Question

In: Finance

You are a consultant to a large manufacturing corporation that is considering a project with the...

You are a consultant to a large manufacturing corporation that is considering a project with the following net after-tax cash flows (in millions of dollars):

Years from Now After-Tax Cash Flow
0 -100
1-10 18

The project's beta is 1.1.

a. Assuming that rf = 5% and E(rM) = 10%, what is the net present value of the project? (Do not round intermediate calculations. Enter your answer in millions rounded to 2 decimal places.)

Net Present Value

b. What is the highest possible beta estimate for the project before its NPV becomes negative? (Round your answer to 2 decimal places.)

Highest Beta   

Solutions

Expert Solution

a) Risk free Rate of return (Rf) = 5%

Return on the market portfolio (Rm) = 10%
Project Beta = 1.1


As per the Capital Asset Pricing Model
Re = Rf + (Rm – Rf) Beta

Where Re = Expected Return on Asset

              Rm - Rf = Market Risk Premium


Re = 5 + (10 – 5) 1.1
     = 5 + (5 )1.1

     = 5 +5.5
     = 10.50%


NPV of a project is the difference between the PV of cash inflows and PV of cash outflows. If NPV of a project is positive it should be accepted, otherwise it should be rejected.

NPV is given by = [CF1/(1+r)] + [CF2/(1+r)2] + [CF3/(1+r)3] +   …… [CFn/(1+r)n] + - CF0

Where

CF1 = Net Cash Inflow in Year 1

r = Discounting Rate or WACC

CF0 = Initial Cash Outflow

NPV = [PVAF (10.50%,10) * 18] – 100
NPV = (6.0147 *18) – 100
NPV = 8.26

Present Value Factor have been calculated as = (1/1+r)n

Where

r= Required rate of Return (Discount rate)

n= No of Periods

PVAF (10.5%,10) is calculated by adding the PV Factor of 10.5% for 10 years

b) Calculation of highest possible beta estimate for the project before its NPV becomes negative.

IRR is the rate at which the PV of Cash Inflows = PV of cash outflows i.e NPV of the project os 0.


Calculation of IRR:

[CF1/(1+IRR)] + [CF2/(1+IRR)2] + ……. + [CF10/(1+IRR)10] + - CF0 = 0
i.e PVAF (IRR, 10) * 18 – 100 = 0

Since at discount rate of 10.50% NPV is positive, IRR should be more than 10.50%

ASSUMING IRR TO BE 12.00% AND COMPUTING

=[PVAF (12%,10) * 18] – 100
= (5.6502 * 18) – 100
= 101.70- 100
= 1.70

Since this is slightly more than 0 IRR should be slightly higher than 12%


ASSUMING IRR TO BE 12.50% AND COMPUTING

=[PVAF (12.50%,10) * 18] – 100
= (5.5364 * 18) – 100
= 99.66 - 100
= -0.34

Since this is slightly more less than 0 IRR should be slightly lower than 12%

ASSUMING IRR TO BE 12.40% AND COMPUTING

=[PVAF (12.40%,10) * 18] – 100
= (5.5589 * 18) – 100
= 100 - 100
= 0

Therefore IRR or the discount rate is 12.4%

Using the CAPM equation to compute the Beta
Risk free Rate of return (Rf) = 5%

Return on the market portfolio (Rm) = 10%
Re = 12.4%


As per the Capital Asset Pricing Model
Re = Rf + (Rm – Rf) Beta


= 12.4 = 5 + (10 – 5) Beta
= 12.4= 5 + 5 Beta
= 7.4 = 5 Beta
i.e Beta = 1.48

Highest possible beta estimate for the project before its NPV becomes negative
is 1.48.


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