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Feb 20, 2024

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In early 2015, Ford Motor (F) had a book value of equity of $24.5 (24.3) billion, 3.9 (3.5) billion shares outstanding, and a market price of $16.25 (16.26) per share. Ford also had cash of $21.9 billion, and total debt of $118.8 (121.1) billion. Three years later, in early 2018, Ford had a book value of equity of $35.4 (34.9) billion, 10.0 (4.6) billion shares outstanding with a market price of $11.55 (11.41) per share, cash of $26.7 (26.5) billion, and total debt of $155.4 (157.1) billion. Over this period, what was the change in Ford’s A market capitalization? B market-to-book ratio? C enterprise value? a. Over the 3-year period, what was the change in Ford’s market capitalization The Market capitalization is: Market Capitalization = Number of shares x Price per share The Market capitalization for year 2015 is: Market Capitalization (2015) = 3.5 billion shares x $16.26 per share = $56.91 billion The Market capitalization for year 2018 is: Market Capitalization (2018) = 4.6 billion shares x $11.41 per share = $52.49 billion The change over the period is: Change in Market Capitalization = Market Capitalization (2018) – Market Capitalization (2015) Change in Market Capitalization = $52.49 billion - $56.91 billion = -$4.42 billion b. Over the 3-year period, what was the change in Ford’s market-to-book ratio? The market-to-book ratio is: Market-to-book = Market Value of Equity / Book Value of Equity The market-to-book ratio for 2015 is: Market-to-book (2015) = $56.91 billion / $24.3 billion = 2.34 The market-to-book ratio for 2018 is: Market-to-book (2018) = $52.49 billion / $34.9 billion = 1.50 The change over the period is: Change in Market-to-Book = Market-to-Book (2018) – Market-to-Book (2015) Change in Market-to-Book = 1.50 – 2.34 = -0.84 c. Over the 3-year period, what is the change in Ford’s enterprise value? The enterprise value is: Enterprise Value = Market Value of Equity + Debit – Cash The enterprise value for 2015 is: Enterprise Value (2015) = $56.91 billion + $121.1 billion – $21.9 billion = $156.11 billion The enterprise value for 2018 is: Enterprise Value (2018) = $52.49 billion + $157.1 billion - $26.5 billion = $183.09 billion

Change in Enterprise Value = Enterprise Value (2018) – Enterprise Value (2015) Change in Enterprise Value = $183.09 billion - $156.11 billion = $26.98 billion See Table 2.5 showing financial statement data and stock price data for Mydeco Corps a. By what percentage did Mydeco’s revenues grow each year from 2016 to 2019? b. By what percentage did net income grow each year? c. Why might the growth rates of revenues and net income differ? a. The revenue growth is: Revenues Growth = Revenues t / Revenues t-1 – 1 Revenue growth for 2016 is: Revenues Growth = $360.9 million / $408.1 million – 1 = -11.56 (5)% Revenue Growth for 2017 is: Revenues Growth = $422.1 million / $360.9 million – 1 = 16.95(7)% Revenues Growth for 2018 is: Revenues Growth = $515.2 million / $422.1 million – 1 = 22.05 (6)% Revenues Growth for 2019 is: Revenues Growth = $603.5 million / $515.2 million – 1 = 17.13 (8)% b. By what percentage did net income grow each year? The net income growth is: Net Income Growth = Net Income t / Net Income t-1 – 1 The net income for year 2016 is: Net Income Growth = $1.3 million / $21.9 million – 1 = -94.06% The net income for year 2017 is: Net Income Growth = $6.2 million / $1.3 million – 1 = 376.92% The net income for year 2018 is: Net Income Growth = $11.8 million / $6.2 million – 1 = 90.32% The net income for year 2019 is: Net Income Growth = $23.8 million / $11.8 million – 1 = 101.69% c. Why might the growth rates of revenues and net income differ? Net income growth rate differs from revenues growth rate because costs of goods sold and other expenses can move at different rates than revenues. For example, revenues declined in 2016 by 5.98%, however, the costs of goods sold declined by 10.7% The total fraction spent on capital expenditures is:

Fraction spent on capital expenditures = Capital Expenditures / Total cash flow from operations Retained Earnings = Net Income – Dividends Gross Profit Margin = Gross Profit / Revenue Net Profit Margin = Net Profit / Revenue ROE = Net Income / Stockholders’ Equity The DuPont Identity is ROE = Net Profit Margin x Asset Turnover x Equity Multiplier (Net Profit/Revenue) x (Revenue/Assets) x (Assets/Shareholders’ Equity) Week 3 Homework Example 1. A 25-year bond with a face value of $1,000 has a coupon rate of 4.50%, with semiannual payments. a . What is the coupon payment for this bond? b. Enter the cash flows for the bond on a timeline. A. To determine the coupon payment: Coupon = Coupon rate x Face Value / Number of coupons per year Coupon = 4.50% x $1,000 / 2 = $22.50 B. Here is the cash flow timeline for this bond (the unit of time on this timeline is six-month periods): Period 0------------1-----------2------ - - -- - - -------49-----------50 Cash flow CF1 CF2 CF49 CF50 So, the CF1 = CF2= * * * = CF49 = Coupon = $22.50, and the cash flow at time 50 is the coupon of $22.50 plus the face value of $1,000, which equals CF50 = $1,022.50. Problem Question 1. A 30-year bond with a face value of $1,000 has a coupon rate of 5.50%, with a semiannual payments. a. What is the coupon payment for this bond? b. Enter the cash flows for the bond on a timeline. A . What is the coupon payment for this bond? Coupon = 5.50% x $1,000 / 2 = $27.50 B. Enter the cash flows for the bond on a timeline.

