Financial Analysis: Dividends, Cash Flows, and Investment Valuation

Posted on Jul 16, 2024 in Economy

Chapter 20: Dividends

If dividend is not annuity then

dividend = cash for dividend / shares-outstanding, Share price of stock = value of firm / shares-outstanding or Dividend 1 / 1+cost of equity + dividend 2/ 1+ cost of equity ^2. if person owns x amount of shares and desire x amount of income at end of specific year. you multiply dividend of that year x Current shares = Current income for year. if he needs more money you calculate share price year after the year end, which is cash flow / 1+cost of equity. Then firm value / shares outstanding = share price at year end. Then divided income needed by share price to see how many shares must be sold. His income in next year will be shares left x dividend in next year.

If firm repurchases shares at year end instead of dividend :

That year cash flow + next year after year-end cash flow / 1+cost of equity = firm value. firm value / shares outstanding = new share price. Number of share repurchased = that year cash flow / new share price. New dividend per share for next year after year-end = next year – after year end cash flow / shares-outstanding – repurchase of shares To compare if he should keep or sell share compare that year purchase price, and new dividend per share after year end / 1 + cost of equity

If firm wants to increase dividend in year 1.

additional cash needed / new share price which is 2nd year cash flow / 1+cost of equity = shares needed to sell for additional cash flow. Then new cash with additional cash / outstanding shares with sell of issues give new dividend per stock

Change in share price due to taxes.

First calculate share price = market value – debt or free cash flow t… / 1 + cost of equity / shares outstanding , Change in share price = Pcum – Pex = Div x (1 – ((td – tg) / 1 – tg), then ex dividend price would = share price – change in share price

Chapter 21: Calculating NPV of cash flows using WACC method

Step 1. Determine the free cash flow of the investment

Step 2. Calculate Wacc

Step 3. Compute the value of the investment, including the tax benefit of leverage by discounting the free cash flow of the investment / by the Wacc.

if cash flow is an perpetuity then value of investment = FCFF / Wacc, if the Cash flow is growing perpetuity, value of investment = FCFF / Rwacc – g. If cash flow is a annuity then to determine value of firm = FCFF / 1 + Wacc ^t. NPV = value of investment – Upfront cost of the project. Ensure to finance the investment based on the D/E ratio. to finance = D + E = Value of investment. Example ( D / E = 1.5 and Value of investment = 120, then D =1.5E, 1.5 E + E = 120 Million , 2.5 E = 120 M, E = 48 M, D = 1.5 ( 48 M) = 72 M

Calculating using APV method = VL = Vu + PV(interest tax shield)

Steps to APV method

Determine investment value without leverage VU by discounting cash flow at the unlevered cost of capital ru, with a constant debt- equity ration, ru may be estimated.
Determine the present value of tax shield; given expected Debt, Dt on date t the interest tax shield = (Dt -1) ( Rd) (Tc). then discount the tax shield using ru if D/E is constant.
Add the unlevered value Vu to the present value of interest tax shield to determine value of investment with Leverage VL.

If there is interest coverage ratio then for PV of interest tax shield = (Interest coverage ratio x Perpeptual Cash flow x TC)

Calculating Using Fc to Equity.

Step 1 calculate Net borrowing at date t = Dt – Dt –1.
Step 2. Calculate Free cash flow to equity = Free cash flow – (1-Tc)(interest payments) + net borrowing.

Chapter 23: Calculation for Right Offer

-Value of a Right: Approx: ,Value of Right if Pon = Pex + R:

Rights needed to buy 1 share:

Find Market Price of Old Shares
Find Subscription Price of New Share
1 Right = Market Price
Find # of Shares Issued: Value of investment Needed / Subscription Price
Right needed for 1 Share = # of Existing Shares / # of New Shares

Value of One Right:

Total Shares Outstanding = Existing # of Shares + # New Shares Issued
Total Value = Existing Shares x Market Price + New Shares x Sub. Price
Ex-right Price: Total Value / Total Shares
Right Value = Market Price – Ex-Right Price

Sources of Funding

Angel Investors:

Individuals who buy equity of a smaller firm, Friends + Family, gets influence of firm

Venture Capital:

Limited partners who focus on raising funds to invest in young private firms. Less risk with partnerships → investors are not personally liable if the partnership doesn’t do well

Private Equity:

Similar to VC but only invest in developed equity. Larger scale investment

Institutional Investors:

Endowment, Foundations, Pension Funds

Sovereign Wealth Funds:

Government controlled pools of money, Worldwide investments, Often financed by resource revenue

Corporate investors:

Larger firm buying equity of a young private firm.

Pre-Money Valuation:

Firms existing shares x Price of new shares.

Post-Money Valuation:

All of firms shares x Price of new shares.

Exit Strategy:

Since private firms does not trade. Most Common Strategy: Being bought out by another firm

Dividends Example

3(a) Firm value; V0 = (20 M – 10 M) / 1.2 + 24 M/ 1.2^2 = 25 M, share price = 25,M / 2 M = 12.50

(b) Suppose you own 25% of firm then you have 2 M * 25% = 500k shares. current income = 10 M / 2 M = $5. Hence you receive $5 per share.you will be receiving 2.5 M instead of Desired 3.5 M, difference of $2. Firm Needs to sell $2 x 2 M shares = 4 M cash. In order to obtain 20% required return, shareholders must receive 4 M * 1.2 = 4.8 M. 24 M – 4.8 M = 19.2 M for shareholders. Dividend = 19.2 M / 2 M shares = 9.60. IMpaying that ex dividend share price = 9.6 / 1.2 = 8. Number of shares issued = 4 M / 8 share price. = 500 k additional shares. income would be $7 x 500 k = 3.5 million in year one and $9.60 x 500,000 = 4.8 million after two years.

