Question

Consider an investment that costs $100,000 and has a cash inflow of $25,000 every year for 5 years. The required return is 9%, and payback cutoff is 4 years.

A. What is the payback period?

B. What is the discounted payback period?

C. What is the NPV? D. What is the IRR?

E. Should we accept the project?

What method should be the primary decision rule?

When is the IRR rule unreliable?

Please include steps on how to solve and all parts to question. Thank you.

Answer 1

Answer:

Initial Outlay = $1,00,000

Annual Cash In-Flow = $ 25,000, Time Period = 5 Years

A) Payback Period: Initial Outlay/Cash Flow per year

Payback Period = 1,00,000/25,000 = 4 Years

B) Discounted Payback Period:

	Year 0	Year 1	Year 2	Year 3	Year 4	Year 5
CashFlows	-1,00,000	25,000	25,000	25,000	25,000	25,000
Present Value (Discounted at 9%)	-1,00,000	22936	21042	19305	17711	16248
Cumulative PV of Cashflows (Discounted)	0	22936	43978	63282	80993	97241

Discounted Pay Back Period = Cumulative Value of PV of Cashflows (Discounted) upto 1 Lac (Initial Outlay)

So adding up Cash Flows we get: Cumulative Value of PV of Cashflows (Discounted) upto year 5 us 97,241 which is less than Initial outlay so discounted payback period is more than 5 year.

3) NPV = Present value of Cash Inflows - Present Value of Cash Outflows(Initial Investment)

NPV = 25,000/(1.09) + 25,000/(1.09)^2 + 25,000/(1.09)^3 + 25,000/(1.09)^4 + 25,000/(1.09)^5 - 1,00,000

NPV = 97241 - 100000

NPV = - $2759

IRR: Discount rate at which NPV is 0. or discount rate at which present value of cash inflows totals to initial investments (1,00,000)

at 9% discount rate: PV of Cash inflows = 97241

at 8% discount rate: PV of Cash inflows = 99,818

at 7.9% discount rate: PV of Cash inflows = 1,00,081

Using interpolation we get

IRR = 7.93%

D) No, we should not accept the project as IRR is less than cost of capital and NPV is negative

For primary decision NPV is preferred over other methods because of following points:

1) NPV assumes that cash flows are reinvested at cost of capital where as IRR assumes that cash flows are reinvested at IRR rate which is not a fair assumption

2) For unconventional cashflows there are multiple IRR possible, but there will only be one NPV

3) NPV helps to know the real creation of wealth for any project