The Nevada inc. is a family owned private firm that is operating in life insuran
ID: 2798330 • Letter: T
Question
The Nevada inc. is a family owned private firm that is operating in life insurance and property&liability; insurance sectors. The life insurance division constitutes 25% of the firm and property & liability insurance division constitutes 75% of the firm. The firm's current free cash flow is $100,000. FCFs are expected to grow 10%, 8%, %6, and %4 for next four years. After year 4 growth will become constant at a rate of 3% forever. Nevada Inc.'s total debt is SS0000 and total equity is S200.000 The firm's interest expense is $8,000 and tax rate is 40%. Alex wants to become the sole owner of the company by buying all the shares from other family members. Using non-constant FCF valuation model, determine the price Alex should pay per each share. Assume market risk premium 7% and long-term government bond rate is 6%. Family members hold 5000 shares of the firm. Publicly traded life insurance firms Publicly traded property and liability insurance firms Debt ($1000) Equity ($1000) Tax (% Beta ABC 50 150 40 140 CDE 60 120 40 1.60 EXM 40 80 40 1.20 TRY 20 60 40 1.30Explanation / Answer
First of all we shall unlever the beta of the firms
Firm
Debt equity ratio
unlevered beta
Debt /equity
beta (levered) /(1+(1-tax rate)D/E)
ABC
150/50= 3
1.4/(1+(1-.4)3=0.5
CDE
120/60=2
(1.6)/((1+(1-0.4)*2))=0.72
EXM
80/40=2
(1.2)/(1+(1-0.4)*2)=0.545
TRY
60/20=3
(1.3)/(1+(1-0.4)*3)=0.464
Take the average of the beta of first two life insurance firms = (.5+.72)/2
0.61
Take the avereage of the beta of two property and liability insurance firms = (.545+.464)/2
0.5045
This can be taken as proxy of unlevered beta of the firms . Ie Beta 1 = 0.61 and Beta 2 = 0.5045
Next we shall lever the beta of given firm as follows:
Beta(levered) = Beta unlevered (1+(1-tax rate)*debt/equity
Beta 1
=0.61*(1+(1-0.4)*80/200)
0.7564
Beta 2
=0.5045*(1+(1-0.4)*80/200)
0.62558
Now the beta of the firm Nevada Inc. will be W1*beta1+W2*beta 2
W1 is .25
W2 is .75
Beta 1 is 0.7564
beta 2 is .6255
0.25*0.7564+0.75*0.6255
0.658225
Hence for calculating the Cost of equity we use the following formula
Cost of equity = Risk free rate of return (rf)+beta ( Risk premium)
=6%+0.658225*7%
10.60757500%
The project Weighted average cost will be
K= D/D+E)*K((debt)*(1-tax))+ E/D+E)*k(equity)
=(80/280)*(8000/80000)*(0.6)+(200/280)*10.6%
9.28
Now, calulation of share value of the firm using cashflow approch
year
Cash flow (Cf*(1+growth)
Cash flow
Disconting factor (@9.28%)
Discounted cash flow
Year 1
=100000*(1+0.1)
$ 110,000
0.915080527
$100,659
Year 2
=110000*(1+0.08)
$ 118,800
0.837372371
$ 99,480
Year 3
=118800*(1+0.06)
$ 125,928
0.766263151
$ 96,494
Year 4
=125928*(1+0.04)
$ 130,965
0.701192488
$ 91,832
constant growth from next years
=(130965*(1+0.03))/(0.0952-0.03)
$ 2,068,926
0.701192488
########
Estimated discounted cash flow
########
Now value per share will be
Estimated cash flow
$ 1,839,180
Total share
5000
Value per share
$ 367.84
Alex should pay $367.84 approximately for per share of firm
First of all we shall unlever the beta of the firms
Firm
Debt equity ratio
unlevered beta
Debt /equity
beta (levered) /(1+(1-tax rate)D/E)
ABC
150/50= 3
1.4/(1+(1-.4)3=0.5
CDE
120/60=2
(1.6)/((1+(1-0.4)*2))=0.72
EXM
80/40=2
(1.2)/(1+(1-0.4)*2)=0.545
TRY
60/20=3
(1.3)/(1+(1-0.4)*3)=0.464
Take the average of the beta of first two life insurance firms = (.5+.72)/2
0.61
Take the avereage of the beta of two property and liability insurance firms = (.545+.464)/2
0.5045
This can be taken as proxy of unlevered beta of the firms . Ie Beta 1 = 0.61 and Beta 2 = 0.5045
Next we shall lever the beta of given firm as follows:
Beta(levered) = Beta unlevered (1+(1-tax rate)*debt/equity
Beta 1
=0.61*(1+(1-0.4)*80/200)
0.7564
Beta 2
=0.5045*(1+(1-0.4)*80/200)
0.62558
Now the beta of the firm Nevada Inc. will be W1*beta1+W2*beta 2
W1 is .25
W2 is .75
Beta 1 is 0.7564
beta 2 is .6255
0.25*0.7564+0.75*0.6255
0.658225
Hence for calculating the Cost of equity we use the following formula
Cost of equity = Risk free rate of return (rf)+beta ( Risk premium)
=6%+0.658225*7%
10.60757500%
The project Weighted average cost will be
K= D/D+E)*K((debt)*(1-tax))+ E/D+E)*k(equity)
=(80/280)*(8000/80000)*(0.6)+(200/280)*10.6%
9.28
Now, calulation of share value of the firm using cashflow approch
year
Cash flow (Cf*(1+growth)
Cash flow
Disconting factor (@9.28%)
Discounted cash flow
Year 1
=100000*(1+0.1)
$ 110,000
0.915080527
$100,659
Year 2
=110000*(1+0.08)
$ 118,800
0.837372371
$ 99,480
Year 3
=118800*(1+0.06)
$ 125,928
0.766263151
$ 96,494
Year 4
=125928*(1+0.04)
$ 130,965
0.701192488
$ 91,832
constant growth from next years
=(130965*(1+0.03))/(0.0952-0.03)
$ 2,068,926
0.701192488
########
Estimated discounted cash flow
########
Now value per share will be
Estimated cash flow
$ 1,839,180
Total share
5000
Value per share
$ 367.84
Alex should pay $367.84 approximately for per share of firm
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