In: Finance
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 |
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.