Net Present Value and Beta Factor

[christopheb]

Hi,

I am supposed to repeat a Financing Management Module and I am a bit stuck with the following question, I am not too sure how to deal with the Beta Factor? Any help is greatly appreciated.
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An investment in a project produces cash inflows of £ 750, £ 750, £ 900, £ 900 and £ 595 at 12 month intervals. The asset created by the project is to be depreciated at £ 500 per annum straightline.

The current yield on Treasury Bond is 4% and the estimated annual return on the capital market is 10%.
The company has a beta factor of 1.33.

You are required to decide whether the project is worthwhile using
a) The Net Present Value
b) The Internal Rate of Return

[sumaaan]

Beta factor will be used to calculate cost of capital to come up with NPV.

cost of capital = 4 + (10-4) x 1.33
= 12%

[christopheb]

Thanks for the tip, I have tried my best to figure out a solution, is there any chance that someone can please comment on the following calculations

SOLUTION
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A) NET PRESENT VALUE

Beta factor will be used to calculate cost of capital to come up with NPV.
Cost of capital = 4 + (10-4) x 1.33 = 12%

(12% discounted factor)

Capital Cash inflows £3895 (750+750+900+900+595)

Add depreciation amount to NP's
Number of years (5) = £500*5=2500
(3895-2500)= 1395

Yr 1 Present Value = 750x1/1.12 = 667.5
Yr 2 Present Value = 750x1/ (1.12) ^2 = 600
Yr 3 Present Value = 900x1/ (1.12) ^3 = 639
Yr 4 Present Value = 900x1/ (1.12) ^4 = 576
Yr 5 Present Value = 595x1/ (1.12) ^5 = 339.15

Present Value of Cash inflows = (667.5+600+639+576+339.15) = 2821.65
Capital outlay = 1395
Net Present Value = (2821.65-1395) = <b>1426.65</b>

(20% discounted factor)

Capital Cash inflows £3895 (750+750+900+900+595)

Add depreciation amount to NP's
Number of years (5) = £500*5=2500
(3895-2500)= 1395

Yr 1 Present Value = 750x1/1.2 = 619.5
Yr 2 Present Value = 750x1/ (1.2) ^2 = 512.25
Yr 3 Present Value = 900x1/ (1.2) ^3 = 522
Yr 4 Present Value = 900x1/ (1.2) ^4 = 432
Yr 5 Present Value = 595x1/ (1.2) ^5 = 238

Present Value of Cash inflows= (619.5+512.25+522+432+238) = 2323.75
Capital outlay = 1395
Net Present Value = (2323.75-1395) = <b>928, 75</b>

B) The Internal Rate of Return

Internal Rate of return formula
IRR = d1 + [n1 / (n1 + n2) x S]
Where d1 = Lower dcf, d2 = higher dcf, n1 = NPV at lower dcf, n2 = NPV at higher dcf, S = d2 - d1

Net Present value@ 10% = 1426.65
Net Present value@ 20% = 928.75
IRR = 10 + [1426.65 / (1426.65 + 928.75) x 10] = <b>16, 05% (about)</b>

[sumaaan]

Its too messy. Cannot comprehend. No offence intended.

[christopheb]

I do agree with you that he looks messy, with an Excel spreadsheet it looks easier. Do you have any other quicker solution to offer?

Best Regards,
Christophe/.

[CBPian]

remove deperciation impact as no cashflow consequences unless you will be using the tax allowance on depreciation as a positive inflow... which supposedly is not the case.
else looks fine.

[Goodman]

Dear Christopheb

I think you need to work on capital outlay part. You mentioned that asset created by the project is depreciated by ....

Now consider replacing your capital outlay cost with the real cash outflow cost of the very asset which you are trying to depreciate.