Question

1. XYZ firm is a technology firm operating in a sector which is highly competitive and disruptive. The management has identified an investment in a new technology that will result in substantial savings. The investment in the new project is $ 10 million. The project delivers the cash flow starting year 1 as follows for the next 5 years: $ 1, 4, 6, 2, and 1 million. You are in the board meeting and want to understand the time taken for the deployed capital to come back to you. The firm is operating in a country that has traditionally high discount rates. The opportunity cost of capital for the investors in this firm is 15%.
2. 1. Compute the payback period and the discounted payback period that you would communicate to the management.
   2. Suppose, in a country with negative benchmark rates, a similar investment would have an opportunity cost of capital of 2%. Will there be any adjust- ments to the payback and discounted payback periods communicated to the management in such a scenario, why ?

Answer 1

	a
		Present Value (PV)of Cash flow=
		(Cash flow0/((1+i)^N)
		i= discount rate =15%=0.15
		N= Year of cash flow
		Payback Preriod =Period when Cumulative Cash Flow=NIL
		Discounted Payback Preriod =Period when Cumulative Present Value of Cash Flow=NIL
			N	A	B	C=A/(1.15^N)	D
				($ Million)
			Year	Cash Flow	Cumulative Cash Flow	PV of Cash Flow	CumulativePV of Cash Flow
			0	($10)	($10)	($10)	($10)
			1	$1	($9)	$0.87	($9.13)
			2	$4	($5)	$3.02	($6.11)
			3	$6	$1	$3.95	($2.16)
			4	$2	$3	$1.14	($1.02)
			5	$1	$4	$0.50	($0.52)
		Payback Preriod =2+(5/6)=	2.83	YEARS
		Total of Discounted Cash Inflow	$9.84	(0.87+3.02+3.95+1.14+0.50)
		Hence , Discounted Payback is higher 5 years
	(b)	ADJUSTMENT TO PAYBACK AND DISCOUNTED PAYBACK
		Discount Rate=2%=0.02
			N	A	B	C=A/(1.02^N)	D
				($ Million)
			Year	Cash Flow	Cumulative Cash Flow	PV of Cash Flow	CumulativePV of Cash Flow
			0	($10)	($10)	($10)	($10)
			1	$1	($9)	$0.98	($9.02)
			2	$4	($5)	$3.84	($5.17)
			3	$6	$1	$5.65	$0.48
			4	$2	$3	$1.85	$2.33
			5	$1	$4	$0.91	$3.23
		PAYBACK PERIOD: NO ADJUSTMENT
		DISCOUNTED PAYBACK=(2+(5.17/5.65)	2.92	Years