(C) if firms doesn’t change dividend policy dividend paid after two years = 2

4 M / 2 M =$12. Ex dividend share price = 12 / 1.2 =10. To earn 3.5 million you must sell $1 M / $10 share price = 100 k shares. you would make $12 x 400 k = 4.8 M after two years.

APA Example: TC = 40%, cost of levered Equity 26%, Interest rate = 10% D/E = 1, hence debt to value = D / D+E = 0.5. Ru = 0.50(0.26) + 0.5(0.10) = 0.18. Unlevered NPV = -100 investment cost + (72 CF / 1.18) + (72/1.18^2) = 12.73. next determine the debt capacity of the project using rwacc as the discount rate. d2 = 0, V1L = (72/1.16) = 62.07, d1 = (0.50 * $62.07) = 31.03. V0L = (62.07 + 72) / 1.16 = 115.58, d0 = (0.50 x 115.58) = 57.79. Pv (intereest tax shields) = (57.79 x 0.10 x0.4 ) / 1.18 ****( 1+ ru) + (31.03 x 0.10 x 0.4) / 1.18^2 = 2.85. This give a levered NPV of 12.73 + 2.85 = 15.58

WACC Method

– Find FCF: EBIT(1 – Tax) + Depreciation – Increase Working Capital 1. Find D/V and E/V from D/E 2. Find rWACC 3. Discount each FCF by rWACC to find VL 4. NPV = VL – Initial Investment

APV Method 1. Find rU 2. Find VU 3. Calculate Debt Capacity per year Find rWACC Find VL for each year – Start at last period (Equals 0) – VL = (FCF + Previous VL) / (1 + rWACC) – Debt Capacity = VL * D / V 4. Find Interest Tax Shield for each year – Debt Capacity of that year x Tax x Interest Rate 5. Find PV of Interest Tax Shields 6. Add them up to get total interest tax shield 7. Add VU and PV of Interest Tax Shield to get VL 8. VL – Initial Investment = NPV FTE Method1. Find rWACC, E/V, and D/V2. Value of firm: (FCF + Previous VL) / (1 + rWACC) (Final Period is 0)3. Debt Capacity: VL of that year x D/V (Final Period is 0)4. Interest: Debt Capacity of year before x rD x (1 – Tc)(Time 0 is 0)5. Net Borrowing: Debt Capacity of that period – Debt Capacity of period before6. FCFE: FCF – Interest + Net Borrowing7. Find PV of each FCFE by discounting by (1 + rE) 8.. Add up the PV to find the NPV

4 Step to Evaluating investment decisions: Forecast FCF, Assess Project Risk, Estimate opportunity cost of capital, Find NPV Use WACC when: Firms policy is to continuously adjust its debt to maintain target debt equity ratio Use APV when: Firm adjust its debt according to a known schedule or to maintain a target interest coverage ratio Assumptions: 1 Project under consideration has the same risk as the existing firm 2. Firm adjusts its debt to maintain a target debt-equity ratio 3. Only market imperfection is corporate taxes Advantages to FTE Method:1. Direct illustration of the benefits and costs of a project to the shareholders 2. Contains securities with unknown market values

NWI Corp. is evaluating a potential investment project which costs $1,000 today and is expected to produce free cash flows of $60 at the end of each year in perpetuity. The firm uses a debtequity ratio of 2 to finance its existing operations. This new project would be of similar risk as the firm’s existing operations and would be financed in the same way as the firm’s existing operations. NWI Corp. faces a corporate tax rate of 40%. The firm’s equity beta is 1.2, and its debt beta is 0.2. The expected return on the market portfolio is 8% and the risk-free rate of interest is 3%. (a) Use the WACC approach to determine the NPV of the project. (b) Show how you can use the APV approach to calculate the same total project value as for the WACC approach in part (a). Solution A) since D/e = 2, DV =2/3 and EV= 1/3, fimrs cost of equity: Re = 0.3 + 1.2(0.08 – 0.03) = 9%. Cost of debt is Rd = 0.03 + 0..2(0.08 – 0.03) = 4%. therefore Rwacc = 1/3(0.09) + 2/3(0.04)(1-0.4) = 4.6%. So NPV = 60/0.046 – 1,000 = 304.35. So that the value of project VL = 1,304.35. B) since pretax wacc is 1/3(0.09) + 2/3 x (0.04) = 0.05667. This implies that unlevered project value of 60 / 0.05667 = 1,058.82. Using VL = 1,304.35 from part (a) we have initialy debt of 1,304.35 x 2/3 – 869.57. This implies intereest tax shield of 859.57(0.04)(0.4) = 13.91. present value of tax shield is 13.91 / 0.056667 = 242.52 adding this to Vu gives a total of 1,304.35 like part a.