Question

Wall Inc. forecasts that it will have the free cash flows (in millions) shown below. Assume the firm has zero non-operating assets. If the weighted average cost of capital is 14% and the free cash flows are expected to continue growing at the same rate after Year 3 as from Year 2 to Year 3, what is the firm’s total corporate value, in millions? Do not round intermediate calculations. Year 1 2 3 Free cash flow -$20.00 $48.00 $50.00 ​ Group of answer choices $492.77 $349.05 $394.22 $418.86 $410.65

Answer 1

Solution :

Calculation of growth rate after Year 3 :

As per the information given in the question we have

The free cash flows are expected to continue growing at the same rate after Year 3 as from Year 2 to Year 3

Thus the constant growth rate after year 3 = increase in growth rate from Year 2 to Year 3

Thus the formula for calculating the growth rate after Year 3 is

g = ( Free cash flow Year 3 – Free cash Flow Year 2 ) / Free cash Flow Year 2

We know that

Free cash flow Year 3 = $ 50 Million   ; Free cash Flow Year 2 = $ 48 Million

Applying the above values in the formula we have

g = ( $ 50,000,000 - $ 48,000,000 ) / $ 48,000,000

= $ 2,000,000 / $ 48,000,000

=0.041667

= 4.1667 %

Thus the growth rate after 3 years = 4.1667 %

Calculation of Terminal cash Flow at Year 3 :

The Terminal cash flow at Year 3 is calculated as follows :

TCF₃ = FCF₃ * ( 1 + g )) / ( r – g ) )

Where

FCF₃ = $ 50 ; g = 4.1667 % = 0.041667 ; r = 14 % = 0.14

Applying the above values in the formula we have

= [ $ 50 * ( 1 + 0.041667 ) ] / ( 0.14 – 0.041667 )

= [ $ 50 * ( 1.041667 ) ] / ( 0.14 – 0.041667 )

= [ $ 50 * ( 1.041667 ) ] / 0.098333

= $ 52.083350 / 0.098333

= $ 529.6630

Thus the Terminal cash flow at Year 3 = $ 529.6630

Calculation of the firm’s corporate value :

The formula for calculating the firm’s corporate value = Present value of free cash flows + Present value of Terminal Cash flow

= [ FCF₁ * ( 1 / ( 1 + r ) ¹ ) ] + [ FCF₂ * ( 1 / ( 1 + r ) ² ) ] + [ FCF₃ * ( 1 / ( 1 + r ) ³ ) ] + [ TCF₃ * ( 1 / ( 1 + r ) ³ ) ]

As per the information given in the question we have

FCF₁ = - $ 20 ; FCF₂ = $ 48 ;   FCF₃ = $ 50   ; g = 4.1667 % = 0.041667   ; r = 14 % = 0.14

Applying the above value in the formula we have

= [ - $ 20 * ( 1 / ( 1 + 0.14 ) ¹ ) ] + [ $ 48 * ( 1 / ( 1 + 0.14 ) ² ) ] + [ $ 50 * ( 1 / ( 1 + 0.14 ) ³ ) ] + [ $ 529.6630 * ( 1 / ( 1 + 0.14 ) ³ ) ]

= [ - $ 20 * ( 1 / ( 1.14 ) ¹ ) ] + [ $ 48 * ( 1 / ( 1.14 ) ² ) ] + [ $ 50 * ( 1 / ( 1.14 ) ³ ) ] + [ $ 529.6630 * ( 1 / ( 1.14 ) ³ ) ]

= [ ( - $ 20 * 0.877193 ) + ( $ 48 * 0.769468 ) + ( $ 50 * 0.674972 ) + ( $ 529.6630 * 0.674972 )

= - $ 17.543860 + $ 36.934441 + $ 33.748576 + $ 357.507426

= $ 410.646584

= $ 410.65 ( When rounded off to two decimal place )

Thus the firm’s total corporate value, in millions = $ 410.65 Million

The solution is Option 5 = $ 410.65 Million