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CF1 = $27.50 CF2 = $27.50 CF59 = $27.50 CF60 = $1,027.50 2. Explain why the yield of a bond that trades at a discount exceeds the bond's coupon rate. a. The bond can be purchased for a discount, which gives it an “extra return”; hence, the yield exceeds the coupon. b. Because the value of the bond is discounted, the return on the bond is reduced, and the yield exceeds the coupon. c. The bond’s coupon yield is irrelevant. It trades at a discount because investors avoid these bonds. d. The bond is trading at a discount because investors don’t like the bond. 3. Assume the zero-coupon yields on default-free securities are as summarized in the following table: (Click on the following icon in order to copy its contents into a spreadsheet.) Maturity (years) 1 2 3 4 5 Zero-coupon YTM 4.00% 4.30% 4.50% 4.70% 4.80% Consider a four-year, default-free security with annual coupon payments and a face value of $ 1,000 that is issued at par. What is the coupon rate of this bond? The par coupon rate is %. $1,000 = CPN x (1 / 1 + 0.040 + 1 / (1 + 0.043)^2 + 1 / (1 + 0.045)^3 + 1 / (0.047)^4) + $1,000 / (1 + 0.047)^4 $1,000 - $1,000 / (1 + 0.047)^4 / (1 / 1 + 0.040 + 1 / (1 + 0.043)^2 + 1 / (1 + 0.045)^3 + 1 / (0.047)^4) = $46.76 $46.76 / $1,000 = 4.676 3 EXAMPLE Assume the zero-coupon yields on default-free securities are as summarized in the following table: (Click on the following icon in order to copy its contents into a spreadsheet.) Maturity (years) 1 2 3 4 5 Zero-coupon YTM 3.40% 3.60% 3.80% 3.90% 4.10%

Consider a four-year, default-free security with annual coupon payments and a face value of $1,000 that is issued at par. What is the coupon rate of this bond? The price of the bond is as follows: Which can be rewritten as this: Solve the following equation: Therefore, CPN = $38.87, and the coupon rate is $38.87 / $1,000 = 3.887% 4. You are considering investing in a start up company. The founder asked you for $250,000 today and you expect to get $930,000 in 8 years. Given the riskiness of the investment opportunity, your cost of capital is 29%. What is the NPV of the investment opportunity? Should you undertake the investment opportunity? Calculate the IRR and use it to determine the maximum deviation allowable in the cost of capital estimate to leave the decision unchanged. Initial Investment = $250,000 Amount after 8 years = $930,000 Number of years = 8 Cost of capital = r= 29% Where NPV is the net present value of the investment, C0 is the amount of your investment, C1 is the amount that you will receive in n year, and r is the opportunity cost. NPV = $250,000 / (1 + 0.029)^8 - $930,000 NPV = -731,108.14 Initial cost = Future value/(1+IRR)^n IRR= (Future value/ Initial cost)^(1/n) -1

IRR = ($240,000 / $960,000) (1/10) – 1 IRR = -1.93 Rate = 2.74% / 2 = 0.0137 Number of periods = 7 * 2 = 14 Coupon = (4.84% of 1,000) / 2 = 24.2 24.2 x 1-(1/(1+0.0137)^14 24.2 x 12.6607757664 + 826.5473714066 NPV = $12,500 / 1.80 - $10,500 = $6,944.444 - $10,500 =-$3,555.556 IRR = (12,500/10,500)^1 – 1 = 1.19 – 1 = 0.19 or 19%

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101,000 = 127,000 / 1.0x Rate 9.3 Nper 3 Pmt 7,600,000 Fv 0 Profitability index = (NPV per bunch + cost per bunch) / cost per bunch Roses (3+20) / 20 = Lilies Pansies Orchids Initial Investment = 260,000 Amount of after 14 years = 1,050,000 Number of years = 14 Cost of capital = r = 23% IRR = (1,050,000/260,000)^(1-14) – 1

Value of royalty = [$5.3/(9.6%- (-30%)] = $ 13.38383 PV of royalty = [ $ 13.38383/(1+9.8%)^3] = $10.1105239743 NPV with royalty = [Amount paid + PV of royalty – PV of cashflows] NPV with royalty = [$10 + $10.1105239743 – ( $8.4/(1+9.8%)^1 + $8.4/(1+9.8%)^2 + $8.4/(1+9.8%)^3 )] NPV with royalty = -$0.07749 OR -$0.077 NPV = [CF0 - CF1/(1+r)^1 + CF2/(1+r)^2 + CF3/(1+r)^3] NPV = [$10 - $7.7/(1+10.4%)^1 + $7.7/(1+10.4%)^2 + $7.7/(1+10.4%)^3] NPV = -$ OR 10.0- 7.7/0.104 x 91 – 1/(1 + 0.104)^3 = 4.8 / 0.104 – (-0.3) 4.8 / 0.404 11.881 / (1 + 0.104)^3 8.8296964942