Question

1A) Your firm is evaluating a capital budgeting project. The estimated cash flows appear below. The board of directors wants to know the expected impact on shareholder wealth. Knowing that the estimated impact on shareholder wealth equates to net present value (NPV), you use your handy calculator to compute the value. What is the project's NPV? Assume that the cash flows occur at the end of each year. The discount rate (i.e., required rate of return, hurdle rate) is 14.5%. (Round to nearest penny)

Year 0 cash flow	-122,000
Year 1 cash flow	59,000
Year 2 cash flow	43,000
Year 3 cash flow	44,000
Year 4 cash flow	43,000
Year 5 cash flow	34,000

1B) What is the discount rate at which the following cash flows have a NPV of $0? Answer in %, rounding to 2 decimals.

Year 0 cash flow = -145,000
Year 1 cash flow = 35,000
Year 2 cash flow = 42,000
Year 3 cash flow = 43,000
Year 4 cash flow = 30,000
Year 5 cash flow = 41,000
Year 6 cash flow = 42,000

ANSWER

Answer 1

Part 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.

Year	CF	PVF @14.5 %	Disc CF
0	$      (122,000.00)	1.0000	$      (122,000.00)
1	$          59,000.00	0.8734	$          51,528.38
2	$          43,000.00	0.7628	$          32,798.76
3	$          44,000.00	0.6662	$          29,311.38
4	$          43,000.00	0.5818	$          25,017.65
5	$          34,000.00	0.5081	$          17,276.33
NPV			$          33,932.50

NPV of Project is $ 33932.50

Part 2:

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

Year	CF	PVF @15 %	Disc CF	PVF @16 %	Disc CF
0	$ -145,000.00	1.0000	$ -145,000.00	1.0000	$ -145,000.00
1	$      35,000.00	0.8696	$      30,434.78	0.8621	$      30,172.41
2	$      42,000.00	0.7561	$      31,758.03	0.7432	$      31,212.84
3	$      43,000.00	0.6575	$      28,273.20	0.6407	$      27,548.28
4	$      30,000.00	0.5718	$      17,152.60	0.5523	$      16,568.73
5	$      41,000.00	0.4972	$      20,384.25	0.4761	$      19,520.63
6	$      42,000.00	0.4323	$      18,157.76	0.4104	$      17,238.57
NPV			$        1,160.62		$      -2,738.52

IRR = Rate at which least +ve NPV + [ NPV at that rate / Change in NPV due to Inc of 1% in Int Rate ] * 1%
= 15 % + [ 1160.62 / ( 1160.62 - ( -2738.52) ) ] * 1 %
= 15 % + [ 1160.62 / ( 3899.14) ] * 1 %
= 15 % + [ 0.3 ] * 1 %
= 15 % + 0.3 %
= 15.30 %
At 15.30%, NPV will be Zero.