Question

A) A company is considering building a new factory to produce aluminum baseball bats. this project would require an initial cash outlay of $5,500,000 and would generate annual net cash inflows of $900,000 per year for seven years. calculate the projects NPVE using a discount rate of 8%.

B) The same company is considering to expand. The expidenture requires $9,500,000 on new service equipment I would generate annual net cash inflows from reduced costs of operations that equal 4 million per year for the next seven years. and year seven the firm will also get back a cash flow equal to the salvage value of the equipment which is valued at .9 million. in your 70 investment cash inflow totals $4,900,000. calculate the projects NPV using a discount rate of 10%.

C) they are considering purchasing a new machine. this investment requires an initial outlay of $95,000 and will generate Net cash inflows of $19,000 per year for 11 years. 1) what is the projects NPV using a discount rate of 9% and should the project be excepted? 2) what is the projects NPV using a discount rate of 13%? 3) what is the projects internal rate of return?

Answer 1

Solution

A) Given,
Initial Cash Outlay = $5,500,000
Net cash inflow = $900,000
Term (n) = 7 Years
Discount rate (r) = 8%

Therefore, to find out the Net Present Value we have to find out the Present Value of Net Cash Inflow first.

Present Value of Net Cash Inflow = Net Cash Inflow x (PVAFr,n)
Or, $900,000 x (PVAF8%,7)

Now, (PVAF8%,7) = {1 - [1 / (1 + 0.08)7]} / 0.08
= (1 - 0.5835) / 0.08 [1 / (1 + 0.08)7 = 0.5835 (Approx.)]
= 0.4165 / 0.08
= 5.2063 (Approx.)

Therefore, Present Value of Net Cash Inflow = $900,000 x 5.2063
= $4,685,670

Therefore, Net Present Value = Present Value of Net Cash Inflow - Initial Cash Outflow
= $4,685,670 - $5,500,000
= $(814,330)

Answer: Net Present Value using 8% discount rate = $(814,330)

B) Given,
Initial Outlay = $9,500,000
Annual Net cash flow = $4,000,000
Salvage Value = $900,000
Term (n) = 7 Years
Discount Rate (r) = 10%

Now, NPV will be calculated as follows = Present Value of Annual cash flows + Present Value of Salvage Value - Initial Cash Outflow
= [Annual Cash Flow x (PVAFr,n)] + {Salvage value x (PVIFr,n)] - Initial Cash Outflow

Now, we need to calculate (PVAF10%,7) as follows,
(PVAF10%,7) = {1 - [1 / (1 + 0.10)7]} / 0.10
= (1 - 0.5132) / 0.10 [1 / (1 + 0.10)7 or  (PVIF10%,7) = 0.5132 (Approx.)]
= 0.4868 / 0.10
= 4.868 (Approx.)

Therefore, NPV = [Annual Cash Flow x (PVAFr,n)] + {Salvage value x (PVIFr,n)] - Initial Cash Outflow
= [$4,000,000 x (PVAF10%,7)] + [$900,000 x (PVIF10%,7)] - $9,500,000
= ($4,000,000 x 4.868) + ($900,000 x 0.5132) - $9,500,000
= $19,472,000 + $461,880 -  $9,500,000
= $10,433,880

Answer: Net Present Value using 10% discount rate = $10,433,880

C) Given,
Initial Outlay = $95,000
Net Cash Inflow = $19,000
Term (n) = 11 Years

(1) Given, Discount Rate (r) = 9%,

So, NPV = [Annual Cash Flow x (PVAFr,n)] - Initial Cash Outflow

Now, we need to calculate (PVAF9%,11) as follows,
(PVAF9%,11) = {1 - [1 / (1 + 0.09)11]} / 0.09
= (1 - 0.3875) / 0.09 [1 / (1 + 0.09)11 = 0.3875 (Approx.)]
= 0.6125 / 0.09
= 6.8056 (Approx.)

Therefore, NPV = [Annual Cash Flow x (PVAFr,n)] - Initial Cash Outflow
= [$19,000 x (PVAF9%,11)] - $95,000
= ($19,000 x 6.8056) - $95,000
= $129,306.40 - $95,000
= $34,306.40

Answer: Net Present Value using 9% discount rate = $34,306.40

(2)

Given, Discount Rate (r) = 13%,

So, NPV = [Annual Cash Flow x (PVAFr,n)] - Initial Cash Outflow

Now, we need to calculate (PVAF13%,11) as follows,
(PVAF13%,11) = {1 - [1 / (1 + 0.13)11]} / 0.13
= (1 - 0.2607) / 0.13 [1 / (1 + 0.13)11 = 0.2607 (Approx.)]
= 0.7393 / 0.13
= 5.6869 (Approx.)

Therefore, NPV = [Annual Cash Flow x (PVAFr,n)] - Initial Cash Outflow
= [$19,000 x (PVAF13%,11)] - $95,000
= ($19,000 x 5.6869) - $95,000
= $108,051.10 - $95,000
= $13,051.10

Answer: Net Present Value using 13% discount rate = $13,051.10

(3) Given,
Initial Outlay = $95,000
Annual Cash Flow = $19,000

At IRR, Initial Outlay = Present Value of Annual Cash Flow
Or, Initial Outlay = Annual Cash Flow x (PVAFr,11)
Or, 95000 = 19000 x (PVAFr,11)
Or, (PVAFr,11) = 95000 / 19000
Or, (PVAFr,11) = 5

Therefore, at the PVAF table, we have to find out at which rate (PVAFr,11) = 5 given as below,

	10%	11%	12%	13%	14%	15%	16%	17%	18%	19%	20%
11 Years	6.495061	6.206515	5.937699	5.686941	5.452733	5.233712	5.028644	4.836413	4.656005	4.4865	4.32706

PVAF = 5 shall fall between 16% to 17%. Therefore, using interpolation,

(r - 16) / (17 - 16) = (5 - 5.028644) / (4.836413 - 5.028644)
Or, (r - 16) = 0.028644 / 0.192231
Or, r - 16 = 0.149 (Approx.)
Or, r = 16.149

Answer: The Internal rate of return of the project = 16.149%