Question

Question 1

The management at Luke Products Inc. is looking at the financials for an innovative new diaper-changing station. The expected life cycle forthe product is four years. The initial projected product design costs are $500,000. Management typically uses a discount rate of 10% for allnew product financials.

a. Using the table below: Calculate the projected NPV, Payback time and IRR.

Year	Projected Cash In-Flows
1	130,000
2	250,000
3	300,000
4	100,000

b. Using the table below: If the product design costs are $250,000. Use a discount rate of 9% for the projected cash in-flows. Assume a five-year lifespan.Calculate the projected NPV, the payback time, and the IRR.

Year	Projected Cash In-Flows
1	120,000
2	90,000
3	75,000
4	50,000
5	20,000

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.

Payback period:

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

PBP = Year in which least +ve Closing Balance + [ Closing balance at that year / Cash flow in Next Year ]
If Actual PBP > Expected PBP - Project will be rejected
Actual PBP </= Expected PBP - Project will be accepted

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

Part A:

NPV:

Year	CF	PVF @10 %	Disc CF
0	$    -500,000.00	1.0000	$     -500,000.00
1	$      130,000.00	0.9091	$      118,181.82
2	$      250,000.00	0.8264	$      206,611.57
3	$      300,000.00	0.7513	$      225,394.44
4	$      100,000.00	0.6830	$        68,301.35
NPV			$      118,489.17

Payback Period:

Year	Opening Balance	Cash Flow	Closing Balance
1	$        500,000.00	$    130,000.00	$     370,000.00
2	$        370,000.00	$    250,000.00	$     120,000.00
3	$        120,000.00	$    300,000.00	$    -180,000.00
4	$      -180,000.00	$    100,000.00	$    -280,000.00

PBP = Year in which least +ve Closing Balance + [ Closing balance at that year / Cash flow in Next Year ]
= 2 Years + [ $ 120000 / $ 300000 ]
= 2 Years + 0.4 Years
= 2.4 Years

Payback Period is 2.4 Years

PBP Refer Payback Period
IRR:

Year	CF	PVF @20 %	Disc CF	PVF @21 %	Disc CF
0	$ -500,000.00	1.0000	$ -500,000.00	1.0000	$ -500,000.00
1	$ 130,000.00	0.8333	$ 108,333.33	0.8264	$ 107,438.02
2	$ 250,000.00	0.6944	$ 173,611.11	0.6830	$ 170,753.36
3	$ 300,000.00	0.5787	$ 173,611.11	0.5645	$ 169,342.18
4	$ 100,000.00	0.4823	$    48,225.31	0.4665	$    46,650.74
NPV			$      3,780.86		$     -5,815.70

IRR = Rate at which least +ve NPV + [ NPV at that rate / Change in NPV due to Inc of 1% in Int Rate ] * 1%
= 20 % + [ 3780.86 / ( 3780.86 - ( -5815.7) ) ] * 1 %
= 20 % + [ 3780.86 / ( 9596.56) ] * 1 %
= 20 % + [ 0.39 ] * 1 %
= 20 % + 0.39 %
= 20.39 %

Part B:

NPV:

Year	CF	PVF @9 %	Disc CF
0	$ (250,000.00)	1.0000	$ (250,000.00)
1	$   120,000.00	0.9174	$   110,091.74
2	$      90,000.00	0.8417	$      75,751.20
3	$      75,000.00	0.7722	$      57,913.76
4	$      50,000.00	0.7084	$      35,421.26
5	$      20,000.00	0.6499	$      12,998.63
NPV			$     42,176.59

Payback Period:

Year	Opening Balance	Cash Flow	Closing Balance
1	$        250,000.00	$    120,000.00	$     130,000.00
2	$        130,000.00	$      90,000.00	$       40,000.00
3	$          40,000.00	$      75,000.00	$      -35,000.00
4	$        -35,000.00	$      50,000.00	$      -85,000.00
5	$        -85,000.00	$      20,000.00	$    -105,000.00

PBP = Year in which least +ve Closing Balance + [ Closing balance at that year / Cash flow in Next Year ]
= 2 Years + [ $ 40000 / $ 75000 ]
= 2 Years + 0.53 Years
= 2.53 Years

Payback Period is 2.53 Years

PBP Refer Payback Period

IRR:

Year	CF	PVF @17 %	Disc CF	PVF @18 %	Disc CF
0	$    (250,000.00)	1.0000	$    -250,000.00	1.0000	$    -250,000.00
1	$      120,000.00	0.8547	$      102,564.10	0.8475	$      101,694.92
2	$        90,000.00	0.7305	$        65,746.22	0.7182	$        64,636.60
3	$        75,000.00	0.6244	$        46,827.79	0.6086	$        45,647.32
4	$        50,000.00	0.5337	$        26,682.50	0.5158	$        25,789.44
5	$        20,000.00	0.4561	$          9,122.22	0.4371	$          8,742.18
NPV			$             942.84		$        -3,489.54

IRR = Rate at which least +ve NPV + [ NPV at that rate / Change in NPV due to Inc of 1% in Int Rate ] * 1%
= 17 % + [ 942.84 / ( 942.84 - ( -3489.54) ) ] * 1 %
= 17 % + [ 942.84 / ( 4432.38) ] * 1 %
= 17 % + [ 0.21 ] * 1 %
= 17 % + 0.21 %
= 17.21 %