Part C:

NPV = PV of Cash Inflows - PV of Cash Outflows

Year	CF	PVF @15%	Disc CF
0	$ -40,00,000.00	1.0000	$ -40,00,000.00
1	$ 10,00,000.00	0.8696	$     8,69,565.22
2	$ 15,00,000.00	0.7561	$ 11,34,215.50
3	$ 20,00,000.00	0.6575	$ 13,15,032.46
4	$ 25,00,000.00	0.5718	$ 14,29,383.11
NPV	$    7,48,196.30

Part D:

PI = [ Initial Investment + NPV] / Initial Investment

= [ 4000000 + 748196.30 ] / 4000000

= 4748196.30 / 4000000

= 1.1870

Part E:

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

Modified IRR is similar to IRR, where in RR intermediary Cfs are assumed as reinvested at IRR only and Where as in MIRR intermediary CFs are assumed to be reinvested at Cost of Capital.

Year	Bal Yrs	CF	FVF @15%	FV of CFs
1	3	$ 10,00,000.00	1.5209	$ 15,20,875.00
2	2	$ 15,00,000.00	1.3225	$ 19,83,750.00
3	1	$ 20,00,000.00	1.1500	$ 23,00,000.00
4	0	$ 25,00,000.00	1.0000	$ 25,00,000.00
FV of CFs	$ 83,04,625.00

Thus $ 4000000 has converted into 8304625 over a period of 4 Years by increasing at "r%".

FV = PV ( 1+r)^n

8304625 = 4000000 ( 1 + r)^4

(1+r)^4 = 8304625 / 4000000

= 2.08

1+r = 2.08^ (1/4)

= 1.2004

r = 1.2004 - 1

= 0.2004 i.e 20.04%

Pls comment, if any further assistance is required