Question

You have been offered a very​ long-term investment opportunity to increase your money one hundredfold. You can invest

$1,500

today and expect to receive

$150,000

in

40

years. Your cost of capital for this​ (very risky) opportunity is

23%.

What does the IRR rule say about whether the investment should be​ undertaken? What about the NPV​ rule? Do they​ agree?

What is the

IRR​?

The IRR of this investment opportunity is

nothing​%.

​(Round to one decimal​ place.)

Answer 1

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.

IRR :
IRR is the Rate at which PV of Cash Inflows are equal to PV of Cash Outflows or Rate of growth is expected from project/ Investment. At IRR, NPV of Project/ Investment will be Zero. It assumes that intermediary Cfs are reinvested at IRR only.

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

If IRR > Cost of Capital - Project can be accepted
IRR = Cost of Capital - Indifferebce Point - Project will be accepted / Rejected
IRR < Cost of Capital - Project will be erejected

NPV:

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

Particulars	Amount
Future Value	$          150,000.00
Int Rate	23.0000%
Periods	40

Present Value = Future Value / ( 1 + r )^n
= $ 150000 / ( 1 + 0.23 ) ^ 40
= $ 150000 / ( 1.23 ) ^ 40
= $ 150000 / 3946.4305
= $ 38.01

NPV = PV of Cash Inflows - PV of Cash Outflows

= $ 38.01- $ 1500

= -$ 1461.99

As it has -ve NPV, Investment shall not undertaken.

IRR:

Year	Cash Flow	PVF/PVAF @ 12 %	PV of Cash Flows	PVF/PVAF @13 %	PV of Cash Flows
1-40	$                             -	8.2438	$                                 -	7.6344	$                               -
40	$            150,000.00	0.0107	$                    1,612.02	0.0075	$                   1,129.68
PV of Cash Inflows			$                    1,612.02		$                  1,129.68
PV of Cash Oiutflows			$                    1,500.00		$                  1,500.00
NPV			$                        112.02		$                    -370.32

IRR = Rate at which least +ve NPV + [ NPV at that rate / Change in NPV due to Inc of 1% in Int Rate ] * 1%
= 12 % + [112.02 / 482.34 ] * 1%
= 12 % + [0.2322 ] * 1%
= 12 % + [0.2322 % ]
= 12.23 %

As IRR ( 12.23% ) < Cost of Capita ( 23% ), Investment shall not undertaken.

Pls comment, if any further assistance is required.