Question

Project L costs $50,000, its expected cash inflows are $15,000 per year for 11 years, and its WACC is 10%. What is the project's NPV? Round your answer to the nearest cent. Do not round your intermediate calculations.

Answer 1

Project L:

Given information,

Cost of project L = $50,000

Expected cash flows = $15,000 per year

NO. of years = 11 years

WACC = 10%

NPV is net present value of project where, it is a difference between project's present value of cash outflows and project's present value of cash inflows.

To calculate present value , we have given WACC i.e. weighted average cost of capital as 10% and by considering this WACC we will calculate present value factors so that we can get present value of cash flows.

Present value factor formula is, 1/(1+r)ⁿ

Now, we will calculate this present value factors for 11 years. These factors will be rounded off to 4 decimal places for easiest calculations.

Present value factor for year 0 is always 1 irrespective of cost of capital.

Year 1 = 1/(1+0.10)¹ = 0.9091

Year 2 = 1/(1+0.10)² = 0.8264

Year 3 = 1/(1+0.10)³ = 0.7513

Year 4 = 1/(1+0.10)⁴ = 0.6830

Year 5 = 1/(1+0.10)⁵ = 0.6209

Year 6 = 1/(1+0.10)⁶ = 0.5645

Year 7 = 1/(1+0.10)⁷ = 0.5132

Year 8 = 1/(1+0.10)⁸ = 0.4665

Year 9 = 1/(1+0.10)⁹ = 0.4241

Year 10 = 1/(1+0.10)¹⁰ = 0.3855

Year 11 = 1/(1+0.10)¹¹ = 0.3505

Beginning cash flows:

We have given costs of project as $50,000, it is initial investment in the project.

Interim cash flows:

We have project L's cash inflows are given as $15,000 per year for 11 years.

Now we will apply present value factor to respective year's cash flow to get present value of cash flows.

Here, we have 11 years so one method is we can individually multiply respective present value factor to respective cash flows and the other method is we can calculate cumulative present value of 11 years and multiply it to interim cash inflow as expected cash inflow is same for all 11 years. If expected cash inflow is different for all 11 years then we cannot apply cumulative present value factor, then we have to do individual calculations for that.

Cumulative present value factor for 11 years is sum of all the present value factors from year 1 to year 11 which is 6.495 rounded off

Calculation of NPV:

Year	Particulars	Cash flows	Present value factor as calculated	Present value of cash flows = Cash flows * present value factor
0	Beginning cash flows	($50,000)	1	($50,000)*1 = ($50,000)
1	Interim cash flows	$15,000	0.9091	$15,000*0.9091 = $13636.5
2	Interim cash flows	$15,000	0.8264	$15,000*0.8264 = $12,396
3	Interim cash flows	$15,000	0.7513	$15,000*0.7513 = $11,269.5
4	Interim cash flows	$15,000	0.6830	$15,000*0.6830 = $10,245
5	Interim cash flows	$15,000	0.6209	$15,000*0.6209 = $9,313.5
6	Interim cash flows	$15,000	0.5645	$15,000*0.5645 = $8,467.5
7	Interim cash flows	$15,000	0.5132	$15,000*0.5132 = $7,698
8	Interim cash flows	$15,000	0.4665	$15,000*0.4665 = $6,997.5
9	Interim cash flows	$15,000	0.4241	$15,000*0.4241 = $6,361.5
10	Interim cash flows	$15,000	0.3855	$15,000*0.3855 = $5,782.5
11	Interim cash flows	$15,000	0.3505	$15,000*0.3505 = $5,257.5
	NPV after difference between cash inflows and cash out flows			$47,425

Other method by taking cumulative present value factor:

Here we will take present value factor as cumulative that means total of all factors as expected cash inflow is same for all the 11 years

Calculation of NPV:

Year	Particulars	Cash flows	Present value factor	Present value of cash flows = Cash flows * present value factor
0	Beginning cash flow	($50,000)	1	($50,000)*1 = ($50,000)
1-11	Interim cash inflows	$15,000	6.4951	$15,000*6.495 = $97,425
	NPV			$47,425

Here, I have given two methods.

Hence, NPV of project L is $47,425