Question

Question 2a-e:

Consider the following forecasts for 2020-2024 of the Future Cash Flows, EBITDA and Future Interest Tax Shield for Firm X if the expansion were not to occur. Assume that the EBITDA Multiple is 8. Assume a discount factor of 9% for the Free Cash Flows and the Continuation Value, and 9% for the Interest Tax Shield.

Firm Value	2020	2021	2022	2023	2024
Free Cash Flow of Firm	3,312,885	3,314,802	3,316,717	3,318,631	3,320,543
EBITDA					5,164,631
Interest Tax Shield	28,350	28,350	28,350	28,350	28,350

What is the Present Value (at December 2019) of the Free Cash Flows forecast of Firm X if the firm where not to do the expansion?

What is the Present Value (at December 2019) of the Continuation Value forecast of Firm X if the firm where not to do the expansion?

What is the Present Value (at December 2019) of the Interest Tax Shield forecast of Firm X if the firm where not to do the expansion?

What is the Firm Value (at December 2019) of Firm X if the firm where not to do the expansion?

True or False: If the Value of Firm X (at December 2019) of doing the expansion is estimated to be $221856517, Firm X should do the expansion (according to the NPV of the expansion)."

Answer 1

Solution 1) Discount rate (r) = 9%

Present value of cash flow at t=i (CFi) is = CFi/(1 + r)^i

where CFi refers to the free cash flow for the year i

The present value of forecasts = Sum of the present values of the free cash flows

Free cash flows are as follows:

Year	2020	2021	2022	2023	2024
Free Cash Flow of Firm	33,12,885	33,14,802	33,16,717	33,18,631	33,20,543

PV of FCF forecast = 3,312,885 / (1 + 9%) + 3,314,802 / (1 + 9%)2 + 3,316,717 / (1 + 9%)3 + 3,318,631 / (1 + 9%)4 + 3,320,543 / (1 + 9%)5

= $12,899,587.62

Alternatively, NPV function in excel can be used as = NPV(rate, cash flows from t=1)

Solution 2) Continuation value = EBITDA Multiple x EBITDA = 8 x 5,164,631 = 41,317,048

PV of continuation value = Continuation value /(1 + r)^5

= 41,317,048/(1 + 9%)^5

= $26,853,246.28

Solution 3) Let X be the interest tax shield for each year for next 5 years

X = $28,350

The interest tax shield over the years is as follows:

Years	2020	2021	2022	2023	2024
Interest Tax Shield	28,350	28,350	28,350	28,350	28,350

PV of interest tax shields can be calculated using the NPV function in excel = NPV(Rate, cash flows)

= $110,271.61

Alternatively, since the cash flows are equal, hence, it will form an annuity.

Present value of annuity = X*[1 - (1 + r)^(-n)]/r = 28,350*[1 - (1 + 9%)^(-5)]/9% = $110,271.61

Solution 4) Firm value can be calculated as the sum of present values of Free Cash Flows, present values of continuation value and present values of interest tax shields

= PV of FCF + PV of continuation value + PV of interest tax shields

= 12,899,587.62 + 26,853,246.28 + 110,271.61

= $39,863,105.52

Solution 5) Value of the firm on doing the expansion = $221856517

Since the value of the firm on doing the expansion is greater than the value of the firm not doing the expansion ($39,863,105.52), thus, the firm should go for expansion. Hence, the correct answer is TRUE.

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